id	sid	tid	token	lemma	pos
ejpam-3545	1	1	european	european	PROPN
ejpam-3545	1	2	journal	journal	PROPN
ejpam-3545	1	3	of	of	ADP
ejpam-3545	1	4	pure	pure	ADJ
ejpam-3545	1	5	and	and	CCONJ
ejpam-3545	1	6	applied	apply	VERB
ejpam-3545	1	7	mathematics	mathematic	NOUN
ejpam-3545	1	8	vol	vol	NOUN
ejpam-3545	1	9	.	.	PROPN
ejpam-3545	2	1	12	12	NUM
ejpam-3545	2	2	,	,	PUNCT
ejpam-3545	2	3	no	no	INTJ
ejpam-3545	2	4	.	.	NOUN
ejpam-3545	2	5	4	4	NUM
ejpam-3545	2	6	,	,	PUNCT
ejpam-3545	2	7	2019	2019	NUM
ejpam-3545	2	8	,	,	PUNCT
ejpam-3545	2	9	1787	1787	NUM
ejpam-3545	2	10	-	-	SYM
ejpam-3545	2	11	1810	1810	NUM
ejpam-3545	2	12	issn	issn	PROPN
ejpam-3545	2	13	1307	1307	NUM
ejpam-3545	2	14	-	-	SYM
ejpam-3545	2	15	5543	5543	NUM
ejpam-3545	2	16	–	–	PUNCT
ejpam-3545	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3545	2	18	published	publish	VERB
ejpam-3545	2	19	by	by	ADP
ejpam-3545	2	20	new	new	PROPN
ejpam-3545	2	21	york	york	PROPN
ejpam-3545	2	22	business	business	PROPN
ejpam-3545	2	23	global	global	ADJ
ejpam-3545	2	24	on	on	ADP
ejpam-3545	2	25	weak	weak	ADJ
ejpam-3545	2	26	projectivity	projectivity	NOUN
ejpam-3545	2	27	in	in	ADP
ejpam-3545	2	28	arithmetic	arithmetic	ADJ
ejpam-3545	2	29	mark	mark	PROPN
ejpam-3545	2	30	burgin	burgin	PROPN
ejpam-3545	2	31	department	department	PROPN
ejpam-3545	2	32	of	of	ADP
ejpam-3545	2	33	mathematics	mathematics	PROPN
ejpam-3545	2	34	,	,	PUNCT
ejpam-3545	2	35	university	university	PROPN
ejpam-3545	2	36	of	of	ADP
ejpam-3545	2	37	california	california	PROPN
ejpam-3545	2	38	,	,	PUNCT
ejpam-3545	2	39	los	los	PROPN
ejpam-3545	2	40	angeles	angeles	PROPN
ejpam-3545	2	41	(	(	PUNCT
ejpam-3545	2	42	ucla	ucla	PROPN
ejpam-3545	2	43	)	)	PUNCT
ejpam-3545	2	44	,	,	PUNCT
ejpam-3545	2	45	520	520	NUM
ejpam-3545	2	46	portola	portola	PROPN
ejpam-3545	2	47	plaza	plaza	PROPN
ejpam-3545	2	48	,	,	PUNCT
ejpam-3545	2	49	los	los	PROPN
ejpam-3545	2	50	angeles	angeles	PROPN
ejpam-3545	2	51	,	,	PUNCT
ejpam-3545	2	52	ca	ca	NOUN
ejpam-3545	2	53	90095	90095	NUM
ejpam-3545	2	54	,	,	PUNCT
ejpam-3545	2	55	usa	usa	PROPN
ejpam-3545	2	56	abstract	abstract	NOUN
ejpam-3545	2	57	.	.	PUNCT
ejpam-3545	3	1	in	in	ADP
ejpam-3545	3	2	the	the	DET
ejpam-3545	3	3	19th	19th	ADJ
ejpam-3545	3	4	century	century	NOUN
ejpam-3545	3	5	,	,	PUNCT
ejpam-3545	3	6	non	non	ADJ
ejpam-3545	3	7	-	-	ADJ
ejpam-3545	3	8	euclidean	euclidean	ADJ
ejpam-3545	3	9	geometries	geometry	NOUN
ejpam-3545	3	10	were	be	AUX
ejpam-3545	3	11	discovered	discover	VERB
ejpam-3545	3	12	and	and	CCONJ
ejpam-3545	3	13	studied	study	VERB
ejpam-3545	3	14	.	.	PUNCT
ejpam-3545	4	1	in	in	ADP
ejpam-3545	4	2	the	the	DET
ejpam-3545	4	3	20th	20th	ADJ
ejpam-3545	4	4	century	century	NOUN
ejpam-3545	4	5	,	,	PUNCT
ejpam-3545	4	6	non	non	ADJ
ejpam-3545	4	7	-	-	ADJ
ejpam-3545	4	8	diophantine	diophantine	ADJ
ejpam-3545	4	9	arithmetics	arithmetic	NOUN
ejpam-3545	4	10	were	be	AUX
ejpam-3545	4	11	discovered	discover	VERB
ejpam-3545	4	12	and	and	CCONJ
ejpam-3545	4	13	studied	study	VERB
ejpam-3545	4	14	.	.	PUNCT
ejpam-3545	5	1	construction	construction	NOUN
ejpam-3545	5	2	of	of	ADP
ejpam-3545	5	3	nondiophantine	nondiophantine	ADJ
ejpam-3545	5	4	arithmetics	arithmetic	NOUN
ejpam-3545	5	5	is	be	AUX
ejpam-3545	5	6	based	base	VERB
ejpam-3545	5	7	on	on	ADP
ejpam-3545	5	8	very	very	ADV
ejpam-3545	5	9	general	general	ADJ
ejpam-3545	5	10	mathematical	mathematical	ADJ
ejpam-3545	5	11	structures	structure	NOUN
ejpam-3545	5	12	,	,	PUNCT
ejpam-3545	5	13	which	which	PRON
ejpam-3545	5	14	are	be	AUX
ejpam-3545	5	15	called	call	VERB
ejpam-3545	5	16	abstract	abstract	ADJ
ejpam-3545	5	17	prearithmetics	prearithmetic	NOUN
ejpam-3545	5	18	,	,	PUNCT
ejpam-3545	5	19	as	as	ADV
ejpam-3545	5	20	well	well	ADV
ejpam-3545	5	21	as	as	ADP
ejpam-3545	5	22	on	on	ADP
ejpam-3545	5	23	the	the	DET
ejpam-3545	5	24	projectivity	projectivity	NOUN
ejpam-3545	5	25	relation	relation	NOUN
ejpam-3545	5	26	between	between	ADP
ejpam-3545	5	27	abstract	abstract	ADJ
ejpam-3545	5	28	prearithmetics	prearithmetic	NOUN
ejpam-3545	5	29	.	.	PUNCT
ejpam-3545	6	1	in	in	ADP
ejpam-3545	6	2	a	a	DET
ejpam-3545	6	3	similar	similar	ADJ
ejpam-3545	6	4	way	way	NOUN
ejpam-3545	6	5	,	,	PUNCT
ejpam-3545	6	6	as	as	SCONJ
ejpam-3545	6	7	set	set	NOUN
ejpam-3545	6	8	theory	theory	NOUN
ejpam-3545	6	9	gives	give	VERB
ejpam-3545	6	10	a	a	DET
ejpam-3545	6	11	foundation	foundation	NOUN
ejpam-3545	6	12	for	for	ADP
ejpam-3545	6	13	mathematics	mathematic	NOUN
ejpam-3545	6	14	,	,	PUNCT
ejpam-3545	6	15	the	the	DET
ejpam-3545	6	16	theory	theory	NOUN
ejpam-3545	6	17	of	of	ADP
ejpam-3545	6	18	abstract	abstract	ADJ
ejpam-3545	6	19	prearithmetics	prearithmetic	NOUN
ejpam-3545	6	20	provides	provide	VERB
ejpam-3545	6	21	foundations	foundation	NOUN
ejpam-3545	6	22	for	for	ADP
ejpam-3545	6	23	the	the	DET
ejpam-3545	6	24	theory	theory	NOUN
ejpam-3545	6	25	of	of	ADP
ejpam-3545	6	26	the	the	DET
ejpam-3545	6	27	diophantine	diophantine	NOUN
ejpam-3545	6	28	and	and	CCONJ
ejpam-3545	6	29	non	non	ADJ
ejpam-3545	6	30	-	-	ADJ
ejpam-3545	6	31	diophantine	diophantine	ADJ
ejpam-3545	6	32	arithmetics	arithmetic	NOUN
ejpam-3545	6	33	.	.	PUNCT
ejpam-3545	7	1	in	in	ADP
ejpam-3545	7	2	this	this	DET
ejpam-3545	7	3	paper	paper	NOUN
ejpam-3545	7	4	,	,	PUNCT
ejpam-3545	7	5	we	we	PRON
ejpam-3545	7	6	study	study	VERB
ejpam-3545	7	7	relations	relation	NOUN
ejpam-3545	7	8	between	between	ADP
ejpam-3545	7	9	operations	operation	NOUN
ejpam-3545	7	10	in	in	ADP
ejpam-3545	7	11	abstract	abstract	ADJ
ejpam-3545	7	12	prearithmetics	prearithmetic	NOUN
ejpam-3545	7	13	exploring	explore	VERB
ejpam-3545	7	14	how	how	SCONJ
ejpam-3545	7	15	properties	property	NOUN
ejpam-3545	7	16	of	of	ADP
ejpam-3545	7	17	operations	operation	NOUN
ejpam-3545	7	18	in	in	ADP
ejpam-3545	7	19	one	one	NUM
ejpam-3545	7	20	prearithmetic	prearithmetic	ADJ
ejpam-3545	7	21	impact	impact	NOUN
ejpam-3545	7	22	properties	property	NOUN
ejpam-3545	7	23	of	of	ADP
ejpam-3545	7	24	operations	operation	NOUN
ejpam-3545	7	25	in	in	ADP
ejpam-3545	7	26	another	another	DET
ejpam-3545	7	27	prearithmetic	prearithmetic	NOUN
ejpam-3545	7	28	.	.	PUNCT
ejpam-3545	8	1	in	in	ADP
ejpam-3545	8	2	addition	addition	NOUN
ejpam-3545	8	3	,	,	PUNCT
ejpam-3545	8	4	we	we	PRON
ejpam-3545	8	5	explore	explore	VERB
ejpam-3545	8	6	how	how	SCONJ
ejpam-3545	8	7	to	to	PART
ejpam-3545	8	8	build	build	VERB
ejpam-3545	8	9	new	new	ADJ
ejpam-3545	8	10	prearithmetics	prearithmetic	NOUN
ejpam-3545	8	11	from	from	ADP
ejpam-3545	8	12	existing	exist	VERB
ejpam-3545	8	13	ones	one	NOUN
ejpam-3545	8	14	.	.	PUNCT
ejpam-3545	9	1	key	key	ADJ
ejpam-3545	9	2	words	word	NOUN
ejpam-3545	9	3	and	and	CCONJ
ejpam-3545	9	4	phrases	phrase	NOUN
ejpam-3545	9	5	:	:	PUNCT
ejpam-3545	9	6	arithmetic	arithmetic	ADJ
ejpam-3545	9	7	,	,	PUNCT
ejpam-3545	9	8	prearithmetic	prearithmetic	ADJ
ejpam-3545	9	9	,	,	PUNCT
ejpam-3545	9	10	vector	vector	NOUN
ejpam-3545	9	11	expansion	expansion	NOUN
ejpam-3545	9	12	,	,	PUNCT
ejpam-3545	9	13	matrix	matrix	NOUN
ejpam-3545	9	14	expansion	expansion	NOUN
ejpam-3545	9	15	,	,	PUNCT
ejpam-3545	9	16	addition	addition	NOUN
ejpam-3545	9	17	,	,	PUNCT
ejpam-3545	9	18	multiplication	multiplication	NOUN
ejpam-3545	9	19	,	,	PUNCT
ejpam-3545	9	20	projectivity	projectivity	NOUN
ejpam-3545	9	21	,	,	PUNCT
ejpam-3545	9	22	category	category	NOUN
ejpam-3545	9	23	1	1	NUM
ejpam-3545	9	24	.	.	PUNCT
ejpam-3545	9	25	introduction	introduction	NOUN
ejpam-3545	9	26	one	one	NUM
ejpam-3545	9	27	of	of	ADP
ejpam-3545	9	28	the	the	DET
ejpam-3545	9	29	most	most	ADV
ejpam-3545	9	30	basic	basic	ADJ
ejpam-3545	9	31	objects	object	NOUN
ejpam-3545	9	32	in	in	ADP
ejpam-3545	9	33	mathematics	mathematics	NOUN
ejpam-3545	9	34	is	be	AUX
ejpam-3545	9	35	the	the	DET
ejpam-3545	9	36	arithmetic	arithmetic	ADJ
ejpam-3545	9	37	n	n	PROPN
ejpam-3545	9	38	of	of	ADP
ejpam-3545	9	39	all	all	DET
ejpam-3545	9	40	natural	natural	ADJ
ejpam-3545	9	41	numbers	number	NOUN
ejpam-3545	9	42	.	.	PUNCT
ejpam-3545	10	1	people	people	NOUN
ejpam-3545	10	2	in	in	ADP
ejpam-3545	10	3	general	general	ADJ
ejpam-3545	10	4	and	and	CCONJ
ejpam-3545	10	5	mathematicians	mathematician	NOUN
ejpam-3545	10	6	in	in	ADP
ejpam-3545	10	7	particular	particular	ADJ
ejpam-3545	10	8	think	think	VERB
ejpam-3545	10	9	that	that	SCONJ
ejpam-3545	10	10	the	the	DET
ejpam-3545	10	11	laws	law	NOUN
ejpam-3545	10	12	of	of	ADP
ejpam-3545	10	13	this	this	DET
ejpam-3545	10	14	arithmetic	arithmetic	NOUN
ejpam-3545	10	15	are	be	AUX
ejpam-3545	10	16	universal	universal	ADJ
ejpam-3545	10	17	and	and	CCONJ
ejpam-3545	10	18	unique	unique	ADJ
ejpam-3545	10	19	.	.	PUNCT
ejpam-3545	11	1	the	the	DET
ejpam-3545	11	2	formula	formula	NOUN
ejpam-3545	11	3	2	2	NUM
ejpam-3545	11	4	×	×	NOUN
ejpam-3545	11	5	2	2	NUM
ejpam-3545	11	6	=	=	SYM
ejpam-3545	11	7	4	4	NUM
ejpam-3545	11	8	is	be	AUX
ejpam-3545	11	9	regarded	regard	VERB
ejpam-3545	11	10	a	a	DET
ejpam-3545	11	11	perpetual	perpetual	ADJ
ejpam-3545	11	12	unconditional	unconditional	ADJ
ejpam-3545	11	13	truth	truth	NOUN
ejpam-3545	11	14	.	.	PUNCT
ejpam-3545	12	1	however	however	ADV
ejpam-3545	12	2	,	,	PUNCT
ejpam-3545	12	3	for	for	ADP
ejpam-3545	12	4	a	a	DET
ejpam-3545	12	5	long	long	ADJ
ejpam-3545	12	6	time	time	NOUN
ejpam-3545	12	7	the	the	DET
ejpam-3545	12	8	best	good	ADJ
ejpam-3545	12	9	thinkers	thinker	NOUN
ejpam-3545	12	10	had	have	VERB
ejpam-3545	12	11	reservations	reservation	NOUN
ejpam-3545	12	12	with	with	ADP
ejpam-3545	12	13	respect	respect	NOUN
ejpam-3545	12	14	to	to	ADP
ejpam-3545	12	15	universality	universality	NOUN
ejpam-3545	12	16	of	of	ADP
ejpam-3545	12	17	n	n	PRON
ejpam-3545	12	18	considering	consider	VERB
ejpam-3545	12	19	numerous	numerous	ADJ
ejpam-3545	12	20	situations	situation	NOUN
ejpam-3545	12	21	when	when	SCONJ
ejpam-3545	12	22	the	the	DET
ejpam-3545	12	23	rules	rule	NOUN
ejpam-3545	12	24	of	of	ADP
ejpam-3545	12	25	this	this	DET
ejpam-3545	12	26	arithmetic	arithmetic	NOUN
ejpam-3545	12	27	,	,	PUNCT
ejpam-3545	12	28	which	which	PRON
ejpam-3545	12	29	is	be	AUX
ejpam-3545	12	30	called	call	VERB
ejpam-3545	12	31	the	the	DET
ejpam-3545	12	32	diophantine	diophantine	NOUN
ejpam-3545	12	33	arithmetic	arithmetic	ADJ
ejpam-3545	12	34	,	,	PUNCT
ejpam-3545	12	35	are	be	AUX
ejpam-3545	12	36	not	not	PART
ejpam-3545	12	37	true	true	ADJ
ejpam-3545	12	38	(	(	PUNCT
ejpam-3545	12	39	cf	cf	NOUN
ejpam-3545	12	40	.	.	PUNCT
ejpam-3545	12	41	,	,	PUNCT
ejpam-3545	12	42	for	for	ADP
ejpam-3545	12	43	example	example	NOUN
ejpam-3545	12	44	,	,	PUNCT
ejpam-3545	12	45	[	[	X
ejpam-3545	12	46	6	6	NUM
ejpam-3545	12	47	,	,	PUNCT
ejpam-3545	12	48	11	11	NUM
ejpam-3545	12	49	,	,	PUNCT
ejpam-3545	12	50	13	13	NUM
ejpam-3545	12	51	,	,	PUNCT
ejpam-3545	12	52	21	21	NUM
ejpam-3545	12	53	,	,	PUNCT
ejpam-3545	12	54	22	22	NUM
ejpam-3545	12	55	,	,	PUNCT
ejpam-3545	12	56	28	28	NUM
ejpam-3545	12	57	,	,	PUNCT
ejpam-3545	12	58	29	29	NUM
ejpam-3545	12	59	,	,	PUNCT
ejpam-3545	12	60	41	41	NUM
ejpam-3545	12	61	,	,	PUNCT
ejpam-3545	12	62	42	42	NUM
ejpam-3545	12	63	,	,	PUNCT
ejpam-3545	12	64	67	67	NUM
ejpam-3545	12	65	,	,	PUNCT
ejpam-3545	12	66	73	73	NUM
ejpam-3545	12	67	]	]	PUNCT
ejpam-3545	12	68	)	)	PUNCT
ejpam-3545	12	69	.	.	PUNCT
ejpam-3545	13	1	here	here	ADV
ejpam-3545	13	2	we	we	PRON
ejpam-3545	13	3	present	present	VERB
ejpam-3545	13	4	only	only	ADV
ejpam-3545	13	5	three	three	NUM
ejpam-3545	13	6	of	of	ADP
ejpam-3545	13	7	such	such	ADJ
ejpam-3545	13	8	examples	example	NOUN
ejpam-3545	13	9	although	although	SCONJ
ejpam-3545	13	10	there	there	PRON
ejpam-3545	13	11	are	be	VERB
ejpam-3545	13	12	much	much	ADV
ejpam-3545	13	13	more	more	ADJ
ejpam-3545	13	14	.	.	PUNCT
ejpam-3545	14	1	(	(	PUNCT
ejpam-3545	14	2	i	i	NOUN
ejpam-3545	14	3	)	)	PUNCT
ejpam-3545	14	4	one	one	NUM
ejpam-3545	14	5	raindrop	raindrop	NOUN
ejpam-3545	14	6	added	add	VERB
ejpam-3545	14	7	to	to	ADP
ejpam-3545	14	8	another	another	DET
ejpam-3545	14	9	raindrop	raindrop	NOUN
ejpam-3545	14	10	does	do	AUX
ejpam-3545	14	11	not	not	PART
ejpam-3545	14	12	make	make	VERB
ejpam-3545	14	13	two	two	NUM
ejpam-3545	14	14	raindrops	raindrop	NOUN
ejpam-3545	14	15	but	but	CCONJ
ejpam-3545	15	1	only	only	ADV
ejpam-3545	15	2	one	one	NUM
ejpam-3545	15	3	[	[	X
ejpam-3545	15	4	73	73	NUM
ejpam-3545	15	5	]	]	PUNCT
ejpam-3545	15	6	.	.	PUNCT
ejpam-3545	16	1	mathematically	mathematically	ADV
ejpam-3545	16	2	,	,	PUNCT
ejpam-3545	16	3	it	it	PRON
ejpam-3545	16	4	is	be	AUX
ejpam-3545	16	5	described	describe	VERB
ejpam-3545	16	6	by	by	ADP
ejpam-3545	16	7	the	the	DET
ejpam-3545	16	8	equality	equality	NOUN
ejpam-3545	16	9	1	1	NUM
ejpam-3545	16	10	+	+	CCONJ
ejpam-3545	16	11	1	1	NUM
ejpam-3545	16	12	=	=	SYM
ejpam-3545	16	13	1	1	NUM
ejpam-3545	16	14	.	.	PUNCT
ejpam-3545	16	15	(	(	PUNCT
ejpam-3545	16	16	ii	ii	NOUN
ejpam-3545	16	17	)	)	PUNCT
ejpam-3545	16	18	if	if	SCONJ
ejpam-3545	16	19	one	one	PRON
ejpam-3545	16	20	puts	put	VERB
ejpam-3545	16	21	a	a	DET
ejpam-3545	16	22	lion	lion	NOUN
ejpam-3545	16	23	and	and	CCONJ
ejpam-3545	16	24	a	a	DET
ejpam-3545	16	25	rabbit	rabbit	NOUN
ejpam-3545	16	26	in	in	ADP
ejpam-3545	16	27	a	a	DET
ejpam-3545	16	28	cage	cage	NOUN
ejpam-3545	16	29	,	,	PUNCT
ejpam-3545	16	30	one	one	PRON
ejpam-3545	16	31	will	will	AUX
ejpam-3545	16	32	not	not	PART
ejpam-3545	16	33	find	find	VERB
ejpam-3545	16	34	two	two	NUM
ejpam-3545	16	35	animals	animal	NOUN
ejpam-3545	16	36	in	in	ADP
ejpam-3545	16	37	the	the	DET
ejpam-3545	16	38	cage	cage	NOUN
ejpam-3545	16	39	later	later	ADV
ejpam-3545	16	40	on	on	ADV
ejpam-3545	16	41	(	(	PUNCT
ejpam-3545	16	42	cf	cf	NOUN
ejpam-3545	16	43	.	.	PUNCT
ejpam-3545	17	1	[	[	X
ejpam-3545	17	2	42	42	NUM
ejpam-3545	17	3	,	,	PUNCT
ejpam-3545	17	4	67	67	NUM
ejpam-3545	17	5	]	]	PUNCT
ejpam-3545	17	6	)	)	PUNCT
ejpam-3545	17	7	.	.	PUNCT
ejpam-3545	18	1	in	in	ADP
ejpam-3545	18	2	terms	term	NOUN
ejpam-3545	18	3	of	of	ADP
ejpam-3545	18	4	numbers	number	NOUN
ejpam-3545	18	5	,	,	PUNCT
ejpam-3545	18	6	it	it	PRON
ejpam-3545	18	7	will	will	AUX
ejpam-3545	18	8	mean	mean	VERB
ejpam-3545	18	9	1	1	NUM
ejpam-3545	19	1	+	+	SYM
ejpam-3545	19	2	1	1	NUM
ejpam-3545	19	3	=	=	SYM
ejpam-3545	19	4	1	1	NUM
ejpam-3545	19	5	.	.	PUNCT
ejpam-3545	19	6	doi	doi	NOUN
ejpam-3545	19	7	:	:	PUNCT
ejpam-3545	19	8	https://doi.org/10.29020/nybg.ejpam.v12i4.3545	https://doi.org/10.29020/nybg.ejpam.v12i4.3545	NOUN
ejpam-3545	19	9	email	email	NOUN
ejpam-3545	19	10	address	address	NOUN
ejpam-3545	19	11	:	:	PUNCT
ejpam-3545	19	12	mburgin@math.ucla.edu	mburgin@math.ucla.edu	PROPN
ejpam-3545	19	13	(	(	PUNCT
ejpam-3545	19	14	m.	m.	NOUN
ejpam-3545	19	15	burgin	burgin	PROPN
ejpam-3545	19	16	)	)	PUNCT
ejpam-3545	19	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3545	19	18	1787	1787	NUM
ejpam-3545	20	1	c	c	X
ejpam-3545	20	2	©	©	PROPN
ejpam-3545	20	3	2019	2019	NUM
ejpam-3545	20	4	ejpam	ejpam	NOUN
ejpam-3545	20	5	all	all	DET
ejpam-3545	20	6	rights	right	NOUN
ejpam-3545	20	7	reserved	reserve	VERB
ejpam-3545	20	8	.	.	PUNCT
ejpam-3545	21	1	m.	m.	NOUN
ejpam-3545	21	2	burgin	burgin	PROPN
ejpam-3545	21	3	/	/	SYM
ejpam-3545	21	4	eur	eur	PROPN
ejpam-3545	21	5	.	.	PUNCT
ejpam-3545	22	1	j.	j.	PROPN
ejpam-3545	22	2	pure	pure	PROPN
ejpam-3545	22	3	appl	appl	PROPN
ejpam-3545	22	4	.	.	PROPN
ejpam-3545	22	5	math	math	PROPN
ejpam-3545	22	6	,	,	PUNCT
ejpam-3545	22	7	12	12	NUM
ejpam-3545	22	8	(	(	PUNCT
ejpam-3545	22	9	4	4	NUM
ejpam-3545	22	10	)	)	PUNCT
ejpam-3545	22	11	(	(	PUNCT
ejpam-3545	22	12	2019	2019	NUM
ejpam-3545	22	13	)	)	PUNCT
ejpam-3545	22	14	,	,	PUNCT
ejpam-3545	22	15	1787	1787	NUM
ejpam-3545	22	16	-	-	SYM
ejpam-3545	22	17	1810	1810	NUM
ejpam-3545	22	18	1788	1788	NUM
ejpam-3545	22	19	(	(	PUNCT
ejpam-3545	22	20	iii	iii	NOUN
ejpam-3545	22	21	)	)	PUNCT
ejpam-3545	22	22	when	when	SCONJ
ejpam-3545	22	23	a	a	DET
ejpam-3545	22	24	cup	cup	NOUN
ejpam-3545	22	25	of	of	ADP
ejpam-3545	22	26	milk	milk	NOUN
ejpam-3545	22	27	is	be	AUX
ejpam-3545	22	28	added	add	VERB
ejpam-3545	22	29	to	to	ADP
ejpam-3545	22	30	a	a	DET
ejpam-3545	22	31	cup	cup	NOUN
ejpam-3545	22	32	of	of	ADP
ejpam-3545	22	33	popcorn	popcorn	NOUN
ejpam-3545	22	34	,	,	PUNCT
ejpam-3545	22	35	then	then	ADV
ejpam-3545	22	36	only	only	ADV
ejpam-3545	22	37	one	one	NUM
ejpam-3545	22	38	cup	cup	NOUN
ejpam-3545	22	39	of	of	ADP
ejpam-3545	22	40	mixture	mixture	NOUN
ejpam-3545	22	41	will	will	AUX
ejpam-3545	22	42	result	result	VERB
ejpam-3545	22	43	because	because	SCONJ
ejpam-3545	22	44	the	the	DET
ejpam-3545	22	45	cup	cup	NOUN
ejpam-3545	22	46	of	of	ADP
ejpam-3545	22	47	popcorn	popcorn	NOUN
ejpam-3545	22	48	will	will	AUX
ejpam-3545	22	49	very	very	ADV
ejpam-3545	22	50	nearly	nearly	ADV
ejpam-3545	22	51	absorb	absorb	VERB
ejpam-3545	22	52	a	a	DET
ejpam-3545	22	53	whole	whole	ADJ
ejpam-3545	22	54	cup	cup	NOUN
ejpam-3545	22	55	of	of	ADP
ejpam-3545	22	56	milk	milk	NOUN
ejpam-3545	22	57	without	without	ADP
ejpam-3545	22	58	spillage	spillage	NOUN
ejpam-3545	22	59	[	[	X
ejpam-3545	22	60	21	21	NUM
ejpam-3545	22	61	]	]	PUNCT
ejpam-3545	22	62	.	.	PUNCT
ejpam-3545	23	1	so	so	ADV
ejpam-3545	23	2	,	,	PUNCT
ejpam-3545	23	3	in	in	ADP
ejpam-3545	23	4	this	this	DET
ejpam-3545	23	5	case	case	NOUN
ejpam-3545	23	6	,	,	PUNCT
ejpam-3545	23	7	we	we	PRON
ejpam-3545	23	8	also	also	ADV
ejpam-3545	23	9	have	have	VERB
ejpam-3545	23	10	1	1	NUM
ejpam-3545	23	11	+	+	SYM
ejpam-3545	23	12	1	1	NUM
ejpam-3545	23	13	=	=	SYM
ejpam-3545	23	14	1	1	NUM
ejpam-3545	23	15	.	.	PUNCT
ejpam-3545	24	1	in	in	ADP
ejpam-3545	24	2	addition	addition	NOUN
ejpam-3545	24	3	,	,	PUNCT
ejpam-3545	24	4	recently	recently	ADV
ejpam-3545	24	5	the	the	DET
ejpam-3545	24	6	expression	expression	NOUN
ejpam-3545	24	7	1	1	NUM
ejpam-3545	24	8	+	+	SYM
ejpam-3545	24	9	1	1	NUM
ejpam-3545	24	10	=	=	SYM
ejpam-3545	24	11	3	3	NUM
ejpam-3545	24	12	has	have	AUX
ejpam-3545	24	13	become	become	VERB
ejpam-3545	24	14	a	a	DET
ejpam-3545	24	15	very	very	ADV
ejpam-3545	24	16	popular	popular	ADJ
ejpam-3545	24	17	metaphor	metaphor	NOUN
ejpam-3545	24	18	for	for	ADP
ejpam-3545	24	19	synergy	synergy	NOUN
ejpam-3545	24	20	in	in	ADP
ejpam-3545	24	21	a	a	DET
ejpam-3545	24	22	variety	variety	NOUN
ejpam-3545	24	23	of	of	ADP
ejpam-3545	24	24	areas	area	NOUN
ejpam-3545	24	25	:	:	PUNCT
ejpam-3545	24	26	in	in	ADP
ejpam-3545	24	27	business	business	NOUN
ejpam-3545	24	28	and	and	CCONJ
ejpam-3545	24	29	industry	industry	NOUN
ejpam-3545	24	30	(	(	PUNCT
ejpam-3545	24	31	cf	cf	NOUN
ejpam-3545	24	32	.	.	PUNCT
ejpam-3545	24	33	,	,	PUNCT
ejpam-3545	24	34	for	for	ADP
ejpam-3545	24	35	example	example	NOUN
ejpam-3545	24	36	,	,	PUNCT
ejpam-3545	24	37	(	(	PUNCT
ejpam-3545	24	38	[	[	X
ejpam-3545	24	39	2	2	NUM
ejpam-3545	24	40	,	,	PUNCT
ejpam-3545	24	41	33	33	NUM
ejpam-3545	24	42	,	,	PUNCT
ejpam-3545	24	43	34	34	NUM
ejpam-3545	24	44	,	,	PUNCT
ejpam-3545	24	45	38	38	NUM
ejpam-3545	24	46	,	,	PUNCT
ejpam-3545	24	47	45	45	NUM
ejpam-3545	24	48	,	,	PUNCT
ejpam-3545	24	49	58	58	NUM
ejpam-3545	24	50	]	]	PUNCT
ejpam-3545	24	51	)	)	PUNCT
ejpam-3545	24	52	)	)	PUNCT
ejpam-3545	24	53	,	,	PUNCT
ejpam-3545	24	54	in	in	ADP
ejpam-3545	24	55	economics	economic	NOUN
ejpam-3545	24	56	and	and	CCONJ
ejpam-3545	24	57	finance	finance	NOUN
ejpam-3545	24	58	(	(	PUNCT
ejpam-3545	24	59	cf	cf	NOUN
ejpam-3545	24	60	.	.	PUNCT
ejpam-3545	24	61	,	,	PUNCT
ejpam-3545	24	62	for	for	ADP
ejpam-3545	24	63	example	example	NOUN
ejpam-3545	24	64	,	,	PUNCT
ejpam-3545	24	65	[	[	X
ejpam-3545	24	66	9	9	NUM
ejpam-3545	24	67	]	]	PUNCT
ejpam-3545	24	68	,	,	PUNCT
ejpam-3545	24	69	in	in	ADP
ejpam-3545	24	70	psychology	psychology	NOUN
ejpam-3545	24	71	and	and	CCONJ
ejpam-3545	24	72	sociology	sociology	NOUN
ejpam-3545	24	73	(	(	PUNCT
ejpam-3545	24	74	cf	cf	NOUN
ejpam-3545	24	75	.	.	PROPN
ejpam-3545	24	76	,	,	PUNCT
ejpam-3545	24	77	for	for	ADP
ejpam-3545	24	78	example,[4	example,[4	PROPN
ejpam-3545	24	79	,	,	PUNCT
ejpam-3545	24	80	12	12	NUM
ejpam-3545	24	81	,	,	PUNCT
ejpam-3545	24	82	25	25	NUM
ejpam-3545	24	83	,	,	PUNCT
ejpam-3545	24	84	26	26	NUM
ejpam-3545	24	85	,	,	PUNCT
ejpam-3545	24	86	40	40	NUM
ejpam-3545	24	87	,	,	PUNCT
ejpam-3545	24	88	55	55	NUM
ejpam-3545	24	89	,	,	PUNCT
ejpam-3545	24	90	72	72	NUM
ejpam-3545	24	91	]	]	PUNCT
ejpam-3545	24	92	)	)	PUNCT
ejpam-3545	24	93	,	,	PUNCT
ejpam-3545	24	94	library	library	NOUN
ejpam-3545	24	95	studies	study	NOUN
ejpam-3545	24	96	(	(	PUNCT
ejpam-3545	24	97	cf	cf	NOUN
ejpam-3545	24	98	.	.	PUNCT
ejpam-3545	24	99	,	,	PUNCT
ejpam-3545	24	100	for	for	ADP
ejpam-3545	24	101	example	example	NOUN
ejpam-3545	24	102	,	,	PUNCT
ejpam-3545	24	103	[	[	X
ejpam-3545	24	104	57	57	NUM
ejpam-3545	24	105	]	]	NUM
ejpam-3545	24	106	)	)	PUNCT
ejpam-3545	24	107	,	,	PUNCT
ejpam-3545	24	108	biochemistry	biochemistry	NOUN
ejpam-3545	24	109	and	and	CCONJ
ejpam-3545	24	110	bioinformatics	bioinformatics	NOUN
ejpam-3545	24	111	(	(	PUNCT
ejpam-3545	24	112	cf	cf	NOUN
ejpam-3545	24	113	.	.	PUNCT
ejpam-3545	24	114	,	,	PUNCT
ejpam-3545	24	115	for	for	ADP
ejpam-3545	24	116	example	example	NOUN
ejpam-3545	24	117	,	,	PUNCT
ejpam-3545	24	118	[	[	X
ejpam-3545	24	119	46	46	NUM
ejpam-3545	24	120	]	]	SYM
ejpam-3545	24	121	)	)	PUNCT
ejpam-3545	24	122	,	,	PUNCT
ejpam-3545	24	123	computer	computer	NOUN
ejpam-3545	24	124	science	science	NOUN
ejpam-3545	24	125	(	(	PUNCT
ejpam-3545	24	126	cf	cf	NOUN
ejpam-3545	24	127	.	.	PUNCT
ejpam-3545	24	128	,	,	PUNCT
ejpam-3545	24	129	for	for	ADP
ejpam-3545	24	130	example	example	NOUN
ejpam-3545	24	131	,	,	PUNCT
ejpam-3545	24	132	[	[	X
ejpam-3545	24	133	24	24	NUM
ejpam-3545	24	134	,	,	PUNCT
ejpam-3545	24	135	30	30	NUM
ejpam-3545	24	136	,	,	PUNCT
ejpam-3545	24	137	50	50	NUM
ejpam-3545	24	138	]	]	NUM
ejpam-3545	24	139	)	)	PUNCT
ejpam-3545	24	140	,	,	PUNCT
ejpam-3545	24	141	physics	physics	NOUN
ejpam-3545	24	142	(	(	PUNCT
ejpam-3545	24	143	cf	cf	NOUN
ejpam-3545	24	144	.	.	PUNCT
ejpam-3545	24	145	,	,	PUNCT
ejpam-3545	24	146	for	for	ADP
ejpam-3545	24	147	example	example	NOUN
ejpam-3545	24	148	,	,	PUNCT
ejpam-3545	24	149	[	[	X
ejpam-3545	24	150	49	49	NUM
ejpam-3545	24	151	]	]	SYM
ejpam-3545	24	152	)	)	PUNCT
ejpam-3545	24	153	,	,	PUNCT
ejpam-3545	24	154	medicine	medicine	NOUN
ejpam-3545	24	155	(	(	PUNCT
ejpam-3545	24	156	cf	cf	NOUN
ejpam-3545	24	157	.	.	PUNCT
ejpam-3545	24	158	,	,	PUNCT
ejpam-3545	24	159	for	for	ADP
ejpam-3545	24	160	example	example	NOUN
ejpam-3545	24	161	,	,	PUNCT
ejpam-3545	24	162	[	[	X
ejpam-3545	24	163	15	15	NUM
ejpam-3545	24	164	,	,	PUNCT
ejpam-3545	24	165	64	64	NUM
ejpam-3545	24	166	,	,	PUNCT
ejpam-3545	24	167	71	71	NUM
ejpam-3545	24	168	]	]	PUNCT
ejpam-3545	24	169	)	)	PUNCT
ejpam-3545	24	170	and	and	CCONJ
ejpam-3545	24	171	pedagogy	pedagogy	NOUN
ejpam-3545	24	172	(	(	PUNCT
ejpam-3545	24	173	cf	cf	NOUN
ejpam-3545	24	174	.	.	PUNCT
ejpam-3545	24	175	,	,	PUNCT
ejpam-3545	24	176	for	for	ADP
ejpam-3545	24	177	example	example	NOUN
ejpam-3545	24	178	,	,	PUNCT
ejpam-3545	24	179	[	[	X
ejpam-3545	24	180	62	62	NUM
ejpam-3545	24	181	]	]	PUNCT
ejpam-3545	24	182	)	)	PUNCT
ejpam-3545	24	183	.	.	PUNCT
ejpam-3545	25	1	all	all	DET
ejpam-3545	25	2	these	these	DET
ejpam-3545	25	3	examples	example	NOUN
ejpam-3545	25	4	indicated	indicate	VERB
ejpam-3545	25	5	existence	existence	NOUN
ejpam-3545	25	6	of	of	ADP
ejpam-3545	25	7	other	other	ADJ
ejpam-3545	25	8	non	non	ADJ
ejpam-3545	25	9	-	-	ADJ
ejpam-3545	25	10	diophantine	diophantine	ADJ
ejpam-3545	25	11	arithmetics	arithmetic	NOUN
ejpam-3545	25	12	,	,	PUNCT
ejpam-3545	25	13	in	in	ADP
ejpam-3545	25	14	which	which	PRON
ejpam-3545	25	15	it	it	PRON
ejpam-3545	25	16	would	would	AUX
ejpam-3545	25	17	be	be	AUX
ejpam-3545	25	18	possible	possible	ADJ
ejpam-3545	25	19	to	to	PART
ejpam-3545	25	20	explain	explain	VERB
ejpam-3545	25	21	all	all	DET
ejpam-3545	25	22	these	these	DET
ejpam-3545	25	23	cases	case	NOUN
ejpam-3545	25	24	in	in	ADP
ejpam-3545	25	25	a	a	DET
ejpam-3545	25	26	rigorous	rigorous	ADJ
ejpam-3545	25	27	mathematical	mathematical	ADJ
ejpam-3545	25	28	way	way	NOUN
ejpam-3545	25	29	.	.	PUNCT
ejpam-3545	26	1	some	some	DET
ejpam-3545	26	2	researchers	researcher	NOUN
ejpam-3545	26	3	predicted	predict	VERB
ejpam-3545	26	4	this	this	PRON
ejpam-3545	26	5	(	(	PUNCT
ejpam-3545	26	6	cf	cf	NOUN
ejpam-3545	26	7	.	.	PUNCT
ejpam-3545	26	8	,	,	PUNCT
ejpam-3545	26	9	for	for	ADP
ejpam-3545	26	10	example	example	NOUN
ejpam-3545	26	11	,	,	PUNCT
ejpam-3545	26	12	[	[	X
ejpam-3545	26	13	29	29	NUM
ejpam-3545	26	14	,	,	PUNCT
ejpam-3545	26	15	41	41	NUM
ejpam-3545	26	16	,	,	PUNCT
ejpam-3545	26	17	66	66	NUM
ejpam-3545	26	18	]	]	PUNCT
ejpam-3545	26	19	.	.	PUNCT
ejpam-3545	27	1	these	these	DET
ejpam-3545	27	2	predictions	prediction	NOUN
ejpam-3545	27	3	became	become	VERB
ejpam-3545	27	4	true	true	ADJ
ejpam-3545	27	5	when	when	SCONJ
ejpam-3545	27	6	the	the	DET
ejpam-3545	27	7	first	first	ADJ
ejpam-3545	27	8	class	class	NOUN
ejpam-3545	27	9	of	of	ADP
ejpam-3545	27	10	non	non	ADJ
ejpam-3545	27	11	-	-	ADJ
ejpam-3545	27	12	diophantine	diophantine	ADJ
ejpam-3545	27	13	arithmetics	arithmetic	NOUN
ejpam-3545	27	14	was	be	AUX
ejpam-3545	27	15	discovered	discover	VERB
ejpam-3545	27	16	and	and	CCONJ
ejpam-3545	27	17	explored	explore	VERB
ejpam-3545	27	18	in	in	ADP
ejpam-3545	27	19	1975	1975	NUM
ejpam-3545	27	20	although	although	SCONJ
ejpam-3545	27	21	the	the	DET
ejpam-3545	27	22	first	first	ADJ
ejpam-3545	27	23	publication	publication	NOUN
ejpam-3545	27	24	appeared	appear	VERB
ejpam-3545	27	25	in	in	ADP
ejpam-3545	27	26	1977	1977	NUM
ejpam-3545	27	27	[	[	X
ejpam-3545	27	28	10	10	NUM
ejpam-3545	27	29	]	]	PUNCT
ejpam-3545	27	30	.	.	PUNCT
ejpam-3545	28	1	later	later	ADV
ejpam-3545	28	2	other	other	ADJ
ejpam-3545	28	3	classes	class	NOUN
ejpam-3545	28	4	of	of	ADP
ejpam-3545	28	5	non	non	ADJ
ejpam-3545	28	6	-	-	ADJ
ejpam-3545	28	7	diophantine	diophantine	ADJ
ejpam-3545	28	8	arithmetics	arithmetic	NOUN
ejpam-3545	28	9	were	be	AUX
ejpam-3545	28	10	constructed	construct	VERB
ejpam-3545	28	11	[	[	X
ejpam-3545	28	12	7	7	NUM
ejpam-3545	28	13	,	,	PUNCT
ejpam-3545	28	14	11	11	NUM
ejpam-3545	28	15	]	]	PUNCT
ejpam-3545	28	16	.	.	PUNCT
ejpam-3545	29	1	recently	recently	ADV
ejpam-3545	29	2	non	non	ADJ
ejpam-3545	29	3	-	-	ADJ
ejpam-3545	29	4	diophantine	diophantine	ADJ
ejpam-3545	29	5	arithmetics	arithmetic	NOUN
ejpam-3545	29	6	found	find	VERB
ejpam-3545	29	7	explicit	explicit	ADJ
ejpam-3545	29	8	applications	application	NOUN
ejpam-3545	29	9	in	in	ADP
ejpam-3545	29	10	physics	physics	NOUN
ejpam-3545	29	11	[	[	X
ejpam-3545	29	12	17	17	NUM
ejpam-3545	29	13	,	,	PUNCT
ejpam-3545	29	14	18	18	NUM
ejpam-3545	29	15	,	,	PUNCT
ejpam-3545	29	16	20	20	NUM
ejpam-3545	29	17	]	]	PUNCT
ejpam-3545	29	18	and	and	CCONJ
ejpam-3545	29	19	psychology	psychology	NOUN
ejpam-3545	29	20	[	[	X
ejpam-3545	29	21	19	19	NUM
ejpam-3545	29	22	]	]	PUNCT
ejpam-3545	29	23	although	although	SCONJ
ejpam-3545	29	24	implicit	implicit	ADJ
ejpam-3545	29	25	utilization	utilization	NOUN
ejpam-3545	29	26	non	non	ADJ
ejpam-3545	29	27	-	-	ADJ
ejpam-3545	29	28	diophantine	diophantine	ADJ
ejpam-3545	29	29	arithmetics	arithmetic	NOUN
ejpam-3545	29	30	in	in	ADP
ejpam-3545	29	31	physics	physics	NOUN
ejpam-3545	29	32	and	and	CCONJ
ejpam-3545	29	33	psychology	psychology	NOUN
ejpam-3545	29	34	existed	exist	VERB
ejpam-3545	29	35	for	for	ADP
ejpam-3545	29	36	quite	quite	DET
ejpam-3545	29	37	a	a	DET
ejpam-3545	29	38	while	while	NOUN
ejpam-3545	29	39	(	(	PUNCT
ejpam-3545	29	40	cf	cf	NOUN
ejpam-3545	29	41	.	.	PUNCT
ejpam-3545	29	42	,	,	PUNCT
ejpam-3545	29	43	for	for	ADP
ejpam-3545	29	44	example	example	NOUN
ejpam-3545	29	45	,	,	PUNCT
ejpam-3545	29	46	[	[	X
ejpam-3545	29	47	52–54	52–54	NUM
ejpam-3545	29	48	,	,	PUNCT
ejpam-3545	29	49	56	56	NUM
ejpam-3545	29	50	]	]	NUM
ejpam-3545	29	51	)	)	PUNCT
ejpam-3545	29	52	.	.	PUNCT
ejpam-3545	30	1	following	follow	VERB
ejpam-3545	30	2	the	the	DET
ejpam-3545	30	3	classical	classical	ADJ
ejpam-3545	30	4	understanding	understanding	NOUN
ejpam-3545	30	5	of	of	ADP
ejpam-3545	30	6	arithmetic	arithmetic	ADJ
ejpam-3545	30	7	,	,	PUNCT
ejpam-3545	30	8	here	here	ADV
ejpam-3545	30	9	non	non	ADJ
ejpam-3545	30	10	-	-	ADJ
ejpam-3545	30	11	diophantine	diophantine	ADJ
ejpam-3545	30	12	arithmetics	arithmetic	NOUN
ejpam-3545	30	13	are	be	AUX
ejpam-3545	30	14	treated	treat	VERB
ejpam-3545	30	15	as	as	ADP
ejpam-3545	30	16	arithmetics	arithmetic	NOUN
ejpam-3545	30	17	of	of	ADP
ejpam-3545	30	18	natural	natural	ADJ
ejpam-3545	30	19	numbers	number	NOUN
ejpam-3545	30	20	although	although	SCONJ
ejpam-3545	30	21	it	it	PRON
ejpam-3545	30	22	is	be	AUX
ejpam-3545	30	23	also	also	ADV
ejpam-3545	30	24	possible	possible	ADJ
ejpam-3545	30	25	,	,	PUNCT
ejpam-3545	30	26	for	for	ADP
ejpam-3545	30	27	example	example	NOUN
ejpam-3545	30	28	,	,	PUNCT
ejpam-3545	30	29	to	to	PART
ejpam-3545	30	30	consider	consider	VERB
ejpam-3545	30	31	non	non	ADJ
ejpam-3545	30	32	-	-	ADJ
ejpam-3545	30	33	diophantine	diophantine	ADJ
ejpam-3545	30	34	arithmetics	arithmetic	NOUN
ejpam-3545	30	35	of	of	ADP
ejpam-3545	30	36	real	real	ADJ
ejpam-3545	30	37	or	or	CCONJ
ejpam-3545	30	38	integer	integer	NOUN
ejpam-3545	30	39	numbers	number	NOUN
ejpam-3545	30	40	.	.	PUNCT
ejpam-3545	31	1	construction	construction	NOUN
ejpam-3545	31	2	of	of	ADP
ejpam-3545	31	3	non	non	ADJ
ejpam-3545	31	4	-	-	ADJ
ejpam-3545	31	5	diophantine	diophantine	ADJ
ejpam-3545	31	6	arithmetics	arithmetic	NOUN
ejpam-3545	31	7	is	be	AUX
ejpam-3545	31	8	based	base	VERB
ejpam-3545	31	9	on	on	ADP
ejpam-3545	31	10	more	more	ADJ
ejpam-3545	31	11	general	general	ADJ
ejpam-3545	31	12	mathematical	mathematical	ADJ
ejpam-3545	31	13	structures	structure	NOUN
ejpam-3545	31	14	,	,	PUNCT
ejpam-3545	31	15	which	which	PRON
ejpam-3545	31	16	are	be	AUX
ejpam-3545	31	17	called	call	VERB
ejpam-3545	31	18	abstract	abstract	ADJ
ejpam-3545	31	19	prearithmetics	prearithmetic	NOUN
ejpam-3545	31	20	,	,	PUNCT
ejpam-3545	31	21	as	as	ADV
ejpam-3545	31	22	well	well	ADV
ejpam-3545	31	23	as	as	ADP
ejpam-3545	31	24	on	on	ADP
ejpam-3545	31	25	the	the	DET
ejpam-3545	31	26	projectivity	projectivity	NOUN
ejpam-3545	31	27	relation	relation	NOUN
ejpam-3545	31	28	between	between	ADP
ejpam-3545	31	29	abstract	abstract	ADJ
ejpam-3545	31	30	prearithmetics	prearithmetic	NOUN
ejpam-3545	31	31	[	[	X
ejpam-3545	31	32	7	7	NUM
ejpam-3545	31	33	,	,	PUNCT
ejpam-3545	31	34	10	10	NUM
ejpam-3545	31	35	,	,	PUNCT
ejpam-3545	31	36	11	11	NUM
ejpam-3545	31	37	]	]	PUNCT
ejpam-3545	31	38	.	.	PUNCT
ejpam-3545	32	1	in	in	ADP
ejpam-3545	32	2	a	a	DET
ejpam-3545	32	3	similar	similar	ADJ
ejpam-3545	32	4	way	way	NOUN
ejpam-3545	32	5	,	,	PUNCT
ejpam-3545	32	6	as	as	SCONJ
ejpam-3545	32	7	set	set	NOUN
ejpam-3545	32	8	theory	theory	NOUN
ejpam-3545	32	9	forms	form	VERB
ejpam-3545	32	10	a	a	DET
ejpam-3545	32	11	foundation	foundation	NOUN
ejpam-3545	32	12	for	for	ADP
ejpam-3545	32	13	mathematics	mathematic	NOUN
ejpam-3545	32	14	,	,	PUNCT
ejpam-3545	32	15	the	the	DET
ejpam-3545	32	16	theory	theory	NOUN
ejpam-3545	32	17	of	of	ADP
ejpam-3545	32	18	abstract	abstract	ADJ
ejpam-3545	32	19	prearithmetics	prearithmetic	NOUN
ejpam-3545	32	20	provides	provide	VERB
ejpam-3545	32	21	foundations	foundation	NOUN
ejpam-3545	32	22	for	for	ADP
ejpam-3545	32	23	the	the	DET
ejpam-3545	32	24	theory	theory	NOUN
ejpam-3545	32	25	of	of	ADP
ejpam-3545	32	26	the	the	DET
ejpam-3545	32	27	diophantine	diophantine	NOUN
ejpam-3545	32	28	arithmetic	arithmetic	ADJ
ejpam-3545	32	29	and	and	CCONJ
ejpam-3545	32	30	non	non	ADJ
ejpam-3545	32	31	-	-	ADJ
ejpam-3545	32	32	diophantine	diophantine	ADJ
ejpam-3545	32	33	arithmetics	arithmetic	NOUN
ejpam-3545	32	34	.	.	PUNCT
ejpam-3545	33	1	the	the	DET
ejpam-3545	33	2	term	term	NOUN
ejpam-3545	33	3	arithmetic	arithmetic	NOUN
ejpam-3545	33	4	means	mean	VERB
ejpam-3545	33	5	not	not	PART
ejpam-3545	33	6	only	only	ADV
ejpam-3545	33	7	a	a	DET
ejpam-3545	33	8	mathematical	mathematical	ADJ
ejpam-3545	33	9	structure	structure	NOUN
ejpam-3545	33	10	but	but	CCONJ
ejpam-3545	33	11	also	also	ADV
ejpam-3545	33	12	a	a	DET
ejpam-3545	33	13	branch	branch	NOUN
ejpam-3545	33	14	of	of	ADP
ejpam-3545	33	15	mathematics	mathematic	NOUN
ejpam-3545	33	16	aimed	aim	VERB
ejpam-3545	33	17	at	at	ADP
ejpam-3545	33	18	the	the	DET
ejpam-3545	33	19	study	study	NOUN
ejpam-3545	33	20	of	of	ADP
ejpam-3545	33	21	number	number	NOUN
ejpam-3545	33	22	systems	system	NOUN
ejpam-3545	33	23	with	with	ADP
ejpam-3545	33	24	operations	operation	NOUN
ejpam-3545	33	25	and	and	CCONJ
ejpam-3545	33	26	relations	relation	NOUN
ejpam-3545	33	27	.	.	PUNCT
ejpam-3545	34	1	this	this	PRON
ejpam-3545	34	2	allows	allow	VERB
ejpam-3545	34	3	treating	treat	VERB
ejpam-3545	34	4	abstract	abstract	ADJ
ejpam-3545	34	5	prearithmetics	prearithmetic	NOUN
ejpam-3545	34	6	as	as	ADP
ejpam-3545	34	7	the	the	DET
ejpam-3545	34	8	basic	basic	ADJ
ejpam-3545	34	9	structures	structure	NOUN
ejpam-3545	34	10	in	in	ADP
ejpam-3545	34	11	the	the	DET
ejpam-3545	34	12	field	field	NOUN
ejpam-3545	34	13	of	of	ADP
ejpam-3545	34	14	arithmetic	arithmetic	ADJ
ejpam-3545	34	15	.	.	PUNCT
ejpam-3545	35	1	in	in	ADP
ejpam-3545	35	2	addition	addition	NOUN
ejpam-3545	35	3	,	,	PUNCT
ejpam-3545	35	4	the	the	DET
ejpam-3545	35	5	theory	theory	NOUN
ejpam-3545	35	6	of	of	ADP
ejpam-3545	35	7	abstract	abstract	ADJ
ejpam-3545	35	8	prearithmetics	prearithmetic	NOUN
ejpam-3545	35	9	includes	include	VERB
ejpam-3545	35	10	theories	theory	NOUN
ejpam-3545	35	11	of	of	ADP
ejpam-3545	35	12	various	various	ADJ
ejpam-3545	35	13	conventional	conventional	ADJ
ejpam-3545	35	14	mathematical	mathematical	ADJ
ejpam-3545	35	15	structures	structure	NOUN
ejpam-3545	35	16	,	,	PUNCT
ejpam-3545	35	17	such	such	ADJ
ejpam-3545	35	18	as	as	ADP
ejpam-3545	35	19	rings	ring	NOUN
ejpam-3545	35	20	,	,	PUNCT
ejpam-3545	35	21	semirings	semiring	NOUN
ejpam-3545	35	22	,	,	PUNCT
ejpam-3545	35	23	fields	field	NOUN
ejpam-3545	35	24	,	,	PUNCT
ejpam-3545	35	25	ordered	order	VERB
ejpam-3545	35	26	rings	ring	NOUN
ejpam-3545	35	27	,	,	PUNCT
ejpam-3545	35	28	ordered	order	VERB
ejpam-3545	35	29	fields	field	NOUN
ejpam-3545	35	30	,	,	PUNCT
ejpam-3545	35	31	lattices	lattice	NOUN
ejpam-3545	35	32	and	and	CCONJ
ejpam-3545	35	33	boolean	boolean	ADJ
ejpam-3545	35	34	algebras	algebra	NOUN
ejpam-3545	35	35	,	,	PUNCT
ejpam-3545	35	36	as	as	ADP
ejpam-3545	35	37	its	its	PRON
ejpam-3545	35	38	subtheories	subtheorie	NOUN
ejpam-3545	35	39	.	.	PUNCT
ejpam-3545	36	1	this	this	PRON
ejpam-3545	36	2	allows	allow	VERB
ejpam-3545	36	3	using	use	VERB
ejpam-3545	36	4	constructions	construction	NOUN
ejpam-3545	36	5	from	from	ADP
ejpam-3545	36	6	the	the	DET
ejpam-3545	36	7	theory	theory	NOUN
ejpam-3545	36	8	of	of	ADP
ejpam-3545	36	9	abstract	abstract	ADJ
ejpam-3545	36	10	prearithmetics	prearithmetic	NOUN
ejpam-3545	36	11	for	for	ADP
ejpam-3545	36	12	its	its	PRON
ejpam-3545	36	13	subtheories	subtheorie	NOUN
ejpam-3545	36	14	of	of	ADP
ejpam-3545	36	15	conventional	conventional	ADJ
ejpam-3545	36	16	mathematical	mathematical	ADJ
ejpam-3545	36	17	structures	structure	NOUN
ejpam-3545	36	18	.	.	PUNCT
ejpam-3545	37	1	for	for	ADP
ejpam-3545	37	2	instance	instance	NOUN
ejpam-3545	37	3	,	,	PUNCT
ejpam-3545	37	4	it	it	PRON
ejpam-3545	37	5	is	be	AUX
ejpam-3545	37	6	possible	possible	ADJ
ejpam-3545	37	7	to	to	PART
ejpam-3545	37	8	study	study	VERB
ejpam-3545	37	9	projectivity	projectivity	NOUN
ejpam-3545	37	10	relations	relation	NOUN
ejpam-3545	37	11	for	for	ADP
ejpam-3545	37	12	rings	ring	NOUN
ejpam-3545	37	13	or	or	CCONJ
ejpam-3545	37	14	boolean	boolean	ADJ
ejpam-3545	37	15	algebras	algebra	NOUN
ejpam-3545	37	16	.	.	PUNCT
ejpam-3545	38	1	abstract	abstract	ADJ
ejpam-3545	38	2	prearithmetics	prearithmetic	NOUN
ejpam-3545	38	3	also	also	ADV
ejpam-3545	38	4	provide	provide	VERB
ejpam-3545	38	5	a	a	DET
ejpam-3545	38	6	unified	unified	ADJ
ejpam-3545	38	7	algebraic	algebraic	ADJ
ejpam-3545	38	8	context	context	NOUN
ejpam-3545	38	9	for	for	ADP
ejpam-3545	38	10	some	some	DET
ejpam-3545	38	11	traditional	traditional	ADJ
ejpam-3545	38	12	mathematical	mathematical	ADJ
ejpam-3545	38	13	constructions	construction	NOUN
ejpam-3545	38	14	,	,	PUNCT
ejpam-3545	38	15	such	such	ADJ
ejpam-3545	38	16	as	as	ADP
ejpam-3545	38	17	logarithmic	logarithmic	ADJ
ejpam-3545	38	18	scales	scale	NOUN
ejpam-3545	38	19	,	,	PUNCT
ejpam-3545	38	20	modular	modular	ADJ
ejpam-3545	38	21	arithmetics	arithmetic	NOUN
ejpam-3545	38	22	and	and	CCONJ
ejpam-3545	38	23	computer	computer	NOUN
ejpam-3545	38	24	arithmetics	arithmetic	NOUN
ejpam-3545	38	25	,	,	PUNCT
ejpam-3545	38	26	which	which	PRON
ejpam-3545	38	27	are	be	AUX
ejpam-3545	38	28	used	use	VERB
ejpam-3545	38	29	in	in	ADP
ejpam-3545	38	30	many	many	ADJ
ejpam-3545	38	31	applications	application	NOUN
ejpam-3545	38	32	in	in	ADP
ejpam-3545	38	33	mathematics	mathematic	NOUN
ejpam-3545	38	34	,	,	PUNCT
ejpam-3545	38	35	science	science	NOUN
ejpam-3545	38	36	and	and	CCONJ
ejpam-3545	38	37	technology	technology	NOUN
ejpam-3545	38	38	.	.	PUNCT
ejpam-3545	39	1	m.	m.	NOUN
ejpam-3545	39	2	burgin	burgin	PROPN
ejpam-3545	39	3	/	/	SYM
ejpam-3545	39	4	eur	eur	PROPN
ejpam-3545	39	5	.	.	PUNCT
ejpam-3545	40	1	j.	j.	PROPN
ejpam-3545	40	2	pure	pure	PROPN
ejpam-3545	40	3	appl	appl	PROPN
ejpam-3545	40	4	.	.	PROPN
ejpam-3545	40	5	math	math	PROPN
ejpam-3545	40	6	,	,	PUNCT
ejpam-3545	40	7	12	12	NUM
ejpam-3545	40	8	(	(	PUNCT
ejpam-3545	40	9	4	4	NUM
ejpam-3545	40	10	)	)	PUNCT
ejpam-3545	40	11	(	(	PUNCT
ejpam-3545	40	12	2019	2019	NUM
ejpam-3545	40	13	)	)	PUNCT
ejpam-3545	40	14	,	,	PUNCT
ejpam-3545	40	15	1787	1787	NUM
ejpam-3545	40	16	-	-	SYM
ejpam-3545	40	17	1810	1810	NUM
ejpam-3545	40	18	1789	1789	NUM
ejpam-3545	40	19	in	in	ADP
ejpam-3545	40	20	essence	essence	NOUN
ejpam-3545	40	21	,	,	PUNCT
ejpam-3545	40	22	an	an	DET
ejpam-3545	40	23	abstract	abstract	ADJ
ejpam-3545	40	24	prearithmetic	prearithmetic	NOUN
ejpam-3545	40	25	is	be	AUX
ejpam-3545	40	26	a	a	DET
ejpam-3545	40	27	universal	universal	ADJ
ejpam-3545	40	28	algebra	algebra	NOUN
ejpam-3545	40	29	(	(	PUNCT
ejpam-3545	40	30	algebraic	algebraic	ADJ
ejpam-3545	40	31	system	system	NOUN
ejpam-3545	40	32	)	)	PUNCT
ejpam-3545	40	33	with	with	ADP
ejpam-3545	40	34	two	two	NUM
ejpam-3545	40	35	binary	binary	ADJ
ejpam-3545	40	36	operations	operation	NOUN
ejpam-3545	40	37	and	and	CCONJ
ejpam-3545	40	38	a	a	DET
ejpam-3545	40	39	partial	partial	ADJ
ejpam-3545	40	40	order	order	NOUN
ejpam-3545	40	41	.	.	PUNCT
ejpam-3545	41	1	operations	operation	NOUN
ejpam-3545	41	2	are	be	AUX
ejpam-3545	41	3	called	call	VERB
ejpam-3545	41	4	addition	addition	NOUN
ejpam-3545	41	5	and	and	CCONJ
ejpam-3545	41	6	multiplication	multiplication	NOUN
ejpam-3545	41	7	but	but	CCONJ
ejpam-3545	41	8	in	in	ADP
ejpam-3545	41	9	a	a	DET
ejpam-3545	41	10	general	general	ADJ
ejpam-3545	41	11	case	case	NOUN
ejpam-3545	41	12	,	,	PUNCT
ejpam-3545	41	13	there	there	PRON
ejpam-3545	41	14	are	be	VERB
ejpam-3545	41	15	no	no	DET
ejpam-3545	41	16	restrictions	restriction	NOUN
ejpam-3545	41	17	on	on	ADP
ejpam-3545	41	18	these	these	DET
ejpam-3545	41	19	operations	operation	NOUN
ejpam-3545	41	20	.	.	PUNCT
ejpam-3545	42	1	some	some	PRON
ejpam-3545	42	2	of	of	ADP
ejpam-3545	42	3	abstract	abstract	ADJ
ejpam-3545	42	4	prearithmetics	prearithmetic	NOUN
ejpam-3545	42	5	are	be	AUX
ejpam-3545	42	6	numerical	numerical	ADJ
ejpam-3545	42	7	,	,	PUNCT
ejpam-3545	42	8	that	that	ADV
ejpam-3545	42	9	is	is	ADV
ejpam-3545	42	10	,	,	PUNCT
ejpam-3545	42	11	their	their	PRON
ejpam-3545	42	12	elements	element	NOUN
ejpam-3545	42	13	are	be	AUX
ejpam-3545	42	14	numbers	number	NOUN
ejpam-3545	42	15	,	,	PUNCT
ejpam-3545	42	16	e.g.	e.g.	ADV
ejpam-3545	42	17	,	,	PUNCT
ejpam-3545	42	18	natural	natural	ADJ
ejpam-3545	42	19	numbers	number	NOUN
ejpam-3545	42	20	or	or	CCONJ
ejpam-3545	42	21	real	real	ADJ
ejpam-3545	42	22	numbers	number	NOUN
ejpam-3545	42	23	.	.	PUNCT
ejpam-3545	43	1	a	a	DET
ejpam-3545	43	2	numerical	numerical	ADJ
ejpam-3545	43	3	prearithmetic	prearithmetic	NOUN
ejpam-3545	43	4	that	that	PRON
ejpam-3545	43	5	satisfies	satisfy	VERB
ejpam-3545	43	6	additional	additional	ADJ
ejpam-3545	43	7	conditions	condition	NOUN
ejpam-3545	43	8	,	,	PUNCT
ejpam-3545	43	9	in	in	ADP
ejpam-3545	43	10	particular	particular	ADJ
ejpam-3545	43	11	,	,	PUNCT
ejpam-3545	43	12	containing	contain	VERB
ejpam-3545	43	13	all	all	DET
ejpam-3545	43	14	natural	natural	ADJ
ejpam-3545	43	15	numbers	number	NOUN
ejpam-3545	43	16	and	and	CCONJ
ejpam-3545	43	17	no	no	DET
ejpam-3545	43	18	other	other	ADJ
ejpam-3545	43	19	elements	element	NOUN
ejpam-3545	43	20	is	be	AUX
ejpam-3545	43	21	called	call	VERB
ejpam-3545	43	22	an	an	DET
ejpam-3545	43	23	arithmetic	arithmetic	NOUN
ejpam-3545	43	24	of	of	ADP
ejpam-3545	43	25	natural	natural	ADJ
ejpam-3545	43	26	numbers	number	NOUN
ejpam-3545	43	27	.	.	PUNCT
ejpam-3545	44	1	a	a	DET
ejpam-3545	44	2	numerical	numerical	ADJ
ejpam-3545	44	3	prearithmetic	prearithmetic	NOUN
ejpam-3545	44	4	that	that	PRON
ejpam-3545	44	5	satisfies	satisfy	VERB
ejpam-3545	44	6	additional	additional	ADJ
ejpam-3545	44	7	conditions	condition	NOUN
ejpam-3545	44	8	,	,	PUNCT
ejpam-3545	44	9	in	in	ADP
ejpam-3545	44	10	particular	particular	ADJ
ejpam-3545	44	11	,	,	PUNCT
ejpam-3545	44	12	contains	contain	VERB
ejpam-3545	44	13	all	all	DET
ejpam-3545	44	14	integer	integer	NOUN
ejpam-3545	44	15	numbers	number	NOUN
ejpam-3545	44	16	and	and	CCONJ
ejpam-3545	44	17	no	no	DET
ejpam-3545	44	18	other	other	ADJ
ejpam-3545	44	19	elements	element	NOUN
ejpam-3545	44	20	is	be	AUX
ejpam-3545	44	21	called	call	VERB
ejpam-3545	44	22	an	an	DET
ejpam-3545	44	23	arithmetic	arithmetic	NOUN
ejpam-3545	44	24	of	of	ADP
ejpam-3545	44	25	integer	integer	NOUN
ejpam-3545	44	26	numbers	number	NOUN
ejpam-3545	44	27	.	.	PUNCT
ejpam-3545	45	1	everybody	everybody	PRON
ejpam-3545	45	2	knows	know	VERB
ejpam-3545	45	3	the	the	DET
ejpam-3545	45	4	conventional	conventional	ADJ
ejpam-3545	45	5	diophantine	diophantine	NOUN
ejpam-3545	45	6	arithmetic	arithmetic	ADJ
ejpam-3545	45	7	n	n	CCONJ
ejpam-3545	45	8	of	of	ADP
ejpam-3545	45	9	natural	natural	ADJ
ejpam-3545	45	10	numbers	number	NOUN
ejpam-3545	45	11	.	.	PUNCT
ejpam-3545	46	1	however	however	ADV
ejpam-3545	46	2	,	,	PUNCT
ejpam-3545	46	3	there	there	PRON
ejpam-3545	46	4	are	be	VERB
ejpam-3545	46	5	also	also	ADV
ejpam-3545	46	6	many	many	ADJ
ejpam-3545	46	7	non	non	ADJ
ejpam-3545	46	8	-	-	ADJ
ejpam-3545	46	9	diophantine	diophantine	ADJ
ejpam-3545	46	10	arithmetics	arithmetic	NOUN
ejpam-3545	46	11	of	of	ADP
ejpam-3545	46	12	natural	natural	ADJ
ejpam-3545	46	13	numbers	number	NOUN
ejpam-3545	46	14	introduced	introduce	VERB
ejpam-3545	46	15	and	and	CCONJ
ejpam-3545	46	16	studied	study	VERB
ejpam-3545	46	17	in	in	ADP
ejpam-3545	46	18	[	[	X
ejpam-3545	46	19	5–7	5–7	NOUN
ejpam-3545	46	20	,	,	PUNCT
ejpam-3545	46	21	10	10	NUM
ejpam-3545	46	22	,	,	PUNCT
ejpam-3545	46	23	11	11	NUM
ejpam-3545	46	24	]	]	PUNCT
ejpam-3545	46	25	.	.	PUNCT
ejpam-3545	47	1	an	an	DET
ejpam-3545	47	2	important	important	ADJ
ejpam-3545	47	3	relation	relation	NOUN
ejpam-3545	47	4	between	between	ADP
ejpam-3545	47	5	prearithmetics	prearithmetic	NOUN
ejpam-3545	47	6	or	or	CCONJ
ejpam-3545	47	7	arithmetics	arithmetic	NOUN
ejpam-3545	47	8	is	be	AUX
ejpam-3545	47	9	projectivity	projectivity	NOUN
ejpam-3545	47	10	as	as	SCONJ
ejpam-3545	47	11	it	it	PRON
ejpam-3545	47	12	is	be	AUX
ejpam-3545	47	13	demonstrated	demonstrate	VERB
ejpam-3545	47	14	in	in	ADP
ejpam-3545	47	15	[	[	X
ejpam-3545	47	16	5	5	NUM
ejpam-3545	47	17	,	,	PUNCT
ejpam-3545	47	18	7	7	NUM
ejpam-3545	47	19	,	,	PUNCT
ejpam-3545	47	20	11	11	NUM
ejpam-3545	47	21	]	]	PUNCT
ejpam-3545	47	22	.	.	PUNCT
ejpam-3545	48	1	it	it	PRON
ejpam-3545	48	2	has	have	VERB
ejpam-3545	48	3	three	three	NUM
ejpam-3545	48	4	types	type	NOUN
ejpam-3545	48	5	:	:	PUNCT
ejpam-3545	48	6	weak	weak	ADJ
ejpam-3545	48	7	projectivity	projectivity	NOUN
ejpam-3545	48	8	,	,	PUNCT
ejpam-3545	48	9	projectivity	projectivity	NOUN
ejpam-3545	48	10	per	per	ADP
ejpam-3545	48	11	se	se	X
ejpam-3545	48	12	and	and	CCONJ
ejpam-3545	48	13	exact	exact	ADJ
ejpam-3545	48	14	projectivity	projectivity	NOUN
ejpam-3545	48	15	.	.	PUNCT
ejpam-3545	49	1	these	these	DET
ejpam-3545	49	2	relations	relation	NOUN
ejpam-3545	49	3	allow	allow	VERB
ejpam-3545	49	4	deducing	deduce	VERB
ejpam-3545	49	5	properties	property	NOUN
ejpam-3545	49	6	of	of	ADP
ejpam-3545	49	7	one	one	NUM
ejpam-3545	49	8	arithmetic	arithmetic	ADJ
ejpam-3545	49	9	or	or	CCONJ
ejpam-3545	49	10	prearithmetic	prearithmetic	ADJ
ejpam-3545	49	11	from	from	ADP
ejpam-3545	49	12	properties	property	NOUN
ejpam-3545	49	13	of	of	ADP
ejpam-3545	49	14	another	another	DET
ejpam-3545	49	15	arithmetic	arithmetic	ADJ
ejpam-3545	49	16	or	or	CCONJ
ejpam-3545	49	17	prearithmetic	prearithmetic	ADJ
ejpam-3545	49	18	.	.	PUNCT
ejpam-3545	50	1	besides	besides	SCONJ
ejpam-3545	50	2	,	,	PUNCT
ejpam-3545	50	3	they	they	PRON
ejpam-3545	50	4	are	be	AUX
ejpam-3545	50	5	used	use	VERB
ejpam-3545	50	6	for	for	ADP
ejpam-3545	50	7	building	build	VERB
ejpam-3545	50	8	new	new	ADJ
ejpam-3545	50	9	prearithmetics	prearithmetic	NOUN
ejpam-3545	50	10	and	and	CCONJ
ejpam-3545	50	11	arithmetics	arithmetic	NOUN
ejpam-3545	50	12	.	.	PUNCT
ejpam-3545	51	1	projectivity	projectivity	NOUN
ejpam-3545	51	2	between	between	ADP
ejpam-3545	51	3	two	two	NUM
ejpam-3545	51	4	prearithmetics	prearithmetic	NOUN
ejpam-3545	51	5	(	(	PUNCT
ejpam-3545	51	6	arithmetics	arithmetic	NOUN
ejpam-3545	51	7	)	)	PUNCT
ejpam-3545	51	8	means	mean	VERB
ejpam-3545	51	9	that	that	SCONJ
ejpam-3545	51	10	both	both	DET
ejpam-3545	51	11	operations	operation	NOUN
ejpam-3545	51	12	–	–	PUNCT
ejpam-3545	51	13	addition	addition	NOUN
ejpam-3545	51	14	and	and	CCONJ
ejpam-3545	51	15	multiplication	multiplication	NOUN
ejpam-3545	51	16	of	of	ADP
ejpam-3545	51	17	one	one	NUM
ejpam-3545	51	18	them	they	PRON
ejpam-3545	51	19	are	be	AUX
ejpam-3545	51	20	expressed	express	VERB
ejpam-3545	51	21	using	use	VERB
ejpam-3545	51	22	the	the	DET
ejpam-3545	51	23	corresponding	corresponding	ADJ
ejpam-3545	51	24	operation	operation	NOUN
ejpam-3545	51	25	in	in	ADP
ejpam-3545	51	26	the	the	DET
ejpam-3545	51	27	second	second	ADJ
ejpam-3545	51	28	one	one	NUM
ejpam-3545	51	29	by	by	ADP
ejpam-3545	51	30	means	mean	NOUN
ejpam-3545	51	31	of	of	ADP
ejpam-3545	51	32	the	the	DET
ejpam-3545	51	33	same	same	ADJ
ejpam-3545	51	34	function	function	NOUN
ejpam-3545	51	35	(	(	PUNCT
ejpam-3545	51	36	parameter	parameter	NOUN
ejpam-3545	51	37	of	of	ADP
ejpam-3545	51	38	the	the	DET
ejpam-3545	51	39	projectivity	projectivity	NOUN
ejpam-3545	51	40	)	)	PUNCT
ejpam-3545	51	41	.	.	PUNCT
ejpam-3545	52	1	the	the	DET
ejpam-3545	52	2	goal	goal	NOUN
ejpam-3545	52	3	of	of	ADP
ejpam-3545	52	4	this	this	DET
ejpam-3545	52	5	paper	paper	NOUN
ejpam-3545	52	6	is	be	AUX
ejpam-3545	52	7	the	the	DET
ejpam-3545	52	8	further	further	ADJ
ejpam-3545	52	9	development	development	NOUN
ejpam-3545	52	10	of	of	ADP
ejpam-3545	52	11	the	the	DET
ejpam-3545	52	12	theory	theory	NOUN
ejpam-3545	52	13	of	of	ADP
ejpam-3545	52	14	abstract	abstract	ADJ
ejpam-3545	52	15	prearithmetics	prearithmetic	NOUN
ejpam-3545	52	16	by	by	ADP
ejpam-3545	52	17	considering	consider	VERB
ejpam-3545	52	18	different	different	ADJ
ejpam-3545	52	19	forms	form	NOUN
ejpam-3545	52	20	of	of	ADP
ejpam-3545	52	21	weak	weak	ADJ
ejpam-3545	52	22	projectivity	projectivity	NOUN
ejpam-3545	52	23	,	,	PUNCT
ejpam-3545	52	24	in	in	ADP
ejpam-3545	52	25	which	which	PRON
ejpam-3545	52	26	projectivity	projectivity	NOUN
ejpam-3545	52	27	connects	connect	VERB
ejpam-3545	52	28	separate	separate	ADJ
ejpam-3545	52	29	operations	operation	NOUN
ejpam-3545	52	30	,	,	PUNCT
ejpam-3545	52	31	e.g.	e.g.	ADV
ejpam-3545	52	32	,	,	PUNCT
ejpam-3545	52	33	addition	addition	NOUN
ejpam-3545	52	34	or	or	CCONJ
ejpam-3545	52	35	multiplication	multiplication	NOUN
ejpam-3545	52	36	.	.	PUNCT
ejpam-3545	53	1	that	that	PRON
ejpam-3545	53	2	is	be	AUX
ejpam-3545	53	3	why	why	SCONJ
ejpam-3545	53	4	it	it	PRON
ejpam-3545	53	5	is	be	AUX
ejpam-3545	53	6	called	call	VERB
ejpam-3545	53	7	partial	partial	ADJ
ejpam-3545	53	8	weak	weak	ADJ
ejpam-3545	53	9	projectivity	projectivity	NOUN
ejpam-3545	53	10	.	.	PUNCT
ejpam-3545	54	1	it	it	PRON
ejpam-3545	54	2	allows	allow	VERB
ejpam-3545	54	3	building	build	VERB
ejpam-3545	54	4	new	new	ADJ
ejpam-3545	54	5	prearithmetics	prearithmetic	NOUN
ejpam-3545	54	6	or	or	CCONJ
ejpam-3545	54	7	arithmetics	arithmetic	NOUN
ejpam-3545	54	8	from	from	ADP
ejpam-3545	54	9	the	the	DET
ejpam-3545	54	10	existing	exist	VERB
ejpam-3545	54	11	ones	one	NOUN
ejpam-3545	54	12	by	by	ADP
ejpam-3545	54	13	changing	change	VERB
ejpam-3545	54	14	only	only	ADV
ejpam-3545	54	15	one	one	NUM
ejpam-3545	54	16	operation	operation	NOUN
ejpam-3545	54	17	or	or	CCONJ
ejpam-3545	54	18	in	in	ADP
ejpam-3545	54	19	a	a	DET
ejpam-3545	54	20	different	different	ADJ
ejpam-3545	54	21	way	way	NOUN
ejpam-3545	54	22	changing	change	VERB
ejpam-3545	54	23	both	both	DET
ejpam-3545	54	24	operations	operation	NOUN
ejpam-3545	54	25	–	–	PUNCT
ejpam-3545	54	26	addition	addition	NOUN
ejpam-3545	54	27	and	and	CCONJ
ejpam-3545	54	28	multiplication	multiplication	NOUN
ejpam-3545	54	29	–	–	PUNCT
ejpam-3545	54	30	using	use	VERB
ejpam-3545	54	31	specific	specific	ADJ
ejpam-3545	54	32	parameters	parameter	NOUN
ejpam-3545	54	33	for	for	ADP
ejpam-3545	54	34	each	each	PRON
ejpam-3545	54	35	of	of	ADP
ejpam-3545	54	36	them	they	PRON
ejpam-3545	54	37	.	.	PUNCT
ejpam-3545	55	1	in	in	ADP
ejpam-3545	55	2	turn	turn	NOUN
ejpam-3545	55	3	,	,	PUNCT
ejpam-3545	55	4	we	we	PRON
ejpam-3545	55	5	also	also	ADV
ejpam-3545	55	6	obtain	obtain	VERB
ejpam-3545	55	7	more	more	ADV
ejpam-3545	55	8	flexible	flexible	ADJ
ejpam-3545	55	9	tools	tool	NOUN
ejpam-3545	55	10	for	for	ADP
ejpam-3545	55	11	finding	find	VERB
ejpam-3545	55	12	relations	relation	NOUN
ejpam-3545	55	13	between	between	ADP
ejpam-3545	55	14	properties	property	NOUN
ejpam-3545	55	15	of	of	ADP
ejpam-3545	55	16	prearithmetics	prearithmetic	NOUN
ejpam-3545	55	17	or	or	CCONJ
ejpam-3545	55	18	arithmetics	arithmetic	NOUN
ejpam-3545	55	19	connected	connect	VERB
ejpam-3545	55	20	by	by	ADP
ejpam-3545	55	21	partial	partial	ADJ
ejpam-3545	55	22	weak	weak	ADJ
ejpam-3545	55	23	projectivity	projectivity	NOUN
ejpam-3545	55	24	relations	relation	NOUN
ejpam-3545	55	25	.	.	PUNCT
ejpam-3545	56	1	the	the	DET
ejpam-3545	56	2	author	author	NOUN
ejpam-3545	56	3	would	would	AUX
ejpam-3545	56	4	like	like	VERB
ejpam-3545	56	5	to	to	PART
ejpam-3545	56	6	express	express	VERB
ejpam-3545	56	7	gratitude	gratitude	NOUN
ejpam-3545	56	8	to	to	ADP
ejpam-3545	56	9	the	the	DET
ejpam-3545	56	10	reviewers	reviewer	NOUN
ejpam-3545	56	11	for	for	ADP
ejpam-3545	56	12	their	their	PRON
ejpam-3545	56	13	useful	useful	ADJ
ejpam-3545	56	14	remarks	remark	NOUN
ejpam-3545	56	15	.	.	PUNCT
ejpam-3545	57	1	2	2	X
ejpam-3545	57	2	.	.	X
ejpam-3545	57	3	abstract	abstract	ADJ
ejpam-3545	57	4	prearithmetics	prearithmetic	NOUN
ejpam-3545	57	5	an	an	DET
ejpam-3545	57	6	abstract	abstract	ADJ
ejpam-3545	57	7	prearithmetic	prearithmetic	NOUN
ejpam-3545	57	8	is	be	AUX
ejpam-3545	57	9	a	a	DET
ejpam-3545	57	10	set	set	NOUN
ejpam-3545	57	11	(	(	PUNCT
ejpam-3545	57	12	often	often	ADV
ejpam-3545	57	13	a	a	DET
ejpam-3545	57	14	set	set	NOUN
ejpam-3545	57	15	of	of	ADP
ejpam-3545	57	16	numbers	number	NOUN
ejpam-3545	57	17	)	)	PUNCT
ejpam-3545	57	18	a	a	PRON
ejpam-3545	57	19	with	with	ADP
ejpam-3545	57	20	a	a	DET
ejpam-3545	57	21	partial	partial	ADJ
ejpam-3545	57	22	order	order	NOUN
ejpam-3545	57	23	≤	≤	NOUN
ejpam-3545	57	24	and	and	CCONJ
ejpam-3545	57	25	two	two	NUM
ejpam-3545	57	26	binary	binary	ADJ
ejpam-3545	57	27	operations	operation	NOUN
ejpam-3545	57	28	+	+	CCONJ
ejpam-3545	57	29	(	(	PUNCT
ejpam-3545	57	30	addition	addition	NOUN
ejpam-3545	57	31	)	)	PUNCT
ejpam-3545	57	32	and	and	CCONJ
ejpam-3545	57	33	◦	◦	NOUN
ejpam-3545	57	34	(	(	PUNCT
ejpam-3545	57	35	multiplication	multiplication	NOUN
ejpam-3545	57	36	)	)	PUNCT
ejpam-3545	57	37	,	,	PUNCT
ejpam-3545	57	38	which	which	PRON
ejpam-3545	57	39	are	be	AUX
ejpam-3545	57	40	defined	define	VERB
ejpam-3545	57	41	for	for	ADP
ejpam-3545	57	42	all	all	DET
ejpam-3545	57	43	its	its	PRON
ejpam-3545	57	44	elements	element	NOUN
ejpam-3545	57	45	.	.	PUNCT
ejpam-3545	58	1	it	it	PRON
ejpam-3545	58	2	is	be	AUX
ejpam-3545	58	3	denoted	denote	VERB
ejpam-3545	58	4	by	by	ADP
ejpam-3545	58	5	a	a	DET
ejpam-3545	58	6	=	=	X
ejpam-3545	58	7	(	(	PUNCT
ejpam-3545	58	8	a	a	X
ejpam-3545	58	9	;	;	PUNCT
ejpam-3545	58	10	+	+	ADJ
ejpam-3545	58	11	,	,	PUNCT
ejpam-3545	58	12	◦	◦	NOUN
ejpam-3545	58	13	,	,	PUNCT
ejpam-3545	58	14	≤	≤	NUM
ejpam-3545	58	15	)	)	PUNCT
ejpam-3545	58	16	.	.	PUNCT
ejpam-3545	59	1	the	the	DET
ejpam-3545	59	2	set	set	NOUN
ejpam-3545	59	3	a	a	PRON
ejpam-3545	59	4	is	be	AUX
ejpam-3545	59	5	called	call	VERB
ejpam-3545	59	6	the	the	DET
ejpam-3545	59	7	set	set	NOUN
ejpam-3545	59	8	of	of	ADP
ejpam-3545	59	9	elements	element	NOUN
ejpam-3545	59	10	or	or	CCONJ
ejpam-3545	59	11	set	set	NOUN
ejpam-3545	59	12	of	of	ADP
ejpam-3545	59	13	numbers	number	NOUN
ejpam-3545	59	14	or	or	CCONJ
ejpam-3545	59	15	the	the	DET
ejpam-3545	59	16	carrier	carrier	NOUN
ejpam-3545	59	17	of	of	ADP
ejpam-3545	59	18	the	the	DET
ejpam-3545	59	19	prearithmetic	prearithmetic	ADJ
ejpam-3545	59	20	a.	a.	NOUN
ejpam-3545	59	21	as	as	ADP
ejpam-3545	59	22	always	always	ADV
ejpam-3545	59	23	,	,	PUNCT
ejpam-3545	59	24	if	if	SCONJ
ejpam-3545	59	25	x	x	ADP
ejpam-3545	59	26	≤	≤	ADJ
ejpam-3545	59	27	y	y	PROPN
ejpam-3545	59	28	and	and	CCONJ
ejpam-3545	59	29	x	x	SYM
ejpam-3545	59	30	6=	6=	PROPN
ejpam-3545	59	31	y	y	PROPN
ejpam-3545	59	32	,	,	PUNCT
ejpam-3545	59	33	then	then	ADV
ejpam-3545	59	34	we	we	PRON
ejpam-3545	59	35	denote	denote	VERB
ejpam-3545	59	36	this	this	DET
ejpam-3545	59	37	relation	relation	NOUN
ejpam-3545	59	38	by	by	ADP
ejpam-3545	59	39	x	x	PUNCT
ejpam-3545	59	40	<	<	X
ejpam-3545	59	41	y.	y.	PROPN
ejpam-3545	59	42	operation	operation	NOUN
ejpam-3545	59	43	+	+	CCONJ
ejpam-3545	59	44	is	be	AUX
ejpam-3545	59	45	called	call	VERB
ejpam-3545	59	46	addition	addition	NOUN
ejpam-3545	59	47	and	and	CCONJ
ejpam-3545	59	48	operation	operation	NOUN
ejpam-3545	59	49	◦	◦	NOUN
ejpam-3545	59	50	is	be	AUX
ejpam-3545	59	51	called	call	VERB
ejpam-3545	59	52	multiplication	multiplication	NOUN
ejpam-3545	59	53	in	in	ADP
ejpam-3545	59	54	the	the	DET
ejpam-3545	59	55	abstract	abstract	ADJ
ejpam-3545	59	56	prearithmetic	prearithmetic	ADJ
ejpam-3545	59	57	a.	a.	NOUN
ejpam-3545	59	58	note	note	NOUN
ejpam-3545	59	59	that	that	SCONJ
ejpam-3545	59	60	an	an	DET
ejpam-3545	59	61	abstract	abstract	ADJ
ejpam-3545	59	62	prearithmetic	prearithmetic	NOUN
ejpam-3545	59	63	can	can	AUX
ejpam-3545	59	64	have	have	VERB
ejpam-3545	59	65	more	more	ADJ
ejpam-3545	59	66	than	than	ADP
ejpam-3545	59	67	two	two	NUM
ejpam-3545	59	68	operations	operation	NOUN
ejpam-3545	59	69	and	and	CCONJ
ejpam-3545	59	70	more	more	ADJ
ejpam-3545	59	71	than	than	ADP
ejpam-3545	59	72	one	one	NUM
ejpam-3545	59	73	order	order	NOUN
ejpam-3545	59	74	relation	relation	NOUN
ejpam-3545	59	75	.	.	PUNCT
ejpam-3545	60	1	m.	m.	NOUN
ejpam-3545	60	2	burgin	burgin	PROPN
ejpam-3545	60	3	/	/	SYM
ejpam-3545	60	4	eur	eur	PROPN
ejpam-3545	60	5	.	.	PUNCT
ejpam-3545	61	1	j.	j.	PROPN
ejpam-3545	61	2	pure	pure	PROPN
ejpam-3545	61	3	appl	appl	PROPN
ejpam-3545	61	4	.	.	PROPN
ejpam-3545	61	5	math	math	PROPN
ejpam-3545	61	6	,	,	PUNCT
ejpam-3545	61	7	12	12	NUM
ejpam-3545	61	8	(	(	PUNCT
ejpam-3545	61	9	4	4	NUM
ejpam-3545	61	10	)	)	PUNCT
ejpam-3545	61	11	(	(	PUNCT
ejpam-3545	61	12	2019	2019	NUM
ejpam-3545	61	13	)	)	PUNCT
ejpam-3545	61	14	,	,	PUNCT
ejpam-3545	61	15	1787	1787	NUM
ejpam-3545	61	16	-	-	SYM
ejpam-3545	61	17	1810	1810	NUM
ejpam-3545	61	18	1790	1790	NUM
ejpam-3545	61	19	example	example	NOUN
ejpam-3545	61	20	1	1	NUM
ejpam-3545	61	21	.	.	PUNCT
ejpam-3545	62	1	naturally	naturally	ADV
ejpam-3545	62	2	,	,	PUNCT
ejpam-3545	62	3	the	the	DET
ejpam-3545	62	4	conventional	conventional	ADJ
ejpam-3545	62	5	diophantine	diophantine	NOUN
ejpam-3545	62	6	arithmetic	arithmetic	ADJ
ejpam-3545	62	7	n	n	PROPN
ejpam-3545	62	8	of	of	ADP
ejpam-3545	62	9	all	all	DET
ejpam-3545	62	10	natural	natural	ADJ
ejpam-3545	62	11	numbers	number	NOUN
ejpam-3545	62	12	,	,	PUNCT
ejpam-3545	62	13	the	the	DET
ejpam-3545	62	14	conventional	conventional	ADJ
ejpam-3545	62	15	arithmetic	arithmetic	PROPN
ejpam-3545	62	16	w	w	PROPN
ejpam-3545	62	17	of	of	ADP
ejpam-3545	62	18	all	all	DET
ejpam-3545	62	19	whole	whole	ADJ
ejpam-3545	62	20	numbers	number	NOUN
ejpam-3545	62	21	,	,	PUNCT
ejpam-3545	62	22	the	the	DET
ejpam-3545	62	23	conventional	conventional	ADJ
ejpam-3545	62	24	arithmetic	arithmetic	ADJ
ejpam-3545	62	25	z	z	NOUN
ejpam-3545	62	26	of	of	ADP
ejpam-3545	62	27	all	all	DET
ejpam-3545	62	28	integer	integer	NOUN
ejpam-3545	62	29	numbers	number	NOUN
ejpam-3545	62	30	,	,	PUNCT
ejpam-3545	62	31	the	the	DET
ejpam-3545	62	32	conventional	conventional	ADJ
ejpam-3545	62	33	arithmetic	arithmetic	ADJ
ejpam-3545	62	34	q	q	NOUN
ejpam-3545	62	35	of	of	ADP
ejpam-3545	62	36	all	all	DET
ejpam-3545	62	37	rational	rational	ADJ
ejpam-3545	62	38	numbers	number	NOUN
ejpam-3545	62	39	,	,	PUNCT
ejpam-3545	62	40	the	the	DET
ejpam-3545	62	41	conventional	conventional	ADJ
ejpam-3545	62	42	arithmetic	arithmetic	ADJ
ejpam-3545	62	43	r	r	NOUN
ejpam-3545	62	44	of	of	ADP
ejpam-3545	62	45	all	all	DET
ejpam-3545	62	46	real	real	ADJ
ejpam-3545	62	47	numbers	number	NOUN
ejpam-3545	62	48	and	and	CCONJ
ejpam-3545	62	49	the	the	DET
ejpam-3545	62	50	conventional	conventional	ADJ
ejpam-3545	62	51	arithmetic	arithmetic	ADJ
ejpam-3545	62	52	c	c	PROPN
ejpam-3545	62	53	of	of	ADP
ejpam-3545	62	54	all	all	DET
ejpam-3545	62	55	complex	complex	ADJ
ejpam-3545	62	56	numbers	number	NOUN
ejpam-3545	62	57	are	be	AUX
ejpam-3545	62	58	abstract	abstract	ADJ
ejpam-3545	62	59	prearithmetics	prearithmetic	NOUN
ejpam-3545	62	60	.	.	PUNCT
ejpam-3545	62	61	example	example	NOUN
ejpam-3545	63	1	2	2	NUM
ejpam-3545	63	2	.	.	PUNCT
ejpam-3545	63	3	another	another	DET
ejpam-3545	63	4	example	example	NOUN
ejpam-3545	63	5	of	of	ADP
ejpam-3545	63	6	abstract	abstract	ADJ
ejpam-3545	63	7	prearithmetics	prearithmetic	NOUN
ejpam-3545	63	8	is	be	AUX
ejpam-3545	63	9	modular	modular	ADJ
ejpam-3545	63	10	arithmetic	arithmetic	ADJ
ejpam-3545	63	11	,	,	PUNCT
ejpam-3545	63	12	which	which	PRON
ejpam-3545	63	13	is	be	AUX
ejpam-3545	63	14	sometimes	sometimes	ADV
ejpam-3545	63	15	known	know	VERB
ejpam-3545	63	16	as	as	ADP
ejpam-3545	63	17	residue	residue	NOUN
ejpam-3545	63	18	arithmetic	arithmetic	ADJ
ejpam-3545	63	19	or	or	CCONJ
ejpam-3545	63	20	clock	clock	VERB
ejpam-3545	63	21	arithmetic	arithmetic	ADJ
ejpam-3545	63	22	[	[	X
ejpam-3545	63	23	48	48	NUM
ejpam-3545	63	24	]	]	PUNCT
ejpam-3545	63	25	.	.	PUNCT
ejpam-3545	64	1	it	it	PRON
ejpam-3545	64	2	is	be	AUX
ejpam-3545	64	3	studied	study	VERB
ejpam-3545	64	4	in	in	ADP
ejpam-3545	64	5	mathematics	mathematic	NOUN
ejpam-3545	64	6	and	and	CCONJ
ejpam-3545	64	7	used	use	VERB
ejpam-3545	64	8	in	in	ADP
ejpam-3545	64	9	physics	physics	NOUN
ejpam-3545	64	10	and	and	CCONJ
ejpam-3545	64	11	computing	computing	NOUN
ejpam-3545	64	12	.	.	PUNCT
ejpam-3545	65	1	in	in	ADP
ejpam-3545	65	2	modular	modular	ADJ
ejpam-3545	65	3	arithmetic	arithmetic	ADJ
ejpam-3545	65	4	,	,	PUNCT
ejpam-3545	65	5	operations	operation	NOUN
ejpam-3545	65	6	of	of	ADP
ejpam-3545	65	7	addition	addition	NOUN
ejpam-3545	65	8	and	and	CCONJ
ejpam-3545	65	9	multiplication	multiplication	NOUN
ejpam-3545	65	10	are	be	AUX
ejpam-3545	65	11	defined	define	VERB
ejpam-3545	65	12	but	but	CCONJ
ejpam-3545	65	13	in	in	ADP
ejpam-3545	65	14	contrast	contrast	NOUN
ejpam-3545	65	15	to	to	ADP
ejpam-3545	65	16	the	the	DET
ejpam-3545	65	17	conventional	conventional	ADJ
ejpam-3545	65	18	arithmetic	arithmetic	NOUN
ejpam-3545	65	19	,	,	PUNCT
ejpam-3545	65	20	its	its	PRON
ejpam-3545	65	21	numbers	number	NOUN
ejpam-3545	65	22	form	form	VERB
ejpam-3545	65	23	a	a	DET
ejpam-3545	65	24	cycle	cycle	NOUN
ejpam-3545	65	25	upon	upon	SCONJ
ejpam-3545	65	26	reaching	reach	VERB
ejpam-3545	65	27	a	a	DET
ejpam-3545	65	28	certain	certain	ADJ
ejpam-3545	65	29	value	value	NOUN
ejpam-3545	65	30	,	,	PUNCT
ejpam-3545	65	31	which	which	PRON
ejpam-3545	65	32	called	call	VERB
ejpam-3545	65	33	the	the	DET
ejpam-3545	65	34	modulus	modulus	NOUN
ejpam-3545	65	35	.	.	PUNCT
ejpam-3545	66	1	a	a	DET
ejpam-3545	66	2	rigorous	rigorous	ADJ
ejpam-3545	66	3	approach	approach	NOUN
ejpam-3545	66	4	to	to	ADP
ejpam-3545	66	5	the	the	DET
ejpam-3545	66	6	theory	theory	NOUN
ejpam-3545	66	7	of	of	ADP
ejpam-3545	66	8	modular	modular	ADJ
ejpam-3545	66	9	arithmetic	arithmetic	NOUN
ejpam-3545	66	10	was	be	AUX
ejpam-3545	66	11	worked	work	VERB
ejpam-3545	66	12	out	out	ADP
ejpam-3545	66	13	by	by	ADP
ejpam-3545	66	14	carl	carl	PROPN
ejpam-3545	66	15	friedrich	friedrich	PROPN
ejpam-3545	66	16	gauss	gauss	PROPN
ejpam-3545	66	17	.	.	PROPN
ejpam-3545	66	18	example	example	NOUN
ejpam-3545	67	1	3	3	X
ejpam-3545	67	2	.	.	X
ejpam-3545	67	3	many	many	ADJ
ejpam-3545	67	4	algebraic	algebraic	ADJ
ejpam-3545	67	5	structures	structure	NOUN
ejpam-3545	67	6	studied	study	VERB
ejpam-3545	67	7	in	in	ADP
ejpam-3545	67	8	algebra	algebra	NOUN
ejpam-3545	67	9	are	be	AUX
ejpam-3545	67	10	abstract	abstract	ADJ
ejpam-3545	67	11	prearithmetics	prearithmetic	NOUN
ejpam-3545	67	12	with	with	ADP
ejpam-3545	67	13	a	a	DET
ejpam-3545	67	14	trivial	trivial	ADJ
ejpam-3545	67	15	order	order	NOUN
ejpam-3545	67	16	,	,	PUNCT
ejpam-3545	67	17	i.e.	i.e.	X
ejpam-3545	67	18	,	,	PUNCT
ejpam-3545	67	19	any	any	DET
ejpam-3545	67	20	ring	ring	NOUN
ejpam-3545	67	21	,	,	PUNCT
ejpam-3545	67	22	lattice	lattice	NOUN
ejpam-3545	67	23	,	,	PUNCT
ejpam-3545	67	24	boolean	boolean	ADJ
ejpam-3545	67	25	algebra	algebra	NOUN
ejpam-3545	67	26	,	,	PUNCT
ejpam-3545	67	27	linear	linear	ADJ
ejpam-3545	67	28	algebra	algebra	NOUN
ejpam-3545	67	29	,	,	PUNCT
ejpam-3545	67	30	field	field	NOUN
ejpam-3545	67	31	,	,	PUNCT
ejpam-3545	67	32	ω	ω	NOUN
ejpam-3545	67	33	-	-	NOUN
ejpam-3545	67	34	group	group	NOUN
ejpam-3545	67	35	,	,	PUNCT
ejpam-3545	67	36	ωring	ωring	NOUN
ejpam-3545	67	37	,	,	PUNCT
ejpam-3545	67	38	ω	ω	NOUN
ejpam-3545	67	39	-	-	NOUN
ejpam-3545	67	40	algebra	algebra	NOUN
ejpam-3545	67	41	[	[	X
ejpam-3545	67	42	1	1	NUM
ejpam-3545	67	43	,	,	PUNCT
ejpam-3545	67	44	48	48	NUM
ejpam-3545	67	45	]	]	PUNCT
ejpam-3545	67	46	,	,	PUNCT
ejpam-3545	67	47	topological	topological	ADJ
ejpam-3545	67	48	ring	ring	NOUN
ejpam-3545	67	49	,	,	PUNCT
ejpam-3545	67	50	topological	topological	ADJ
ejpam-3545	67	51	field	field	NOUN
ejpam-3545	67	52	,	,	PUNCT
ejpam-3545	67	53	normed	normed	PROPN
ejpam-3545	67	54	ring	ring	PROPN
ejpam-3545	67	55	,	,	PUNCT
ejpam-3545	67	56	normed	normed	PROPN
ejpam-3545	67	57	algebra	algebra	PROPN
ejpam-3545	67	58	,	,	PUNCT
ejpam-3545	67	59	normed	normed	ADJ
ejpam-3545	67	60	field	field	NOUN
ejpam-3545	67	61	,	,	PUNCT
ejpam-3545	67	62	and	and	CCONJ
ejpam-3545	67	63	in	in	ADP
ejpam-3545	67	64	essence	essence	NOUN
ejpam-3545	67	65	,	,	PUNCT
ejpam-3545	67	66	any	any	DET
ejpam-3545	67	67	universal	universal	ADJ
ejpam-3545	67	68	algebra	algebra	NOUN
ejpam-3545	67	69	with	with	ADP
ejpam-3545	67	70	two	two	NUM
ejpam-3545	67	71	operations	operation	NOUN
ejpam-3545	67	72	is	be	AUX
ejpam-3545	67	73	an	an	DET
ejpam-3545	67	74	abstract	abstract	ADJ
ejpam-3545	67	75	prearithmetic	prearithmetic	NOUN
ejpam-3545	67	76	with	with	ADP
ejpam-3545	67	77	a	a	DET
ejpam-3545	67	78	trivial	trivial	ADJ
ejpam-3545	67	79	order	order	NOUN
ejpam-3545	67	80	.	.	PUNCT
ejpam-3545	68	1	the	the	DET
ejpam-3545	68	2	same	same	ADJ
ejpam-3545	68	3	structures	structure	NOUN
ejpam-3545	68	4	with	with	ADP
ejpam-3545	68	5	nontrivial	nontrivial	ADJ
ejpam-3545	68	6	order	order	NOUN
ejpam-3545	68	7	are	be	AUX
ejpam-3545	68	8	also	also	ADV
ejpam-3545	68	9	abstract	abstract	ADJ
ejpam-3545	68	10	prearithmetics	prearithmetic	NOUN
ejpam-3545	68	11	.	.	PUNCT
ejpam-3545	69	1	examples	example	NOUN
ejpam-3545	69	2	are	be	AUX
ejpam-3545	69	3	given	give	VERB
ejpam-3545	69	4	by	by	ADP
ejpam-3545	69	5	ordered	order	VERB
ejpam-3545	69	6	rings	ring	NOUN
ejpam-3545	69	7	,	,	PUNCT
ejpam-3545	69	8	ordered	order	VERB
ejpam-3545	69	9	linear	linear	PROPN
ejpam-3545	69	10	algebras	algebra	NOUN
ejpam-3545	69	11	and	and	CCONJ
ejpam-3545	69	12	ordered	order	VERB
ejpam-3545	69	13	fields	field	NOUN
ejpam-3545	69	14	.	.	PUNCT
ejpam-3545	70	1	besides	besides	SCONJ
ejpam-3545	70	2	,	,	PUNCT
ejpam-3545	70	3	it	it	PRON
ejpam-3545	70	4	is	be	AUX
ejpam-3545	70	5	possible	possible	ADJ
ejpam-3545	70	6	to	to	PART
ejpam-3545	70	7	treat	treat	VERB
ejpam-3545	70	8	universal	universal	ADJ
ejpam-3545	70	9	algebras	algebra	NOUN
ejpam-3545	70	10	with	with	ADP
ejpam-3545	70	11	one	one	NUM
ejpam-3545	70	12	operation	operation	NOUN
ejpam-3545	70	13	as	as	ADP
ejpam-3545	70	14	abstract	abstract	ADJ
ejpam-3545	70	15	prearithmetics	prearithmetic	NOUN
ejpam-3545	70	16	with	with	ADP
ejpam-3545	70	17	a	a	DET
ejpam-3545	70	18	trivial	trivial	ADJ
ejpam-3545	70	19	order	order	NOUN
ejpam-3545	70	20	and	and	CCONJ
ejpam-3545	70	21	trivial	trivial	ADJ
ejpam-3545	70	22	multiplication	multiplication	NOUN
ejpam-3545	70	23	.	.	PUNCT
ejpam-3545	71	1	all	all	DET
ejpam-3545	71	2	these	these	DET
ejpam-3545	71	3	examples	example	NOUN
ejpam-3545	71	4	show	show	VERB
ejpam-3545	71	5	that	that	SCONJ
ejpam-3545	71	6	conventional	conventional	ADJ
ejpam-3545	71	7	mathematical	mathematical	ADJ
ejpam-3545	71	8	structures	structure	NOUN
ejpam-3545	71	9	are	be	AUX
ejpam-3545	71	10	abstract	abstract	ADJ
ejpam-3545	71	11	prearithmetics	prearithmetic	NOUN
ejpam-3545	71	12	.	.	PUNCT
ejpam-3545	72	1	however	however	ADV
ejpam-3545	72	2	,	,	PUNCT
ejpam-3545	72	3	there	there	PRON
ejpam-3545	72	4	are	be	VERB
ejpam-3545	72	5	many	many	ADJ
ejpam-3545	72	6	unusual	unusual	ADJ
ejpam-3545	72	7	abstract	abstract	ADJ
ejpam-3545	72	8	prearithmetics	prearithmetic	NOUN
ejpam-3545	72	9	.	.	PUNCT
ejpam-3545	72	10	example	example	NOUN
ejpam-3545	73	1	4	4	NUM
ejpam-3545	73	2	.	.	PUNCT
ejpam-3545	73	3	let	let	VERB
ejpam-3545	73	4	us	we	PRON
ejpam-3545	73	5	consider	consider	VERB
ejpam-3545	73	6	the	the	DET
ejpam-3545	73	7	set	set	NOUN
ejpam-3545	73	8	n	n	PROPN
ejpam-3545	73	9	of	of	ADP
ejpam-3545	73	10	all	all	DET
ejpam-3545	73	11	natural	natural	ADJ
ejpam-3545	73	12	numbers	number	NOUN
ejpam-3545	73	13	with	with	ADP
ejpam-3545	73	14	the	the	DET
ejpam-3545	73	15	standard	standard	ADJ
ejpam-3545	73	16	order	order	NOUN
ejpam-3545	73	17	≤	≤	NOUN
ejpam-3545	73	18	,	,	PUNCT
ejpam-3545	73	19	addition	addition	NOUN
ejpam-3545	73	20	+	+	NOUN
ejpam-3545	73	21	,	,	PUNCT
ejpam-3545	73	22	multiplication	multiplication	NOUN
ejpam-3545	73	23	·	·	PUNCT
ejpam-3545	73	24	and	and	CCONJ
ejpam-3545	73	25	introduce	introduce	VERB
ejpam-3545	73	26	the	the	DET
ejpam-3545	73	27	following	follow	VERB
ejpam-3545	73	28	operations	operation	NOUN
ejpam-3545	73	29	:	:	PUNCT
ejpam-3545	74	1	a⊕	a⊕	PROPN
ejpam-3545	74	2	b	b	X
ejpam-3545	74	3	=	=	PUNCT
ejpam-3545	74	4	a	a	DET
ejpam-3545	74	5	·	·	PUNCT
ejpam-3545	74	6	b	b	NOUN
ejpam-3545	74	7	a⊗	a⊗	NOUN
ejpam-3545	74	8	b	b	PROPN
ejpam-3545	74	9	=	=	SYM
ejpam-3545	74	10	ab	ab	PROPN
ejpam-3545	74	11	then	then	ADV
ejpam-3545	74	12	the	the	DET
ejpam-3545	74	13	system	system	NOUN
ejpam-3545	74	14	a	a	X
ejpam-3545	74	15	=	=	X
ejpam-3545	74	16	(	(	PUNCT
ejpam-3545	74	17	n	n	NOUN
ejpam-3545	74	18	;	;	PUNCT
ejpam-3545	74	19	⊕,⊗,≤	⊕,⊗,≤	X
ejpam-3545	74	20	)	)	PUNCT
ejpam-3545	74	21	is	be	AUX
ejpam-3545	74	22	an	an	DET
ejpam-3545	74	23	abstract	abstract	ADJ
ejpam-3545	74	24	prearithmetic	prearithmetic	NOUN
ejpam-3545	74	25	with	with	ADP
ejpam-3545	74	26	addition	addition	NOUN
ejpam-3545	74	27	⊕	⊕	PROPN
ejpam-3545	74	28	and	and	CCONJ
ejpam-3545	74	29	multiplication	multiplication	NOUN
ejpam-3545	74	30	⊗.	⊗.	NOUN
ejpam-3545	74	31	example	example	NOUN
ejpam-3545	74	32	5	5	NUM
ejpam-3545	74	33	.	.	PUNCT
ejpam-3545	75	1	let	let	VERB
ejpam-3545	75	2	us	we	PRON
ejpam-3545	75	3	consider	consider	VERB
ejpam-3545	75	4	the	the	DET
ejpam-3545	75	5	set	set	NOUN
ejpam-3545	75	6	r++	r++	NOUN
ejpam-3545	75	7	of	of	ADP
ejpam-3545	75	8	all	all	DET
ejpam-3545	75	9	positive	positive	ADJ
ejpam-3545	75	10	real	real	ADJ
ejpam-3545	75	11	numbers	number	NOUN
ejpam-3545	75	12	is	be	AUX
ejpam-3545	75	13	with	with	ADP
ejpam-3545	75	14	the	the	DET
ejpam-3545	75	15	standard	standard	ADJ
ejpam-3545	75	16	order	order	NOUN
ejpam-3545	75	17	≤	≤	NOUN
ejpam-3545	75	18	,	,	PUNCT
ejpam-3545	75	19	addition	addition	NOUN
ejpam-3545	75	20	+	+	NOUN
ejpam-3545	75	21	,	,	PUNCT
ejpam-3545	75	22	multiplication	multiplication	NOUN
ejpam-3545	75	23	·	·	PUNCT
ejpam-3545	75	24	,	,	PUNCT
ejpam-3545	75	25	division	division	NOUN
ejpam-3545	75	26	÷	÷	PUNCT
ejpam-3545	75	27	and	and	CCONJ
ejpam-3545	75	28	introduce	introduce	VERB
ejpam-3545	75	29	the	the	DET
ejpam-3545	75	30	following	follow	VERB
ejpam-3545	75	31	operations	operation	NOUN
ejpam-3545	75	32	:	:	PUNCT
ejpam-3545	75	33	a	a	DET
ejpam-3545	75	34	�	�	PROPN
ejpam-3545	75	35	b	b	PROPN
ejpam-3545	75	36	=	=	PUNCT
ejpam-3545	75	37	a	a	PROPN
ejpam-3545	75	38	+	+	X
ejpam-3545	75	39	b	b	X
ejpam-3545	75	40	a	a	PRON
ejpam-3545	75	41	>	>	X
ejpam-3545	75	42	b	b	PROPN
ejpam-3545	75	43	=	=	SYM
ejpam-3545	75	44	a÷	a÷	PROPN
ejpam-3545	75	45	b	b	PROPN
ejpam-3545	75	46	then	then	ADV
ejpam-3545	75	47	the	the	DET
ejpam-3545	75	48	system	system	NOUN
ejpam-3545	75	49	b	b	NOUN
ejpam-3545	75	50	=	=	PUNCT
ejpam-3545	75	51	(	(	PUNCT
ejpam-3545	75	52	r++;	r++;	PROPN
ejpam-3545	75	53	�	�	PROPN
ejpam-3545	75	54	,>,≤	,>,≤	PUNCT
ejpam-3545	75	55	)	)	PUNCT
ejpam-3545	75	56	is	be	AUX
ejpam-3545	75	57	an	an	DET
ejpam-3545	75	58	abstract	abstract	ADJ
ejpam-3545	75	59	prearithmetic	prearithmetic	NOUN
ejpam-3545	75	60	with	with	ADP
ejpam-3545	75	61	addition	addition	NOUN
ejpam-3545	75	62	�	�	NOUN
ejpam-3545	75	63	and	and	CCONJ
ejpam-3545	75	64	multiplication	multiplication	NOUN
ejpam-3545	75	65	>	>	PUNCT
ejpam-3545	75	66	.	.	PUNCT
ejpam-3545	76	1	m.	m.	NOUN
ejpam-3545	76	2	burgin	burgin	PROPN
ejpam-3545	76	3	/	/	SYM
ejpam-3545	76	4	eur	eur	PROPN
ejpam-3545	76	5	.	.	PUNCT
ejpam-3545	77	1	j.	j.	PROPN
ejpam-3545	77	2	pure	pure	PROPN
ejpam-3545	77	3	appl	appl	PROPN
ejpam-3545	77	4	.	.	PROPN
ejpam-3545	77	5	math	math	PROPN
ejpam-3545	77	6	,	,	PUNCT
ejpam-3545	77	7	12	12	NUM
ejpam-3545	77	8	(	(	PUNCT
ejpam-3545	77	9	4	4	NUM
ejpam-3545	77	10	)	)	PUNCT
ejpam-3545	77	11	(	(	PUNCT
ejpam-3545	77	12	2019	2019	NUM
ejpam-3545	77	13	)	)	PUNCT
ejpam-3545	77	14	,	,	PUNCT
ejpam-3545	77	15	1787	1787	NUM
ejpam-3545	77	16	-	-	SYM
ejpam-3545	77	17	1810	1810	NUM
ejpam-3545	77	18	1791	1791	NUM
ejpam-3545	77	19	example	example	NOUN
ejpam-3545	77	20	6	6	NUM
ejpam-3545	77	21	.	.	PUNCT
ejpam-3545	78	1	semirings	semiring	NOUN
ejpam-3545	78	2	in	in	ADP
ejpam-3545	78	3	general	general	ADJ
ejpam-3545	78	4	and	and	CCONJ
ejpam-3545	78	5	idempotent	idempotent	ADJ
ejpam-3545	78	6	semirings	semiring	NOUN
ejpam-3545	78	7	,	,	PUNCT
ejpam-3545	78	8	in	in	ADP
ejpam-3545	78	9	particular	particular	ADJ
ejpam-3545	78	10	,	,	PUNCT
ejpam-3545	78	11	are	be	AUX
ejpam-3545	78	12	abstract	abstract	ADJ
ejpam-3545	78	13	prearithmetics	prearithmetic	NOUN
ejpam-3545	78	14	with	with	ADP
ejpam-3545	78	15	a	a	DET
ejpam-3545	78	16	trivial	trivial	ADJ
ejpam-3545	78	17	order	order	NOUN
ejpam-3545	78	18	(	(	PUNCT
ejpam-3545	78	19	[	[	X
ejpam-3545	78	20	47	47	NUM
ejpam-3545	78	21	]	]	X
ejpam-3545	78	22	golan	golan	PROPN
ejpam-3545	78	23	,	,	PUNCT
ejpam-3545	78	24	1999	1999	NUM
ejpam-3545	78	25	)	)	PUNCT
ejpam-3545	78	26	.	.	PUNCT
ejpam-3545	79	1	many	many	ADJ
ejpam-3545	79	2	researchers	researcher	NOUN
ejpam-3545	79	3	utilized	utilize	VERB
ejpam-3545	79	4	idempotent	idempotent	ADJ
ejpam-3545	79	5	semirings	semiring	NOUN
ejpam-3545	79	6	and	and	CCONJ
ejpam-3545	79	7	matrices	matrix	NOUN
ejpam-3545	79	8	over	over	ADP
ejpam-3545	79	9	such	such	ADJ
ejpam-3545	79	10	semirings	semiring	NOUN
ejpam-3545	79	11	for	for	ADP
ejpam-3545	79	12	solving	solve	VERB
ejpam-3545	79	13	various	various	ADJ
ejpam-3545	79	14	applied	apply	VERB
ejpam-3545	79	15	problems	problem	NOUN
ejpam-3545	79	16	in	in	ADP
ejpam-3545	79	17	computer	computer	NOUN
ejpam-3545	79	18	science	science	NOUN
ejpam-3545	79	19	and	and	CCONJ
ejpam-3545	79	20	discrete	discrete	ADJ
ejpam-3545	79	21	mathematics	mathematic	NOUN
ejpam-3545	79	22	(	(	PUNCT
ejpam-3545	79	23	cf	cf	NOUN
ejpam-3545	79	24	.	.	PUNCT
ejpam-3545	79	25	,	,	PUNCT
ejpam-3545	79	26	for	for	ADP
ejpam-3545	79	27	example	example	NOUN
ejpam-3545	79	28	,	,	PUNCT
ejpam-3545	79	29	[	[	X
ejpam-3545	79	30	14	14	NUM
ejpam-3545	79	31	,	,	PUNCT
ejpam-3545	79	32	16	16	NUM
ejpam-3545	79	33	,	,	PUNCT
ejpam-3545	79	34	32	32	NUM
ejpam-3545	79	35	,	,	PUNCT
ejpam-3545	79	36	39	39	NUM
ejpam-3545	79	37	,	,	PUNCT
ejpam-3545	79	38	63	63	NUM
ejpam-3545	79	39	,	,	PUNCT
ejpam-3545	79	40	74	74	NUM
ejpam-3545	79	41	,	,	PUNCT
ejpam-3545	79	42	75	75	NUM
ejpam-3545	79	43	]	]	PUNCT
ejpam-3545	79	44	)	)	PUNCT
ejpam-3545	79	45	.	.	PUNCT
ejpam-3545	80	1	idempotent	idempotent	ADJ
ejpam-3545	80	2	semi	semi	NOUN
ejpam-3545	80	3	-	-	NOUN
ejpam-3545	80	4	rings	ring	NOUN
ejpam-3545	80	5	also	also	ADV
ejpam-3545	80	6	have	have	AUX
ejpam-3545	80	7	many	many	ADJ
ejpam-3545	80	8	other	other	ADJ
ejpam-3545	80	9	applications	application	NOUN
ejpam-3545	80	10	,	,	PUNCT
ejpam-3545	80	11	in	in	ADP
ejpam-3545	80	12	particular	particular	ADJ
ejpam-3545	80	13	,	,	PUNCT
ejpam-3545	80	14	as	as	ADP
ejpam-3545	80	15	the	the	DET
ejpam-3545	80	16	basic	basic	ADJ
ejpam-3545	80	17	structure	structure	NOUN
ejpam-3545	80	18	of	of	ADP
ejpam-3545	80	19	idempotent	idempotent	ADJ
ejpam-3545	80	20	analysis	analysis	NOUN
ejpam-3545	80	21	[	[	X
ejpam-3545	80	22	44	44	NUM
ejpam-3545	80	23	,	,	PUNCT
ejpam-3545	80	24	59	59	NUM
ejpam-3545	80	25	,	,	PUNCT
ejpam-3545	80	26	60	60	NUM
ejpam-3545	80	27	]	]	PUNCT
ejpam-3545	80	28	and	and	CCONJ
ejpam-3545	80	29	of	of	ADP
ejpam-3545	80	30	its	its	PRON
ejpam-3545	80	31	special	special	ADJ
ejpam-3545	80	32	case	case	NOUN
ejpam-3545	80	33	tropical	tropical	ADJ
ejpam-3545	80	34	analysis	analysis	NOUN
ejpam-3545	80	35	[	[	X
ejpam-3545	80	36	51	51	NUM
ejpam-3545	80	37	,	,	PUNCT
ejpam-3545	80	38	70	70	NUM
ejpam-3545	80	39	]	]	PUNCT
ejpam-3545	80	40	.	.	PUNCT
ejpam-3545	81	1	example	example	NOUN
ejpam-3545	82	1	7	7	NUM
ejpam-3545	82	2	.	.	PUNCT
ejpam-3545	83	1	let	let	VERB
ejpam-3545	83	2	rmax	rmax	ADV
ejpam-3545	83	3	be	be	AUX
ejpam-3545	83	4	the	the	DET
ejpam-3545	83	5	set	set	NOUN
ejpam-3545	83	6	a	a	DET
ejpam-3545	83	7	=	=	SYM
ejpam-3545	83	8	r∪{−∞	r∪{−∞	NOUN
ejpam-3545	83	9	}	}	PUNCT
ejpam-3545	83	10	with	with	ADP
ejpam-3545	83	11	the	the	DET
ejpam-3545	83	12	operations	operation	NOUN
ejpam-3545	83	13	⊕	⊕	PROPN
ejpam-3545	83	14	=	=	SYM
ejpam-3545	83	15	max	max	PROPN
ejpam-3545	83	16	and	and	CCONJ
ejpam-3545	83	17	�	�	PROPN
ejpam-3545	84	1	=	=	SYM
ejpam-3545	84	2	+	+	PROPN
ejpam-3545	84	3	,	,	PUNCT
ejpam-3545	84	4	which	which	PRON
ejpam-3545	84	5	is	be	AUX
ejpam-3545	84	6	the	the	DET
ejpam-3545	84	7	usual	usual	ADJ
ejpam-3545	84	8	addition	addition	NOUN
ejpam-3545	84	9	in	in	ADP
ejpam-3545	84	10	r	r	NOUN
ejpam-3545	84	11	and	and	CCONJ
ejpam-3545	84	12	defining	define	VERB
ejpam-3545	84	13	0	0	NUM
ejpam-3545	84	14	=	=	SYM
ejpam-3545	84	15	−∞	−∞	NOUN
ejpam-3545	84	16	and	and	CCONJ
ejpam-3545	84	17	1	1	NUM
ejpam-3545	84	18	=	=	SYM
ejpam-3545	84	19	0	0	NUM
ejpam-3545	84	20	.	.	PUNCT
ejpam-3545	85	1	by	by	ADP
ejpam-3545	85	2	construction	construction	NOUN
ejpam-3545	85	3	,	,	PUNCT
ejpam-3545	85	4	rmax	rmax	PROPN
ejpam-3545	85	5	is	be	AUX
ejpam-3545	85	6	a	a	DET
ejpam-3545	85	7	commutative	commutative	ADJ
ejpam-3545	85	8	idempotent	idempotent	NOUN
ejpam-3545	85	9	semi	semi	ADJ
ejpam-3545	85	10	-	-	ADJ
ejpam-3545	85	11	ring	ring	ADJ
ejpam-3545	85	12	and	and	CCONJ
ejpam-3545	85	13	thus	thus	ADV
ejpam-3545	85	14	,	,	PUNCT
ejpam-3545	85	15	a	a	DET
ejpam-3545	85	16	prearithmetic	prearithmetic	NOUN
ejpam-3545	85	17	.	.	PUNCT
ejpam-3545	86	1	it	it	PRON
ejpam-3545	86	2	is	be	AUX
ejpam-3545	86	3	very	very	ADV
ejpam-3545	86	4	useful	useful	ADJ
ejpam-3545	86	5	in	in	ADP
ejpam-3545	86	6	idempotent	idempotent	ADJ
ejpam-3545	86	7	analysis	analysis	NOUN
ejpam-3545	86	8	[	[	X
ejpam-3545	86	9	44	44	NUM
ejpam-3545	86	10	,	,	PUNCT
ejpam-3545	86	11	59	59	NUM
ejpam-3545	86	12	,	,	PUNCT
ejpam-3545	86	13	60	60	NUM
ejpam-3545	86	14	]	]	PUNCT
ejpam-3545	86	15	.	.	PUNCT
ejpam-3545	87	1	example	example	NOUN
ejpam-3545	87	2	8	8	NUM
ejpam-3545	87	3	.	.	PUNCT
ejpam-3545	88	1	let	let	VERB
ejpam-3545	88	2	rmin	rmin	NOUN
ejpam-3545	88	3	be	be	AUX
ejpam-3545	88	4	the	the	DET
ejpam-3545	88	5	set	set	NOUN
ejpam-3545	88	6	a	a	DET
ejpam-3545	88	7	=	=	SYM
ejpam-3545	88	8	r∪{+∞	r∪{+∞	VERB
ejpam-3545	88	9	}	}	PUNCT
ejpam-3545	88	10	with	with	ADP
ejpam-3545	88	11	the	the	DET
ejpam-3545	88	12	operations	operation	NOUN
ejpam-3545	88	13	⊕	⊕	PROPN
ejpam-3545	88	14	=	=	SYM
ejpam-3545	88	15	min	min	PROPN
ejpam-3545	88	16	and	and	CCONJ
ejpam-3545	88	17	�	�	PROPN
ejpam-3545	88	18	=	=	SYM
ejpam-3545	89	1	+	+	PROPN
ejpam-3545	89	2	,	,	PUNCT
ejpam-3545	89	3	which	which	PRON
ejpam-3545	89	4	is	be	AUX
ejpam-3545	89	5	the	the	DET
ejpam-3545	89	6	usual	usual	ADJ
ejpam-3545	89	7	addition	addition	NOUN
ejpam-3545	89	8	in	in	ADP
ejpam-3545	89	9	r	r	NOUN
ejpam-3545	89	10	and	and	CCONJ
ejpam-3545	89	11	defining	define	VERB
ejpam-3545	89	12	0	0	NUM
ejpam-3545	90	1	=	=	PUNCT
ejpam-3545	91	1	+	+	NOUN
ejpam-3545	91	2	∞	∞	NUM
ejpam-3545	91	3	and	and	CCONJ
ejpam-3545	91	4	1	1	NUM
ejpam-3545	91	5	=	=	SYM
ejpam-3545	91	6	0	0	NUM
ejpam-3545	91	7	.	.	PUNCT
ejpam-3545	92	1	by	by	ADP
ejpam-3545	92	2	construction	construction	NOUN
ejpam-3545	92	3	,	,	PUNCT
ejpam-3545	92	4	rmin	rmin	NOUN
ejpam-3545	92	5	is	be	AUX
ejpam-3545	92	6	a	a	DET
ejpam-3545	92	7	commutative	commutative	ADJ
ejpam-3545	92	8	idempotent	idempotent	NOUN
ejpam-3545	92	9	semi	semi	ADJ
ejpam-3545	92	10	-	-	ADJ
ejpam-3545	92	11	ring	ring	ADJ
ejpam-3545	92	12	and	and	CCONJ
ejpam-3545	92	13	thus	thus	ADV
ejpam-3545	92	14	,	,	PUNCT
ejpam-3545	92	15	a	a	DET
ejpam-3545	92	16	prearithmetic	prearithmetic	NOUN
ejpam-3545	92	17	.	.	PUNCT
ejpam-3545	93	1	it	it	PRON
ejpam-3545	93	2	is	be	AUX
ejpam-3545	93	3	also	also	ADV
ejpam-3545	93	4	very	very	ADV
ejpam-3545	93	5	useful	useful	ADJ
ejpam-3545	93	6	in	in	ADP
ejpam-3545	93	7	idempotent	idempotent	ADJ
ejpam-3545	93	8	analysis	analysis	NOUN
ejpam-3545	93	9	[	[	X
ejpam-3545	93	10	44	44	NUM
ejpam-3545	93	11	,	,	PUNCT
ejpam-3545	93	12	59	59	NUM
ejpam-3545	93	13	,	,	PUNCT
ejpam-3545	93	14	60	60	NUM
ejpam-3545	93	15	]	]	PUNCT
ejpam-3545	93	16	.	.	PUNCT
ejpam-3545	94	1	example	example	NOUN
ejpam-3545	94	2	9	9	NUM
ejpam-3545	94	3	.	.	PUNCT
ejpam-3545	94	4	tropical	tropical	ADJ
ejpam-3545	94	5	semirings	semiring	NOUN
ejpam-3545	95	1	[	[	X
ejpam-3545	95	2	65	65	NUM
ejpam-3545	95	3	]	]	PUNCT
ejpam-3545	95	4	and	and	CCONJ
ejpam-3545	95	5	subtropical	subtropical	ADJ
ejpam-3545	95	6	algebras	algebra	NOUN
ejpam-3545	95	7	with	with	ADP
ejpam-3545	95	8	max	max	PROPN
ejpam-3545	95	9	or	or	CCONJ
ejpam-3545	95	10	min	min	NOUN
ejpam-3545	95	11	as	as	ADP
ejpam-3545	95	12	multiplication	multiplication	NOUN
ejpam-3545	95	13	(	(	PUNCT
ejpam-3545	95	14	shiozawa	shiozawa	PROPN
ejpam-3545	95	15	,	,	PUNCT
ejpam-3545	95	16	1998	1998	NUM
ejpam-3545	95	17	)	)	PUNCT
ejpam-3545	95	18	are	be	AUX
ejpam-3545	95	19	prearithmetics	prearithmetic	NOUN
ejpam-3545	95	20	.	.	PUNCT
ejpam-3545	96	1	there	there	PRON
ejpam-3545	96	2	is	be	VERB
ejpam-3545	96	3	a	a	DET
ejpam-3545	96	4	possibility	possibility	NOUN
ejpam-3545	96	5	to	to	PART
ejpam-3545	96	6	assemble	assemble	VERB
ejpam-3545	96	7	different	different	ADJ
ejpam-3545	96	8	algebraic	algebraic	ADJ
ejpam-3545	96	9	constructions	construction	NOUN
ejpam-3545	96	10	similar	similar	ADJ
ejpam-3545	96	11	to	to	ADP
ejpam-3545	96	12	modules	module	NOUN
ejpam-3545	96	13	and	and	CCONJ
ejpam-3545	96	14	vector	vector	NOUN
ejpam-3545	96	15	spaces	space	NOUN
ejpam-3545	96	16	using	use	VERB
ejpam-3545	96	17	abstract	abstract	ADJ
ejpam-3545	96	18	prearithmetics	prearithmetic	NOUN
ejpam-3545	96	19	instead	instead	ADV
ejpam-3545	96	20	of	of	ADP
ejpam-3545	96	21	rings	ring	NOUN
ejpam-3545	96	22	or	or	CCONJ
ejpam-3545	96	23	fields	field	NOUN
ejpam-3545	96	24	.	.	PUNCT
ejpam-3545	97	1	for	for	ADP
ejpam-3545	97	2	instance	instance	NOUN
ejpam-3545	97	3	,	,	PUNCT
ejpam-3545	97	4	taking	take	VERB
ejpam-3545	97	5	an	an	DET
ejpam-3545	97	6	abstract	abstract	ADJ
ejpam-3545	97	7	prearithmetic	prearithmetic	NOUN
ejpam-3545	97	8	a	a	DET
ejpam-3545	97	9	=	=	X
ejpam-3545	97	10	(	(	PUNCT
ejpam-3545	97	11	a	a	X
ejpam-3545	97	12	;	;	PUNCT
ejpam-3545	97	13	+	+	ADJ
ejpam-3545	97	14	,	,	PUNCT
ejpam-3545	97	15	◦	◦	NOUN
ejpam-3545	97	16	,	,	PUNCT
ejpam-3545	97	17	≤	≤	NUM
ejpam-3545	97	18	)	)	PUNCT
ejpam-3545	97	19	and	and	CCONJ
ejpam-3545	97	20	a	a	DET
ejpam-3545	97	21	natural	natural	ADJ
ejpam-3545	97	22	number	number	NOUN
ejpam-3545	97	23	n	n	CCONJ
ejpam-3545	97	24	,	,	PUNCT
ejpam-3545	97	25	it	it	PRON
ejpam-3545	97	26	is	be	AUX
ejpam-3545	97	27	possible	possible	ADJ
ejpam-3545	97	28	to	to	PART
ejpam-3545	97	29	build	build	VERB
ejpam-3545	97	30	the	the	DET
ejpam-3545	97	31	abstract	abstract	ADJ
ejpam-3545	97	32	prearithmetic	prearithmetic	NOUN
ejpam-3545	97	33	of	of	ADP
ejpam-3545	97	34	n	n	CCONJ
ejpam-3545	97	35	-	-	PUNCT
ejpam-3545	97	36	dimensional	dimensional	ADJ
ejpam-3545	97	37	a	a	DET
ejpam-3545	97	38	-	-	PUNCT
ejpam-3545	97	39	vectors	vector	NOUN
ejpam-3545	97	40	v	v	NOUN
ejpam-3545	97	41	na	na	NOUN
ejpam-3545	97	42	=	=	PUNCT
ejpam-3545	97	43	(	(	PUNCT
ejpam-3545	97	44	v	v	NOUN
ejpam-3545	97	45	na	na	NOUN
ejpam-3545	97	46	;	;	PUNCT
ejpam-3545	97	47	+	+	ADJ
ejpam-3545	97	48	,	,	PUNCT
ejpam-3545	97	49	◦	◦	NOUN
ejpam-3545	97	50	,	,	PUNCT
ejpam-3545	97	51	≤	≤	NUM
ejpam-3545	97	52	)	)	PUNCT
ejpam-3545	97	53	,	,	PUNCT
ejpam-3545	97	54	elements	element	NOUN
ejpam-3545	97	55	of	of	ADP
ejpam-3545	97	56	which	which	PRON
ejpam-3545	97	57	are	be	AUX
ejpam-3545	97	58	vectors	vector	NOUN
ejpam-3545	97	59	in	in	ADP
ejpam-3545	97	60	a.	a.	NOUN
ejpam-3545	97	61	namely	namely	ADV
ejpam-3545	97	62	,	,	PUNCT
ejpam-3545	97	63	elements	element	NOUN
ejpam-3545	97	64	of	of	ADP
ejpam-3545	97	65	n	n	ADV
ejpam-3545	97	66	-	-	PUNCT
ejpam-3545	97	67	dimensional	dimensional	ADJ
ejpam-3545	97	68	a	a	DET
ejpam-3545	97	69	-	-	PUNCT
ejpam-3545	97	70	vector	vector	NOUN
ejpam-3545	97	71	prearithmetic	prearithmetic	NOUN
ejpam-3545	97	72	v	v	NOUN
ejpam-3545	97	73	na	na	ADP
ejpam-3545	97	74	=	=	PUNCT
ejpam-3545	97	75	(	(	PUNCT
ejpam-3545	97	76	v	v	NOUN
ejpam-3545	97	77	na	na	NOUN
ejpam-3545	97	78	;	;	PUNCT
ejpam-3545	97	79	+	+	ADJ
ejpam-3545	97	80	,	,	PUNCT
ejpam-3545	97	81	◦	◦	NOUN
ejpam-3545	97	82	,	,	PUNCT
ejpam-3545	97	83	≤	≤	NUM
ejpam-3545	97	84	)	)	PUNCT
ejpam-3545	97	85	,	,	PUNCT
ejpam-3545	97	86	i.e.	i.e.	X
ejpam-3545	97	87	,	,	PUNCT
ejpam-3545	97	88	a	a	DET
ejpam-3545	97	89	-	-	PUNCT
ejpam-3545	97	90	vectors	vector	NOUN
ejpam-3545	97	91	,	,	PUNCT
ejpam-3545	97	92	have	have	VERB
ejpam-3545	97	93	the	the	DET
ejpam-3545	97	94	form	form	NOUN
ejpam-3545	97	95	(	(	PUNCT
ejpam-3545	97	96	a1	a1	NOUN
ejpam-3545	97	97	,	,	PUNCT
ejpam-3545	97	98	a2	a2	PROPN
ejpam-3545	97	99	,	,	PUNCT
ejpam-3545	97	100	.	.	PUNCT
ejpam-3545	97	101	.	.	PUNCT
ejpam-3545	98	1	.	.	PUNCT
ejpam-3545	99	1	,	,	PUNCT
ejpam-3545	99	2	an	an	X
ejpam-3545	99	3	)	)	PUNCT
ejpam-3545	99	4	where	where	SCONJ
ejpam-3545	99	5	a1	a1	NOUN
ejpam-3545	99	6	,	,	PUNCT
ejpam-3545	99	7	a2	a2	PROPN
ejpam-3545	99	8	,	,	PUNCT
ejpam-3545	99	9	.	.	PUNCT
ejpam-3545	99	10	.	.	PUNCT
ejpam-3545	100	1	.	.	PUNCT
ejpam-3545	101	1	,	,	PUNCT
ejpam-3545	101	2	an	an	PRON
ejpam-3545	101	3	are	be	AUX
ejpam-3545	101	4	elements	element	NOUN
ejpam-3545	101	5	from	from	ADP
ejpam-3545	101	6	the	the	DET
ejpam-3545	101	7	abstract	abstract	ADJ
ejpam-3545	101	8	prearithmetic	prearithmetic	ADJ
ejpam-3545	101	9	a.	a.	NOUN
ejpam-3545	101	10	the	the	DET
ejpam-3545	101	11	prearithmetic	prearithmetic	ADJ
ejpam-3545	101	12	v	v	NOUN
ejpam-3545	101	13	na	na	NOUN
ejpam-3545	101	14	is	be	AUX
ejpam-3545	101	15	called	call	VERB
ejpam-3545	101	16	a	a	DET
ejpam-3545	101	17	vector	vector	NOUN
ejpam-3545	101	18	expansion	expansion	NOUN
ejpam-3545	101	19	of	of	ADP
ejpam-3545	101	20	the	the	DET
ejpam-3545	101	21	abstract	abstract	ADJ
ejpam-3545	101	22	prearithmetic	prearithmetic	ADJ
ejpam-3545	101	23	a.	a.	NOUN
ejpam-3545	101	24	in	in	ADP
ejpam-3545	101	25	a	a	DET
ejpam-3545	101	26	similar	similar	ADJ
ejpam-3545	101	27	way	way	NOUN
ejpam-3545	101	28	,	,	PUNCT
ejpam-3545	101	29	taking	take	VERB
ejpam-3545	101	30	an	an	DET
ejpam-3545	101	31	abstract	abstract	ADJ
ejpam-3545	101	32	prearithmetic	prearithmetic	NOUN
ejpam-3545	101	33	a	a	DET
ejpam-3545	101	34	=	=	X
ejpam-3545	101	35	(	(	PUNCT
ejpam-3545	101	36	a	a	X
ejpam-3545	101	37	;	;	PUNCT
ejpam-3545	101	38	+	+	ADJ
ejpam-3545	101	39	,	,	PUNCT
ejpam-3545	101	40	◦	◦	NOUN
ejpam-3545	101	41	,	,	PUNCT
ejpam-3545	101	42	≤	≤	NUM
ejpam-3545	101	43	)	)	PUNCT
ejpam-3545	101	44	and	and	CCONJ
ejpam-3545	101	45	a	a	DET
ejpam-3545	101	46	pair	pair	NOUN
ejpam-3545	101	47	of	of	ADP
ejpam-3545	101	48	natural	natural	ADJ
ejpam-3545	101	49	numbers	number	NOUN
ejpam-3545	101	50	n	n	PRON
ejpam-3545	101	51	and	and	CCONJ
ejpam-3545	101	52	m	m	PROPN
ejpam-3545	101	53	,	,	PUNCT
ejpam-3545	101	54	it	it	PRON
ejpam-3545	101	55	is	be	AUX
ejpam-3545	101	56	also	also	ADV
ejpam-3545	101	57	possible	possible	ADJ
ejpam-3545	101	58	to	to	PART
ejpam-3545	101	59	build	build	VERB
ejpam-3545	101	60	the	the	DET
ejpam-3545	101	61	abstract	abstract	ADJ
ejpam-3545	101	62	prearithmetic	prearithmetic	NOUN
ejpam-3545	101	63	of	of	ADP
ejpam-3545	101	64	n	n	PRON
ejpam-3545	101	65	×m	×m	NOUN
ejpam-3545	101	66	-	-	PUNCT
ejpam-3545	101	67	dimensional	dimensional	ADJ
ejpam-3545	101	68	a	a	DET
ejpam-3545	101	69	-	-	PUNCT
ejpam-3545	101	70	matrices	matrix	NOUN
ejpam-3545	101	71	mn×ma	mn×ma	NOUN
ejpam-3545	101	72	=	=	SYM
ejpam-3545	101	73	(	(	PUNCT
ejpam-3545	101	74	mn×ma	mn×ma	PROPN
ejpam-3545	101	75	;	;	PUNCT
ejpam-3545	101	76	+	+	ADJ
ejpam-3545	101	77	,	,	PUNCT
ejpam-3545	101	78	◦	◦	NOUN
ejpam-3545	101	79	,	,	PUNCT
ejpam-3545	101	80	≤	≤	NUM
ejpam-3545	101	81	)	)	PUNCT
ejpam-3545	101	82	,	,	PUNCT
ejpam-3545	101	83	elements	element	NOUN
ejpam-3545	101	84	of	of	ADP
ejpam-3545	101	85	which	which	PRON
ejpam-3545	101	86	are	be	AUX
ejpam-3545	101	87	matrices	matrix	NOUN
ejpam-3545	101	88	in	in	ADP
ejpam-3545	101	89	a.	a.	NOUN
ejpam-3545	101	90	namely	namely	ADV
ejpam-3545	101	91	,	,	PUNCT
ejpam-3545	101	92	elements	element	NOUN
ejpam-3545	101	93	of	of	ADP
ejpam-3545	101	94	n	n	PRON
ejpam-3545	101	95	×m	×m	NOUN
ejpam-3545	101	96	-	-	PUNCT
ejpam-3545	101	97	dimensional	dimensional	ADJ
ejpam-3545	101	98	a	a	DET
ejpam-3545	101	99	-	-	PUNCT
ejpam-3545	101	100	matrix	matrix	NOUN
ejpam-3545	101	101	prearithmetic	prearithmetic	ADJ
ejpam-3545	101	102	mn×ma	mn×ma	NOUN
ejpam-3545	102	1	=	=	SYM
ejpam-3545	102	2	(	(	PUNCT
ejpam-3545	102	3	mn×ma	mn×ma	PROPN
ejpam-3545	102	4	;	;	PUNCT
ejpam-3545	102	5	+	+	ADJ
ejpam-3545	102	6	,	,	PUNCT
ejpam-3545	102	7	◦	◦	NOUN
ejpam-3545	102	8	,	,	PUNCT
ejpam-3545	102	9	≤	≤	NUM
ejpam-3545	102	10	)	)	PUNCT
ejpam-3545	102	11	,	,	PUNCT
ejpam-3545	102	12	i.e.	i.e.	X
ejpam-3545	102	13	,	,	PUNCT
ejpam-3545	102	14	a	a	DET
ejpam-3545	102	15	-	-	PUNCT
ejpam-3545	102	16	matrices	matrix	NOUN
ejpam-3545	102	17	,	,	PUNCT
ejpam-3545	102	18	have	have	VERB
ejpam-3545	102	19	the	the	DET
ejpam-3545	102	20	form	form	PROPN
ejpam-3545	102	21	a11	a11	PROPN
ejpam-3545	102	22	a12	a12	PROPN
ejpam-3545	102	23	a13	a13	PROPN
ejpam-3545	102	24	.	.	PUNCT
ejpam-3545	102	25	.	.	PUNCT
ejpam-3545	102	26	.	.	PUNCT
ejpam-3545	103	1	a1n	a1n	PRON
ejpam-3545	103	2	a21	a21	PROPN
ejpam-3545	103	3	a22	a22	PROPN
ejpam-3545	103	4	a23	a23	PROPN
ejpam-3545	103	5	.	.	PUNCT
ejpam-3545	103	6	.	.	PUNCT
ejpam-3545	103	7	.	.	PUNCT
ejpam-3545	104	1	a2n	a2n	PROPN
ejpam-3545	104	2	.	.	PUNCT
ejpam-3545	104	3	.	.	PUNCT
ejpam-3545	104	4	.	.	PUNCT
ejpam-3545	104	5	.	.	PUNCT
ejpam-3545	104	6	.	.	PUNCT
ejpam-3545	104	7	.	.	PUNCT
ejpam-3545	104	8	.	.	PUNCT
ejpam-3545	104	9	.	.	PUNCT
ejpam-3545	104	10	.	.	PUNCT
ejpam-3545	104	11	.	.	PUNCT
ejpam-3545	104	12	.	.	PUNCT
ejpam-3545	104	13	.	.	PUNCT
ejpam-3545	104	14	.	.	PUNCT
ejpam-3545	104	15	.	.	PUNCT
ejpam-3545	104	16	.	.	PUNCT
ejpam-3545	105	1	am1	am1	X
ejpam-3545	106	1	am2	am2	DET
ejpam-3545	106	2	am3	am3	NOUN
ejpam-3545	106	3	.	.	PUNCT
ejpam-3545	106	4	.	.	PUNCT
ejpam-3545	106	5	.	.	PUNCT
ejpam-3545	107	1	amn	amn	PROPN
ejpam-3545	107	2			NOUN
ejpam-3545	107	3	where	where	SCONJ
ejpam-3545	107	4	all	all	PRON
ejpam-3545	107	5	aij(i	aij(i	PROPN
ejpam-3545	107	6	=	=	SYM
ejpam-3545	107	7	1	1	NUM
ejpam-3545	107	8	,	,	PUNCT
ejpam-3545	107	9	2	2	NUM
ejpam-3545	107	10	,	,	PUNCT
ejpam-3545	107	11	3	3	NUM
ejpam-3545	107	12	,	,	PUNCT
ejpam-3545	107	13	.	.	PUNCT
ejpam-3545	107	14	.	.	PUNCT
ejpam-3545	108	1	.	.	PUNCT
ejpam-3545	109	1	,	,	PUNCT
ejpam-3545	109	2	m	m	PROPN
ejpam-3545	109	3	;	;	PUNCT
ejpam-3545	109	4	j	j	PROPN
ejpam-3545	109	5	=	=	SYM
ejpam-3545	109	6	1	1	NUM
ejpam-3545	109	7	,	,	PUNCT
ejpam-3545	109	8	2	2	NUM
ejpam-3545	109	9	,	,	PUNCT
ejpam-3545	109	10	3	3	NUM
ejpam-3545	109	11	,	,	PUNCT
ejpam-3545	109	12	.	.	PUNCT
ejpam-3545	109	13	.	.	PUNCT
ejpam-3545	110	1	.	.	PUNCT
ejpam-3545	111	1	,	,	PUNCT
ejpam-3545	111	2	n	n	CCONJ
ejpam-3545	111	3	)	)	PUNCT
ejpam-3545	111	4	are	be	AUX
ejpam-3545	111	5	elements	element	NOUN
ejpam-3545	111	6	from	from	ADP
ejpam-3545	111	7	the	the	DET
ejpam-3545	111	8	abstract	abstract	ADJ
ejpam-3545	111	9	prearithmetic	prearithmetic	ADJ
ejpam-3545	111	10	a.	a.	NOUN
ejpam-3545	111	11	the	the	DET
ejpam-3545	111	12	prearithmetic	prearithmetic	ADJ
ejpam-3545	111	13	mn×ma	mn×ma	PROPN
ejpam-3545	111	14	is	be	AUX
ejpam-3545	111	15	called	call	VERB
ejpam-3545	111	16	a	a	DET
ejpam-3545	111	17	matrix	matrix	NOUN
ejpam-3545	111	18	expansion	expansion	NOUN
ejpam-3545	111	19	of	of	ADP
ejpam-3545	111	20	the	the	DET
ejpam-3545	111	21	abstract	abstract	ADJ
ejpam-3545	111	22	prearithmetic	prearithmetic	ADJ
ejpam-3545	111	23	a.	a.	NOUN
ejpam-3545	111	24	addition	addition	NOUN
ejpam-3545	111	25	and	and	CCONJ
ejpam-3545	111	26	multiplication	multiplication	NOUN
ejpam-3545	111	27	in	in	ADP
ejpam-3545	111	28	these	these	DET
ejpam-3545	111	29	prearithmetics	prearithmetic	NOUN
ejpam-3545	111	30	are	be	AUX
ejpam-3545	111	31	defined	define	VERB
ejpam-3545	111	32	coordinate	coordinate	NOUN
ejpam-3545	111	33	-	-	PUNCT
ejpam-3545	111	34	wise	wise	ADJ
ejpam-3545	111	35	.	.	PUNCT
ejpam-3545	112	1	for	for	ADP
ejpam-3545	112	2	instance	instance	NOUN
ejpam-3545	112	3	,	,	PUNCT
ejpam-3545	112	4	taking	take	VERB
ejpam-3545	112	5	the	the	DET
ejpam-3545	112	6	arithmetic	arithmetic	ADJ
ejpam-3545	112	7	z	z	NOUN
ejpam-3545	112	8	of	of	ADP
ejpam-3545	112	9	integer	integer	NOUN
ejpam-3545	112	10	numbers	number	NOUN
ejpam-3545	112	11	and	and	CCONJ
ejpam-3545	112	12	two	two	NUM
ejpam-3545	112	13	two	two	NUM
ejpam-3545	112	14	-	-	PUNCT
ejpam-3545	112	15	dimensional	dimensional	ADJ
ejpam-3545	112	16	z	z	NOUN
ejpam-3545	112	17	-	-	PUNCT
ejpam-3545	112	18	vectors	vector	NOUN
ejpam-3545	112	19	(	(	PUNCT
ejpam-3545	112	20	2	2	NUM
ejpam-3545	112	21	,	,	PUNCT
ejpam-3545	112	22	3	3	NUM
ejpam-3545	112	23	)	)	PUNCT
ejpam-3545	112	24	and	and	CCONJ
ejpam-3545	112	25	(	(	PUNCT
ejpam-3545	112	26	4	4	NUM
ejpam-3545	112	27	,	,	PUNCT
ejpam-3545	112	28	5	5	NUM
ejpam-3545	112	29	)	)	PUNCT
ejpam-3545	112	30	from	from	ADP
ejpam-3545	112	31	the	the	DET
ejpam-3545	112	32	prearithmetic	prearithmetic	ADJ
ejpam-3545	112	33	v	v	ADP
ejpam-3545	112	34	2z	2z	NUM
ejpam-3545	112	35	of	of	ADP
ejpam-3545	112	36	z	z	NOUN
ejpam-3545	112	37	-	-	PUNCT
ejpam-3545	112	38	vectors	vector	NOUN
ejpam-3545	112	39	,	,	PUNCT
ejpam-3545	112	40	we	we	PRON
ejpam-3545	112	41	define	define	VERB
ejpam-3545	112	42	their	their	PRON
ejpam-3545	112	43	sum	sum	NOUN
ejpam-3545	112	44	as	as	ADP
ejpam-3545	112	45	(	(	PUNCT
ejpam-3545	112	46	2	2	NUM
ejpam-3545	112	47	,	,	PUNCT
ejpam-3545	112	48	3	3	NUM
ejpam-3545	112	49	)	)	PUNCT
ejpam-3545	112	50	+	+	CCONJ
ejpam-3545	112	51	(	(	PUNCT
ejpam-3545	112	52	4	4	NUM
ejpam-3545	112	53	,	,	PUNCT
ejpam-3545	112	54	5	5	NUM
ejpam-3545	112	55	)	)	PUNCT
ejpam-3545	112	56	=	=	NOUN
ejpam-3545	112	57	(	(	PUNCT
ejpam-3545	112	58	2	2	NUM
ejpam-3545	112	59	+	+	NUM
ejpam-3545	112	60	4	4	NUM
ejpam-3545	112	61	,	,	PUNCT
ejpam-3545	112	62	3	3	NUM
ejpam-3545	112	63	+	+	SYM
ejpam-3545	112	64	5	5	NUM
ejpam-3545	112	65	)	)	PUNCT
ejpam-3545	112	66	=	=	NOUN
ejpam-3545	112	67	(	(	PUNCT
ejpam-3545	112	68	6	6	NUM
ejpam-3545	112	69	,	,	PUNCT
ejpam-3545	112	70	8)	8)	NUM
ejpam-3545	112	71	and	and	CCONJ
ejpam-3545	112	72	their	their	PRON
ejpam-3545	112	73	product	product	NOUN
ejpam-3545	112	74	as	as	ADP
ejpam-3545	112	75	(	(	PUNCT
ejpam-3545	112	76	2	2	NUM
ejpam-3545	112	77	,	,	PUNCT
ejpam-3545	112	78	3	3	X
ejpam-3545	112	79	)	)	PUNCT
ejpam-3545	112	80	◦	◦	NOUN
ejpam-3545	112	81	(	(	PUNCT
ejpam-3545	112	82	4	4	NUM
ejpam-3545	112	83	,	,	PUNCT
ejpam-3545	112	84	5	5	NUM
ejpam-3545	112	85	)	)	PUNCT
ejpam-3545	112	86	=	=	SYM
ejpam-3545	112	87	(	(	PUNCT
ejpam-3545	112	88	2	2	NUM
ejpam-3545	112	89	·	·	SYM
ejpam-3545	112	90	4	4	NUM
ejpam-3545	112	91	,	,	PUNCT
ejpam-3545	112	92	3	3	NUM
ejpam-3545	112	93	·	·	SYM
ejpam-3545	112	94	5	5	NUM
ejpam-3545	112	95	)	)	PUNCT
ejpam-3545	112	96	=	=	NOUN
ejpam-3545	112	97	(	(	PUNCT
ejpam-3545	112	98	8	8	NUM
ejpam-3545	112	99	,	,	PUNCT
ejpam-3545	112	100	15	15	NUM
ejpam-3545	112	101	)	)	PUNCT
ejpam-3545	112	102	.	.	PUNCT
ejpam-3545	113	1	m.	m.	NOUN
ejpam-3545	113	2	burgin	burgin	PROPN
ejpam-3545	113	3	/	/	SYM
ejpam-3545	113	4	eur	eur	PROPN
ejpam-3545	113	5	.	.	PUNCT
ejpam-3545	114	1	j.	j.	PROPN
ejpam-3545	114	2	pure	pure	PROPN
ejpam-3545	114	3	appl	appl	PROPN
ejpam-3545	114	4	.	.	PROPN
ejpam-3545	114	5	math	math	PROPN
ejpam-3545	114	6	,	,	PUNCT
ejpam-3545	114	7	12	12	NUM
ejpam-3545	114	8	(	(	PUNCT
ejpam-3545	114	9	4	4	NUM
ejpam-3545	114	10	)	)	PUNCT
ejpam-3545	114	11	(	(	PUNCT
ejpam-3545	114	12	2019	2019	NUM
ejpam-3545	114	13	)	)	PUNCT
ejpam-3545	114	14	,	,	PUNCT
ejpam-3545	114	15	1787	1787	NUM
ejpam-3545	114	16	-	-	SYM
ejpam-3545	114	17	1810	1810	NUM
ejpam-3545	114	18	1792	1792	NUM
ejpam-3545	114	19	order	order	NOUN
ejpam-3545	114	20	in	in	ADP
ejpam-3545	114	21	v	v	NUM
ejpam-3545	114	22	na	na	NOUN
ejpam-3545	114	23	is	be	AUX
ejpam-3545	114	24	defined	define	VERB
ejpam-3545	114	25	by	by	ADP
ejpam-3545	114	26	the	the	DET
ejpam-3545	114	27	following	follow	VERB
ejpam-3545	114	28	condition	condition	NOUN
ejpam-3545	114	29	:	:	PUNCT
ejpam-3545	114	30	if	if	SCONJ
ejpam-3545	114	31	(	(	PUNCT
ejpam-3545	114	32	a1	a1	NOUN
ejpam-3545	114	33	,	,	PUNCT
ejpam-3545	114	34	a2	a2	PROPN
ejpam-3545	114	35	,	,	PUNCT
ejpam-3545	114	36	.	.	PUNCT
ejpam-3545	114	37	.	.	PUNCT
ejpam-3545	115	1	.	.	PUNCT
ejpam-3545	116	1	,	,	PUNCT
ejpam-3545	116	2	an	an	X
ejpam-3545	116	3	)	)	PUNCT
ejpam-3545	116	4	and	and	CCONJ
ejpam-3545	116	5	(	(	PUNCT
ejpam-3545	116	6	b1	b1	NOUN
ejpam-3545	116	7	,	,	PUNCT
ejpam-3545	116	8	b2	b2	NOUN
ejpam-3545	116	9	,	,	PUNCT
ejpam-3545	116	10	.	.	PUNCT
ejpam-3545	116	11	.	.	PUNCT
ejpam-3545	117	1	.	.	PUNCT
ejpam-3545	118	1	,	,	PUNCT
ejpam-3545	118	2	bn	bn	X
ejpam-3545	118	3	)	)	PUNCT
ejpam-3545	118	4	are	be	AUX
ejpam-3545	118	5	vectors	vector	NOUN
ejpam-3545	118	6	from	from	ADP
ejpam-3545	118	7	v	v	NOUN
ejpam-3545	118	8	na	na	ADP
ejpam-3545	118	9	,	,	PUNCT
ejpam-3545	118	10	then	then	ADV
ejpam-3545	118	11	(	(	PUNCT
ejpam-3545	118	12	a1	a1	PROPN
ejpam-3545	118	13	,	,	PUNCT
ejpam-3545	118	14	a2	a2	PROPN
ejpam-3545	118	15	,	,	PUNCT
ejpam-3545	118	16	.	.	PUNCT
ejpam-3545	118	17	.	.	PUNCT
ejpam-3545	119	1	.	.	PUNCT
ejpam-3545	120	1	,	,	PUNCT
ejpam-3545	120	2	an	an	X
ejpam-3545	120	3	)	)	PUNCT
ejpam-3545	120	4	≤	≤	NOUN
ejpam-3545	120	5	(	(	PUNCT
ejpam-3545	120	6	b1	b1	NOUN
ejpam-3545	120	7	,	,	PUNCT
ejpam-3545	120	8	b2	b2	NOUN
ejpam-3545	120	9	,	,	PUNCT
ejpam-3545	120	10	.	.	PUNCT
ejpam-3545	120	11	.	.	PUNCT
ejpam-3545	121	1	.	.	PUNCT
ejpam-3545	122	1	,	,	PUNCT
ejpam-3545	122	2	bn	bn	X
ejpam-3545	122	3	)	)	PUNCT
ejpam-3545	123	1	if	if	SCONJ
ejpam-3545	123	2	and	and	CCONJ
ejpam-3545	123	3	only	only	ADV
ejpam-3545	123	4	if	if	SCONJ
ejpam-3545	123	5	aj	aj	PROPN
ejpam-3545	123	6	≤	≤	PRON
ejpam-3545	123	7	bj	bj	VERB
ejpam-3545	123	8	for	for	ADP
ejpam-3545	123	9	all	all	DET
ejpam-3545	123	10	j	j	NOUN
ejpam-3545	123	11	=	=	SYM
ejpam-3545	123	12	1	1	NUM
ejpam-3545	123	13	,	,	PUNCT
ejpam-3545	123	14	2	2	NUM
ejpam-3545	123	15	,	,	PUNCT
ejpam-3545	123	16	3	3	NUM
ejpam-3545	123	17	,	,	PUNCT
ejpam-3545	123	18	.	.	PUNCT
ejpam-3545	123	19	.	.	PUNCT
ejpam-3545	124	1	.	.	PUNCT
ejpam-3545	125	1	,	,	PUNCT
ejpam-3545	125	2	n	n	CCONJ
ejpam-3545	125	3	for	for	ADP
ejpam-3545	125	4	matrices	matrix	NOUN
ejpam-3545	125	5	,	,	PUNCT
ejpam-3545	125	6	addition	addition	NOUN
ejpam-3545	125	7	,	,	PUNCT
ejpam-3545	125	8	multiplication	multiplication	NOUN
ejpam-3545	125	9	and	and	CCONJ
ejpam-3545	125	10	order	order	NOUN
ejpam-3545	125	11	are	be	AUX
ejpam-3545	125	12	defined	define	VERB
ejpam-3545	125	13	in	in	ADP
ejpam-3545	125	14	a	a	DET
ejpam-3545	125	15	similar	similar	ADJ
ejpam-3545	125	16	way	way	NOUN
ejpam-3545	125	17	.	.	PUNCT
ejpam-3545	126	1	note	note	VERB
ejpam-3545	126	2	that	that	SCONJ
ejpam-3545	126	3	the	the	DET
ejpam-3545	126	4	defined	define	VERB
ejpam-3545	126	5	multiplication	multiplication	NOUN
ejpam-3545	126	6	is	be	AUX
ejpam-3545	126	7	scalar	scalar	ADJ
ejpam-3545	126	8	multiplication	multiplication	NOUN
ejpam-3545	126	9	of	of	ADP
ejpam-3545	126	10	vectors	vector	NOUN
ejpam-3545	126	11	and	and	CCONJ
ejpam-3545	126	12	matrices	matrix	NOUN
ejpam-3545	126	13	,	,	PUNCT
ejpam-3545	126	14	which	which	PRON
ejpam-3545	126	15	is	be	AUX
ejpam-3545	126	16	different	different	ADJ
ejpam-3545	126	17	from	from	ADP
ejpam-3545	126	18	vector	vector	NOUN
ejpam-3545	126	19	and	and	CCONJ
ejpam-3545	126	20	matrix	matrix	NOUN
ejpam-3545	126	21	multiplication	multiplication	NOUN
ejpam-3545	126	22	.	.	PUNCT
ejpam-3545	127	1	prearithmetics	prearithmetic	NOUN
ejpam-3545	127	2	v	v	VERB
ejpam-3545	127	3	na	na	NOUN
ejpam-3545	127	4	and	and	CCONJ
ejpam-3545	127	5	mn×ma	mn×ma	PROPN
ejpam-3545	127	6	preserve	preserve	VERB
ejpam-3545	127	7	many	many	ADJ
ejpam-3545	127	8	properties	property	NOUN
ejpam-3545	127	9	of	of	ADP
ejpam-3545	127	10	the	the	DET
ejpam-3545	127	11	abstract	abstract	ADJ
ejpam-3545	127	12	prearithmetic	prearithmetic	ADJ
ejpam-3545	127	13	a.	a.	NOUN
ejpam-3545	127	14	for	for	ADP
ejpam-3545	127	15	instance	instance	NOUN
ejpam-3545	127	16	,	,	PUNCT
ejpam-3545	127	17	we	we	PRON
ejpam-3545	127	18	have	have	VERB
ejpam-3545	127	19	the	the	DET
ejpam-3545	127	20	following	follow	VERB
ejpam-3545	127	21	results	result	NOUN
ejpam-3545	127	22	.	.	PUNCT
ejpam-3545	128	1	proposition	proposition	NOUN
ejpam-3545	128	2	2.1	2.1	NUM
ejpam-3545	128	3	.	.	PUNCT
ejpam-3545	129	1	if	if	SCONJ
ejpam-3545	129	2	addition	addition	NOUN
ejpam-3545	129	3	is	be	AUX
ejpam-3545	129	4	commutative	commutative	ADJ
ejpam-3545	129	5	in	in	ADP
ejpam-3545	129	6	an	an	DET
ejpam-3545	129	7	abstract	abstract	ADJ
ejpam-3545	129	8	prearithmetic	prearithmetic	NOUN
ejpam-3545	129	9	a	a	PRON
ejpam-3545	129	10	,	,	PUNCT
ejpam-3545	129	11	then	then	ADV
ejpam-3545	129	12	addition	addition	NOUN
ejpam-3545	129	13	is	be	AUX
ejpam-3545	129	14	commutative	commutative	ADJ
ejpam-3545	129	15	in	in	ADP
ejpam-3545	129	16	the	the	DET
ejpam-3545	129	17	vector	vector	NOUN
ejpam-3545	129	18	prearithmetic	prearithmetic	ADJ
ejpam-3545	129	19	v	v	X
ejpam-3545	129	20	na	na	INTJ
ejpam-3545	130	1	and	and	CCONJ
ejpam-3545	130	2	in	in	ADP
ejpam-3545	130	3	the	the	DET
ejpam-3545	130	4	matrix	matrix	NOUN
ejpam-3545	130	5	prearithmetic	prearithmetic	ADJ
ejpam-3545	130	6	mn×ma	mn×ma	PROPN
ejpam-3545	130	7	.	.	PUNCT
ejpam-3545	131	1	indeed	indeed	ADV
ejpam-3545	131	2	,	,	PUNCT
ejpam-3545	131	3	if	if	SCONJ
ejpam-3545	131	4	the	the	DET
ejpam-3545	131	5	identity	identity	NOUN
ejpam-3545	131	6	a	a	DET
ejpam-3545	131	7	+	+	NOUN
ejpam-3545	131	8	b	b	NOUN
ejpam-3545	131	9	=	=	SYM
ejpam-3545	131	10	b	b	PROPN
ejpam-3545	131	11	+	+	CCONJ
ejpam-3545	131	12	a	a	PRON
ejpam-3545	131	13	is	be	AUX
ejpam-3545	131	14	true	true	ADJ
ejpam-3545	131	15	in	in	ADP
ejpam-3545	131	16	the	the	DET
ejpam-3545	131	17	abstract	abstract	ADJ
ejpam-3545	131	18	prearithmetic	prearithmetic	NOUN
ejpam-3545	131	19	a	a	PRON
ejpam-3545	131	20	,	,	PUNCT
ejpam-3545	131	21	then	then	ADV
ejpam-3545	131	22	in	in	ADP
ejpam-3545	131	23	the	the	DET
ejpam-3545	131	24	vector	vector	NOUN
ejpam-3545	131	25	prearithmetic	prearithmetic	ADJ
ejpam-3545	131	26	v	v	ADP
ejpam-3545	131	27	na	na	NOUN
ejpam-3545	131	28	,	,	PUNCT
ejpam-3545	131	29	we	we	PRON
ejpam-3545	131	30	have	have	VERB
ejpam-3545	131	31	(	(	PUNCT
ejpam-3545	131	32	a1	a1	NOUN
ejpam-3545	131	33	,	,	PUNCT
ejpam-3545	131	34	a2	a2	PROPN
ejpam-3545	131	35	,	,	PUNCT
ejpam-3545	131	36	.	.	PUNCT
ejpam-3545	131	37	.	.	PUNCT
ejpam-3545	131	38	.	.	PUNCT
ejpam-3545	132	1	,	,	PUNCT
ejpam-3545	132	2	an)+(b1	an)+(b1	VERB
ejpam-3545	132	3	,	,	PUNCT
ejpam-3545	132	4	b2	b2	NOUN
ejpam-3545	132	5	,	,	PUNCT
ejpam-3545	132	6	.	.	PUNCT
ejpam-3545	132	7	.	.	PUNCT
ejpam-3545	133	1	.	.	PUNCT
ejpam-3545	134	1	,	,	PUNCT
ejpam-3545	134	2	bn	bn	X
ejpam-3545	134	3	)	)	PUNCT
ejpam-3545	134	4	=	=	SYM
ejpam-3545	134	5	(	(	PUNCT
ejpam-3545	134	6	a1+b1	a1+b1	PROPN
ejpam-3545	134	7	,	,	PUNCT
ejpam-3545	134	8	a2+b2	a2+b2	PROPN
ejpam-3545	134	9	,	,	PUNCT
ejpam-3545	134	10	.	.	PUNCT
ejpam-3545	134	11	.	.	PUNCT
ejpam-3545	134	12	.	.	PUNCT
ejpam-3545	135	1	,	,	PUNCT
ejpam-3545	135	2	an+bn	an+bn	X
ejpam-3545	135	3	)	)	PUNCT
ejpam-3545	135	4	=	=	SYM
ejpam-3545	135	5	(	(	PUNCT
ejpam-3545	135	6	b1+a1	b1+a1	PROPN
ejpam-3545	135	7	,	,	PUNCT
ejpam-3545	135	8	b2+a2	b2+a2	PROPN
ejpam-3545	135	9	,	,	PUNCT
ejpam-3545	135	10	.	.	PUNCT
ejpam-3545	135	11	.	.	PUNCT
ejpam-3545	136	1	.	.	PUNCT
ejpam-3545	137	1	,	,	PUNCT
ejpam-3545	137	2	bn+	bn+	VERB
ejpam-3545	137	3	an	an	PRON
ejpam-3545	137	4	)	)	PUNCT
ejpam-3545	137	5	=	=	SYM
ejpam-3545	137	6	(	(	PUNCT
ejpam-3545	137	7	b1	b1	NOUN
ejpam-3545	137	8	,	,	PUNCT
ejpam-3545	137	9	b2	b2	NOUN
ejpam-3545	137	10	,	,	PUNCT
ejpam-3545	137	11	.	.	PUNCT
ejpam-3545	137	12	.	.	PUNCT
ejpam-3545	138	1	.	.	PUNCT
ejpam-3545	139	1	,	,	PUNCT
ejpam-3545	139	2	bn	bn	X
ejpam-3545	139	3	)	)	PUNCT
ejpam-3545	139	4	+	+	CCONJ
ejpam-3545	139	5	(	(	PUNCT
ejpam-3545	139	6	a1	a1	PROPN
ejpam-3545	139	7	,	,	PUNCT
ejpam-3545	139	8	a2	a2	PROPN
ejpam-3545	139	9	,	,	PUNCT
ejpam-3545	139	10	.	.	PUNCT
ejpam-3545	139	11	.	.	PUNCT
ejpam-3545	140	1	.	.	PUNCT
ejpam-3545	141	1	,	,	PUNCT
ejpam-3545	141	2	an	an	X
ejpam-3545	141	3	)	)	PUNCT
ejpam-3545	141	4	it	it	PRON
ejpam-3545	141	5	means	mean	VERB
ejpam-3545	141	6	that	that	SCONJ
ejpam-3545	141	7	addition	addition	NOUN
ejpam-3545	141	8	is	be	AUX
ejpam-3545	141	9	commutative	commutative	ADJ
ejpam-3545	141	10	in	in	ADP
ejpam-3545	141	11	the	the	DET
ejpam-3545	141	12	vector	vector	NOUN
ejpam-3545	141	13	prearithmetic	prearithmetic	ADJ
ejpam-3545	141	14	v	v	ADP
ejpam-3545	141	15	na	na	NOUN
ejpam-3545	141	16	.	.	PUNCT
ejpam-3545	141	17	commutativity	commutativity	NOUN
ejpam-3545	141	18	of	of	ADP
ejpam-3545	141	19	addition	addition	NOUN
ejpam-3545	141	20	in	in	ADP
ejpam-3545	141	21	the	the	DET
ejpam-3545	141	22	matrix	matrix	NOUN
ejpam-3545	141	23	prearithmetic	prearithmetic	ADJ
ejpam-3545	141	24	mn×ma	mn×ma	NOUN
ejpam-3545	141	25	is	be	AUX
ejpam-3545	141	26	proved	prove	VERB
ejpam-3545	141	27	in	in	ADP
ejpam-3545	141	28	a	a	DET
ejpam-3545	141	29	similar	similar	ADJ
ejpam-3545	141	30	way	way	NOUN
ejpam-3545	141	31	.	.	PUNCT
ejpam-3545	142	1	the	the	DET
ejpam-3545	142	2	same	same	ADJ
ejpam-3545	142	3	is	be	AUX
ejpam-3545	142	4	true	true	ADJ
ejpam-3545	142	5	for	for	ADP
ejpam-3545	142	6	multiplication	multiplication	NOUN
ejpam-3545	142	7	.	.	PUNCT
ejpam-3545	143	1	proposition	proposition	NOUN
ejpam-3545	143	2	2.2	2.2	NUM
ejpam-3545	143	3	.	.	PUNCT
ejpam-3545	144	1	if	if	SCONJ
ejpam-3545	144	2	multiplication	multiplication	NOUN
ejpam-3545	144	3	is	be	AUX
ejpam-3545	144	4	commutative	commutative	ADJ
ejpam-3545	144	5	in	in	ADP
ejpam-3545	144	6	an	an	DET
ejpam-3545	144	7	abstract	abstract	ADJ
ejpam-3545	144	8	prearithmetic	prearithmetic	NOUN
ejpam-3545	144	9	a	a	PRON
ejpam-3545	144	10	,	,	PUNCT
ejpam-3545	144	11	then	then	ADV
ejpam-3545	144	12	multiplication	multiplication	NOUN
ejpam-3545	144	13	is	be	AUX
ejpam-3545	144	14	commutative	commutative	ADJ
ejpam-3545	144	15	in	in	ADP
ejpam-3545	144	16	the	the	DET
ejpam-3545	144	17	vector	vector	NOUN
ejpam-3545	144	18	prearithmetic	prearithmetic	ADJ
ejpam-3545	144	19	v	v	X
ejpam-3545	144	20	na	na	INTJ
ejpam-3545	145	1	and	and	CCONJ
ejpam-3545	145	2	in	in	ADP
ejpam-3545	145	3	the	the	DET
ejpam-3545	145	4	matrix	matrix	NOUN
ejpam-3545	145	5	prearithmetic	prearithmetic	ADJ
ejpam-3545	145	6	mn×ma	mn×ma	PROPN
ejpam-3545	145	7	.	.	PUNCT
ejpam-3545	146	1	proof	proof	NOUN
ejpam-3545	146	2	is	be	AUX
ejpam-3545	146	3	similar	similar	ADJ
ejpam-3545	146	4	to	to	ADP
ejpam-3545	146	5	the	the	DET
ejpam-3545	146	6	proof	proof	NOUN
ejpam-3545	146	7	of	of	ADP
ejpam-3545	146	8	proposition	proposition	NOUN
ejpam-3545	146	9	2.1	2.1	NUM
ejpam-3545	146	10	.	.	PUNCT
ejpam-3545	147	1	proposition	proposition	NOUN
ejpam-3545	147	2	2.3	2.3	NUM
ejpam-3545	147	3	.	.	PUNCT
ejpam-3545	148	1	if	if	SCONJ
ejpam-3545	148	2	addition	addition	NOUN
ejpam-3545	148	3	is	be	AUX
ejpam-3545	148	4	associative	associative	ADJ
ejpam-3545	148	5	in	in	ADP
ejpam-3545	148	6	an	an	DET
ejpam-3545	148	7	abstract	abstract	ADJ
ejpam-3545	148	8	prearithmetic	prearithmetic	NOUN
ejpam-3545	148	9	a	a	PRON
ejpam-3545	148	10	,	,	PUNCT
ejpam-3545	148	11	then	then	ADV
ejpam-3545	148	12	addition	addition	NOUN
ejpam-3545	148	13	is	be	AUX
ejpam-3545	148	14	associative	associative	ADJ
ejpam-3545	148	15	in	in	ADP
ejpam-3545	148	16	the	the	DET
ejpam-3545	148	17	vector	vector	NOUN
ejpam-3545	148	18	prearithmetic	prearithmetic	ADJ
ejpam-3545	148	19	v	v	X
ejpam-3545	148	20	na	na	INTJ
ejpam-3545	148	21	and	and	CCONJ
ejpam-3545	148	22	in	in	ADP
ejpam-3545	148	23	the	the	DET
ejpam-3545	148	24	matrix	matrix	NOUN
ejpam-3545	148	25	prearithmetic	prearithmetic	ADJ
ejpam-3545	148	26	mn×ma	mn×ma	PROPN
ejpam-3545	148	27	.	.	PUNCT
ejpam-3545	149	1	proof	proof	NOUN
ejpam-3545	149	2	is	be	AUX
ejpam-3545	149	3	similar	similar	ADJ
ejpam-3545	149	4	to	to	ADP
ejpam-3545	149	5	the	the	DET
ejpam-3545	149	6	proof	proof	NOUN
ejpam-3545	149	7	of	of	ADP
ejpam-3545	149	8	proposition	proposition	NOUN
ejpam-3545	149	9	2.1	2.1	NUM
ejpam-3545	149	10	.	.	PUNCT
ejpam-3545	150	1	the	the	DET
ejpam-3545	150	2	same	same	ADJ
ejpam-3545	150	3	is	be	AUX
ejpam-3545	150	4	true	true	ADJ
ejpam-3545	150	5	for	for	ADP
ejpam-3545	150	6	multiplication	multiplication	NOUN
ejpam-3545	150	7	.	.	PUNCT
ejpam-3545	151	1	proposition	proposition	NOUN
ejpam-3545	151	2	2.4	2.4	NUM
ejpam-3545	151	3	.	.	PUNCT
ejpam-3545	152	1	if	if	SCONJ
ejpam-3545	152	2	multiplication	multiplication	NOUN
ejpam-3545	152	3	is	be	AUX
ejpam-3545	152	4	associative	associative	ADJ
ejpam-3545	152	5	in	in	ADP
ejpam-3545	152	6	an	an	DET
ejpam-3545	152	7	abstract	abstract	ADJ
ejpam-3545	152	8	prearithmetic	prearithmetic	NOUN
ejpam-3545	152	9	a	a	PRON
ejpam-3545	152	10	,	,	PUNCT
ejpam-3545	152	11	then	then	ADV
ejpam-3545	152	12	multiplication	multiplication	NOUN
ejpam-3545	152	13	is	be	AUX
ejpam-3545	152	14	associative	associative	ADJ
ejpam-3545	152	15	in	in	ADP
ejpam-3545	152	16	the	the	DET
ejpam-3545	152	17	vector	vector	NOUN
ejpam-3545	152	18	prearithmetic	prearithmetic	ADJ
ejpam-3545	152	19	v	v	AUX
ejpam-3545	152	20	na	na	INTJ
ejpam-3545	152	21	and	and	CCONJ
ejpam-3545	152	22	in	in	ADP
ejpam-3545	152	23	the	the	DET
ejpam-3545	152	24	matrix	matrix	NOUN
ejpam-3545	152	25	prearithmetic	prearithmetic	ADJ
ejpam-3545	152	26	mn×ma	mn×ma	PROPN
ejpam-3545	152	27	.	.	PUNCT
ejpam-3545	153	1	proof	proof	NOUN
ejpam-3545	153	2	is	be	AUX
ejpam-3545	153	3	similar	similar	ADJ
ejpam-3545	153	4	to	to	ADP
ejpam-3545	153	5	the	the	DET
ejpam-3545	153	6	proof	proof	NOUN
ejpam-3545	153	7	of	of	ADP
ejpam-3545	153	8	proposition	proposition	NOUN
ejpam-3545	153	9	2.1	2.1	NUM
ejpam-3545	153	10	.	.	PUNCT
ejpam-3545	154	1	in	in	ADP
ejpam-3545	154	2	the	the	DET
ejpam-3545	154	3	diophantine	diophantine	NOUN
ejpam-3545	154	4	arithmetic	arithmetic	ADJ
ejpam-3545	154	5	n	n	NOUN
ejpam-3545	154	6	,	,	PUNCT
ejpam-3545	154	7	multiplication	multiplication	NOUN
ejpam-3545	154	8	is	be	AUX
ejpam-3545	154	9	distributive	distributive	ADJ
ejpam-3545	154	10	with	with	ADP
ejpam-3545	154	11	respect	respect	NOUN
ejpam-3545	154	12	to	to	ADP
ejpam-3545	154	13	addition	addition	NOUN
ejpam-3545	154	14	,	,	PUNCT
ejpam-3545	154	15	i.e.	i.e.	X
ejpam-3545	154	16	,	,	PUNCT
ejpam-3545	154	17	the	the	DET
ejpam-3545	154	18	following	follow	VERB
ejpam-3545	154	19	identities	identity	NOUN
ejpam-3545	154	20	hold	hold	VERB
ejpam-3545	154	21	x	x	X
ejpam-3545	154	22	·	·	PUNCT
ejpam-3545	154	23	(	(	PUNCT
ejpam-3545	154	24	y	y	PROPN
ejpam-3545	154	25	+	+	PROPN
ejpam-3545	154	26	z	z	X
ejpam-3545	154	27	)	)	PUNCT
ejpam-3545	154	28	=	=	PUNCT
ejpam-3545	155	1	x	x	PUNCT
ejpam-3545	155	2	·	·	PUNCT
ejpam-3545	155	3	y	y	X
ejpam-3545	155	4	+	+	NOUN
ejpam-3545	155	5	x	x	X
ejpam-3545	155	6	·	·	PUNCT
ejpam-3545	155	7	z	z	X
ejpam-3545	155	8	(	(	PUNCT
ejpam-3545	155	9	y	y	PROPN
ejpam-3545	155	10	+	+	PROPN
ejpam-3545	155	11	z	z	NOUN
ejpam-3545	155	12	)	)	PUNCT
ejpam-3545	155	13	·	·	PUNCT
ejpam-3545	156	1	x	x	PUNCT
ejpam-3545	156	2	=	=	PUNCT
ejpam-3545	156	3	y	y	PROPN
ejpam-3545	156	4	·	·	PUNCT
ejpam-3545	156	5	x	x	PUNCT
ejpam-3545	157	1	+	+	PUNCT
ejpam-3545	157	2	z	z	NOUN
ejpam-3545	157	3	·	·	PUNCT
ejpam-3545	157	4	x	x	PUNCT
ejpam-3545	157	5	however	however	ADV
ejpam-3545	157	6	,	,	PUNCT
ejpam-3545	157	7	in	in	ADP
ejpam-3545	157	8	abstract	abstract	ADJ
ejpam-3545	157	9	prearithmetics	prearithmetic	NOUN
ejpam-3545	157	10	,	,	PUNCT
ejpam-3545	157	11	multiplication	multiplication	NOUN
ejpam-3545	157	12	is	be	AUX
ejpam-3545	157	13	not	not	PART
ejpam-3545	157	14	always	always	ADV
ejpam-3545	157	15	commutative	commutative	ADJ
ejpam-3545	157	16	and	and	CCONJ
ejpam-3545	157	17	we	we	PRON
ejpam-3545	157	18	need	need	VERB
ejpam-3545	157	19	to	to	PART
ejpam-3545	157	20	discern	discern	VERB
ejpam-3545	157	21	three	three	NUM
ejpam-3545	157	22	kinds	kind	NOUN
ejpam-3545	157	23	of	of	ADP
ejpam-3545	157	24	distributivity	distributivity	NOUN
ejpam-3545	157	25	.	.	PUNCT
ejpam-3545	158	1	namely	namely	ADV
ejpam-3545	158	2	,	,	PUNCT
ejpam-3545	158	3	distributivity	distributivity	NOUN
ejpam-3545	158	4	from	from	ADP
ejpam-3545	158	5	the	the	DET
ejpam-3545	158	6	left	left	NOUN
ejpam-3545	158	7	x	x	X
ejpam-3545	158	8	·	·	PUNCT
ejpam-3545	158	9	(	(	PUNCT
ejpam-3545	158	10	y	y	PROPN
ejpam-3545	158	11	+	+	PROPN
ejpam-3545	158	12	z	z	X
ejpam-3545	158	13	)	)	PUNCT
ejpam-3545	158	14	=	=	PUNCT
ejpam-3545	159	1	x	x	PUNCT
ejpam-3545	159	2	·	·	PUNCT
ejpam-3545	159	3	y	y	X
ejpam-3545	159	4	+	+	NOUN
ejpam-3545	159	5	x	x	X
ejpam-3545	159	6	·	·	PUNCT
ejpam-3545	159	7	z	z	NOUN
ejpam-3545	159	8	and	and	CCONJ
ejpam-3545	159	9	distributivity	distributivity	NOUN
ejpam-3545	159	10	from	from	ADP
ejpam-3545	159	11	the	the	DET
ejpam-3545	159	12	right	right	ADJ
ejpam-3545	159	13	m.	m.	NOUN
ejpam-3545	159	14	burgin	burgin	PROPN
ejpam-3545	159	15	/	/	SYM
ejpam-3545	159	16	eur	eur	PROPN
ejpam-3545	159	17	.	.	PUNCT
ejpam-3545	160	1	j.	j.	PROPN
ejpam-3545	160	2	pure	pure	PROPN
ejpam-3545	160	3	appl	appl	PROPN
ejpam-3545	160	4	.	.	PROPN
ejpam-3545	160	5	math	math	PROPN
ejpam-3545	160	6	,	,	PUNCT
ejpam-3545	160	7	12	12	NUM
ejpam-3545	160	8	(	(	PUNCT
ejpam-3545	160	9	4	4	NUM
ejpam-3545	160	10	)	)	PUNCT
ejpam-3545	160	11	(	(	PUNCT
ejpam-3545	160	12	2019	2019	NUM
ejpam-3545	160	13	)	)	PUNCT
ejpam-3545	160	14	,	,	PUNCT
ejpam-3545	160	15	1787	1787	NUM
ejpam-3545	160	16	-	-	SYM
ejpam-3545	160	17	1810	1810	NUM
ejpam-3545	160	18	1793	1793	NUM
ejpam-3545	160	19	(	(	PUNCT
ejpam-3545	160	20	y	y	PROPN
ejpam-3545	160	21	+	+	PROPN
ejpam-3545	160	22	z	z	NOUN
ejpam-3545	160	23	)	)	PUNCT
ejpam-3545	160	24	·	·	PUNCT
ejpam-3545	161	1	x	x	PUNCT
ejpam-3545	161	2	=	=	PUNCT
ejpam-3545	161	3	y	y	PROPN
ejpam-3545	161	4	·	·	PUNCT
ejpam-3545	161	5	x	x	PUNCT
ejpam-3545	162	1	+	+	PUNCT
ejpam-3545	162	2	z	z	NOUN
ejpam-3545	162	3	·	·	PUNCT
ejpam-3545	162	4	x	x	PUNCT
ejpam-3545	162	5	besides	besides	SCONJ
ejpam-3545	162	6	,	,	PUNCT
ejpam-3545	162	7	multiplication	multiplication	NOUN
ejpam-3545	162	8	is	be	AUX
ejpam-3545	162	9	distributive	distributive	ADJ
ejpam-3545	162	10	with	with	ADP
ejpam-3545	162	11	respect	respect	NOUN
ejpam-3545	162	12	to	to	ADP
ejpam-3545	162	13	addition	addition	NOUN
ejpam-3545	162	14	when	when	SCONJ
ejpam-3545	162	15	both	both	DET
ejpam-3545	162	16	identities	identity	NOUN
ejpam-3545	162	17	hold	hold	VERB
ejpam-3545	162	18	.	.	PUNCT
ejpam-3545	163	1	proposition	proposition	NOUN
ejpam-3545	163	2	2.5	2.5	NUM
ejpam-3545	163	3	.	.	PUNCT
ejpam-3545	164	1	if	if	SCONJ
ejpam-3545	164	2	multiplication	multiplication	NOUN
ejpam-3545	164	3	is	be	AUX
ejpam-3545	164	4	distributive	distributive	ADJ
ejpam-3545	164	5	(	(	PUNCT
ejpam-3545	164	6	distributive	distributive	ADJ
ejpam-3545	164	7	from	from	ADP
ejpam-3545	164	8	the	the	DET
ejpam-3545	164	9	left	left	NOUN
ejpam-3545	164	10	or	or	CCONJ
ejpam-3545	164	11	distributive	distributive	ADJ
ejpam-3545	164	12	from	from	ADP
ejpam-3545	164	13	the	the	DET
ejpam-3545	164	14	right	right	NOUN
ejpam-3545	164	15	)	)	PUNCT
ejpam-3545	164	16	with	with	ADP
ejpam-3545	164	17	respect	respect	NOUN
ejpam-3545	164	18	to	to	ADP
ejpam-3545	164	19	addition	addition	NOUN
ejpam-3545	164	20	in	in	ADP
ejpam-3545	164	21	an	an	DET
ejpam-3545	164	22	abstract	abstract	ADJ
ejpam-3545	164	23	prearithmetic	prearithmetic	NOUN
ejpam-3545	164	24	a	a	PRON
ejpam-3545	164	25	,	,	PUNCT
ejpam-3545	164	26	then	then	ADV
ejpam-3545	164	27	multiplication	multiplication	NOUN
ejpam-3545	164	28	is	be	AUX
ejpam-3545	164	29	distributive	distributive	ADJ
ejpam-3545	164	30	(	(	PUNCT
ejpam-3545	164	31	distributive	distributive	ADJ
ejpam-3545	164	32	from	from	ADP
ejpam-3545	164	33	the	the	DET
ejpam-3545	164	34	left	left	NOUN
ejpam-3545	164	35	or	or	CCONJ
ejpam-3545	164	36	distributive	distributive	ADJ
ejpam-3545	164	37	from	from	ADP
ejpam-3545	164	38	the	the	DET
ejpam-3545	164	39	right	right	NOUN
ejpam-3545	164	40	)	)	PUNCT
ejpam-3545	164	41	with	with	ADP
ejpam-3545	164	42	respect	respect	NOUN
ejpam-3545	164	43	to	to	ADP
ejpam-3545	164	44	addition	addition	NOUN
ejpam-3545	164	45	in	in	ADP
ejpam-3545	164	46	the	the	DET
ejpam-3545	164	47	vector	vector	NOUN
ejpam-3545	164	48	prearithmetic	prearithmetic	ADJ
ejpam-3545	164	49	v	v	X
ejpam-3545	164	50	na	na	INTJ
ejpam-3545	164	51	and	and	CCONJ
ejpam-3545	164	52	in	in	ADP
ejpam-3545	164	53	the	the	DET
ejpam-3545	164	54	matrix	matrix	NOUN
ejpam-3545	164	55	prearithmetic	prearithmetic	ADJ
ejpam-3545	164	56	mn×ma	mn×ma	PROPN
ejpam-3545	164	57	.	.	PUNCT
ejpam-3545	165	1	proof	proof	NOUN
ejpam-3545	165	2	is	be	AUX
ejpam-3545	165	3	similar	similar	ADJ
ejpam-3545	165	4	to	to	ADP
ejpam-3545	165	5	the	the	DET
ejpam-3545	165	6	proof	proof	NOUN
ejpam-3545	165	7	of	of	ADP
ejpam-3545	165	8	proposition	proposition	NOUN
ejpam-3545	165	9	2.1	2.1	NUM
ejpam-3545	165	10	.	.	PUNCT
ejpam-3545	166	1	remark	remark	NOUN
ejpam-3545	166	2	1	1	NUM
ejpam-3545	166	3	.	.	PUNCT
ejpam-3545	167	1	having	have	VERB
ejpam-3545	167	2	an	an	DET
ejpam-3545	167	3	abstract	abstract	ADJ
ejpam-3545	167	4	prearithmetic	prearithmetic	NOUN
ejpam-3545	167	5	a	a	DET
ejpam-3545	167	6	=	=	X
ejpam-3545	167	7	(	(	PUNCT
ejpam-3545	167	8	a	a	X
ejpam-3545	167	9	;	;	PUNCT
ejpam-3545	167	10	+	+	ADJ
ejpam-3545	167	11	,	,	PUNCT
ejpam-3545	167	12	◦	◦	NOUN
ejpam-3545	167	13	,	,	PUNCT
ejpam-3545	167	14	≤	≤	NUM
ejpam-3545	167	15	)	)	PUNCT
ejpam-3545	167	16	,	,	PUNCT
ejpam-3545	167	17	it	it	PRON
ejpam-3545	167	18	is	be	AUX
ejpam-3545	167	19	possible	possible	ADJ
ejpam-3545	167	20	to	to	PART
ejpam-3545	167	21	build	build	VERB
ejpam-3545	167	22	not	not	PART
ejpam-3545	167	23	only	only	ADV
ejpam-3545	167	24	abstract	abstract	ADJ
ejpam-3545	167	25	prearithmetics	prearithmetic	NOUN
ejpam-3545	167	26	of	of	ADP
ejpam-3545	167	27	a	a	DET
ejpam-3545	167	28	-	-	PUNCT
ejpam-3545	167	29	vectors	vector	NOUN
ejpam-3545	167	30	and	and	CCONJ
ejpam-3545	167	31	a	a	DET
ejpam-3545	167	32	-	-	PUNCT
ejpam-3545	167	33	matrices	matrix	NOUN
ejpam-3545	167	34	but	but	CCONJ
ejpam-3545	167	35	also	also	ADV
ejpam-3545	167	36	abstract	abstract	ADJ
ejpam-3545	167	37	prearithmetics	prearithmetic	NOUN
ejpam-3545	167	38	of	of	ADP
ejpam-3545	167	39	multidimensional	multidimensional	ADJ
ejpam-3545	167	40	matrices	matrix	NOUN
ejpam-3545	167	41	or	or	CCONJ
ejpam-3545	167	42	arrays	array	NOUN
ejpam-3545	167	43	in	in	ADP
ejpam-3545	167	44	a	a	PRON
ejpam-3545	167	45	of	of	ADP
ejpam-3545	167	46	arbitrary	arbitrary	ADJ
ejpam-3545	167	47	dimensions	dimension	NOUN
ejpam-3545	167	48	,	,	PUNCT
ejpam-3545	167	49	i.e.	i.e.	X
ejpam-3545	167	50	,	,	PUNCT
ejpam-3545	167	51	multidimensional	multidimensional	ADJ
ejpam-3545	167	52	a	a	DET
ejpam-3545	167	53	-	-	PUNCT
ejpam-3545	167	54	matrices	matrix	NOUN
ejpam-3545	167	55	or	or	CCONJ
ejpam-3545	167	56	a	a	PRON
ejpam-3545	167	57	-	-	PUNCT
ejpam-3545	167	58	arrays	array	NOUN
ejpam-3545	167	59	,	,	PUNCT
ejpam-3545	167	60	and	and	CCONJ
ejpam-3545	167	61	form	form	VERB
ejpam-3545	167	62	their	their	PRON
ejpam-3545	167	63	prearithmetics	prearithmetic	NOUN
ejpam-3545	167	64	exploring	explore	VERB
ejpam-3545	167	65	what	what	PRON
ejpam-3545	167	66	properties	property	NOUN
ejpam-3545	167	67	they	they	PRON
ejpam-3545	167	68	inherit	inherit	VERB
ejpam-3545	167	69	from	from	ADP
ejpam-3545	167	70	the	the	DET
ejpam-3545	167	71	initial	initial	ADJ
ejpam-3545	167	72	abstract	abstract	ADJ
ejpam-3545	167	73	prearithmetic	prearithmetic	ADJ
ejpam-3545	167	74	a.	a.	NOUN
ejpam-3545	167	75	another	another	DET
ejpam-3545	167	76	way	way	NOUN
ejpam-3545	167	77	to	to	PART
ejpam-3545	167	78	build	build	VERB
ejpam-3545	167	79	new	new	ADJ
ejpam-3545	167	80	prearithmetics	prearithmetic	NOUN
ejpam-3545	167	81	from	from	ADP
ejpam-3545	167	82	the	the	DET
ejpam-3545	167	83	existing	exist	VERB
ejpam-3545	167	84	ones	one	NOUN
ejpam-3545	167	85	utilizes	utilize	VERB
ejpam-3545	167	86	projectivity	projectivity	NOUN
ejpam-3545	167	87	relations	relation	NOUN
ejpam-3545	167	88	,	,	PUNCT
ejpam-3545	167	89	different	different	ADJ
ejpam-3545	167	90	kinds	kind	NOUN
ejpam-3545	167	91	of	of	ADP
ejpam-3545	167	92	which	which	PRON
ejpam-3545	167	93	are	be	AUX
ejpam-3545	167	94	studied	study	VERB
ejpam-3545	167	95	in	in	ADP
ejpam-3545	167	96	the	the	DET
ejpam-3545	167	97	next	next	ADJ
ejpam-3545	167	98	section	section	NOUN
ejpam-3545	167	99	.	.	PUNCT
ejpam-3545	168	1	3	3	X
ejpam-3545	168	2	.	.	X
ejpam-3545	168	3	weak	weak	ADJ
ejpam-3545	168	4	projectivity	projectivity	NOUN
ejpam-3545	168	5	in	in	ADP
ejpam-3545	168	6	abstract	abstract	ADJ
ejpam-3545	168	7	prearithmetics	prearithmetic	NOUN
ejpam-3545	168	8	let	let	VERB
ejpam-3545	168	9	us	we	PRON
ejpam-3545	168	10	take	take	VERB
ejpam-3545	168	11	two	two	NUM
ejpam-3545	168	12	abstract	abstract	ADJ
ejpam-3545	168	13	prearithmetics	prearithmetic	NOUN
ejpam-3545	168	14	a1	a1	NOUN
ejpam-3545	168	15	=	=	SYM
ejpam-3545	168	16	(	(	PUNCT
ejpam-3545	168	17	a1	a1	PROPN
ejpam-3545	168	18	;	;	PUNCT
ejpam-3545	168	19	+1	+1	PROPN
ejpam-3545	168	20	,	,	PUNCT
ejpam-3545	168	21	◦	◦	NOUN
ejpam-3545	168	22	1,≤1	1,≤1	ADJ
ejpam-3545	168	23	)	)	PUNCT
ejpam-3545	168	24	and	and	CCONJ
ejpam-3545	168	25	a2	a2	PROPN
ejpam-3545	168	26	=	=	SYM
ejpam-3545	168	27	(	(	PUNCT
ejpam-3545	168	28	a2	a2	PROPN
ejpam-3545	168	29	;	;	PUNCT
ejpam-3545	168	30	+2	+2	PROPN
ejpam-3545	168	31	,	,	PUNCT
ejpam-3545	168	32	◦	◦	NOUN
ejpam-3545	168	33	2,≤2	2,≤2	NOUN
ejpam-3545	168	34	)	)	PUNCT
ejpam-3545	168	35	.	.	PUNCT
ejpam-3545	169	1	definition	definition	NOUN
ejpam-3545	169	2	1	1	NUM
ejpam-3545	169	3	.	.	PUNCT
ejpam-3545	170	1	a	a	X
ejpam-3545	170	2	)	)	PUNCT
ejpam-3545	170	3	addition	addition	NOUN
ejpam-3545	170	4	+1	+1	PRON
ejpam-3545	170	5	in	in	ADP
ejpam-3545	170	6	the	the	DET
ejpam-3545	170	7	abstract	abstract	ADJ
ejpam-3545	170	8	prearithmetic	prearithmetic	ADJ
ejpam-3545	170	9	a1	a1	NOUN
ejpam-3545	170	10	=	=	SYM
ejpam-3545	170	11	(	(	PUNCT
ejpam-3545	170	12	a1	a1	PROPN
ejpam-3545	170	13	;	;	PUNCT
ejpam-3545	170	14	+1	+1	PROPN
ejpam-3545	170	15	,	,	PUNCT
ejpam-3545	170	16	◦	◦	NOUN
ejpam-3545	170	17	1	1	NUM
ejpam-3545	170	18	,	,	PUNCT
ejpam-3545	170	19	·	·	PUNCT
ejpam-3545	170	20	≤1	≤1	NOUN
ejpam-3545	170	21	)	)	PUNCT
ejpam-3545	170	22	is	be	AUX
ejpam-3545	170	23	called	call	VERB
ejpam-3545	170	24	weakly	weakly	ADV
ejpam-3545	170	25	projective	projective	NOUN
ejpam-3545	170	26	with	with	ADP
ejpam-3545	170	27	respect	respect	NOUN
ejpam-3545	170	28	to	to	ADP
ejpam-3545	170	29	addition	addition	NOUN
ejpam-3545	170	30	+2	+2	ADP
ejpam-3545	170	31	in	in	ADP
ejpam-3545	170	32	the	the	DET
ejpam-3545	170	33	abstract	abstract	ADJ
ejpam-3545	170	34	prearithmetic	prearithmetic	ADJ
ejpam-3545	170	35	a2	a2	PROPN
ejpam-3545	170	36	=	=	SYM
ejpam-3545	170	37	(	(	PUNCT
ejpam-3545	170	38	a2	a2	PROPN
ejpam-3545	170	39	;	;	PUNCT
ejpam-3545	170	40	+2	+2	PROPN
ejpam-3545	170	41	,	,	PUNCT
ejpam-3545	170	42	◦	◦	NOUN
ejpam-3545	170	43	2,≤2	2,≤2	NOUN
ejpam-3545	170	44	)	)	PUNCT
ejpam-3545	170	45	if	if	SCONJ
ejpam-3545	170	46	there	there	PRON
ejpam-3545	170	47	are	be	VERB
ejpam-3545	170	48	three	three	NUM
ejpam-3545	170	49	mappings	mapping	NOUN
ejpam-3545	170	50	g1	g1	NOUN
ejpam-3545	170	51	:	:	PUNCT
ejpam-3545	170	52	a1	a1	NOUN
ejpam-3545	170	53	→	→	SYM
ejpam-3545	170	54	a2	a2	PROPN
ejpam-3545	170	55	,	,	PUNCT
ejpam-3545	170	56	g2	g2	PROPN
ejpam-3545	170	57	:	:	PUNCT
ejpam-3545	170	58	a1	a1	PROPN
ejpam-3545	170	59	→	→	SYM
ejpam-3545	170	60	a2	a2	PROPN
ejpam-3545	170	61	and	and	CCONJ
ejpam-3545	170	62	h	h	NOUN
ejpam-3545	170	63	:	:	PUNCT
ejpam-3545	170	64	a2	a2	PROPN
ejpam-3545	170	65	→	→	SYM
ejpam-3545	170	66	a1	a1	NOUN
ejpam-3545	170	67	and	and	CCONJ
ejpam-3545	170	68	the	the	DET
ejpam-3545	170	69	following	follow	VERB
ejpam-3545	170	70	equality	equality	NOUN
ejpam-3545	170	71	is	be	AUX
ejpam-3545	170	72	valid	valid	ADJ
ejpam-3545	170	73	for	for	ADP
ejpam-3545	170	74	all	all	DET
ejpam-3545	170	75	elements	element	NOUN
ejpam-3545	170	76	a	a	PRON
ejpam-3545	170	77	and	and	CCONJ
ejpam-3545	170	78	b	b	NOUN
ejpam-3545	170	79	from	from	ADP
ejpam-3545	170	80	a1	a1	PROPN
ejpam-3545	170	81	:	:	PUNCT
ejpam-3545	170	82	a	a	DET
ejpam-3545	170	83	+1	+1	PROPN
ejpam-3545	170	84	b	b	PROPN
ejpam-3545	170	85	=	=	SYM
ejpam-3545	170	86	h(g1(a	h(g1(a	PROPN
ejpam-3545	170	87	)	)	PUNCT
ejpam-3545	170	88	+2	+2	PROPN
ejpam-3545	170	89	g2(b	g2(b	PROPN
ejpam-3545	170	90	)	)	PUNCT
ejpam-3545	170	91	)	)	PUNCT
ejpam-3545	171	1	b	b	X
ejpam-3545	171	2	)	)	PUNCT
ejpam-3545	171	3	the	the	DET
ejpam-3545	171	4	mappings	mapping	NOUN
ejpam-3545	171	5	g1	g1	NOUN
ejpam-3545	171	6	and	and	CCONJ
ejpam-3545	171	7	g2	g2	PROPN
ejpam-3545	171	8	are	be	AUX
ejpam-3545	171	9	called	call	VERB
ejpam-3545	171	10	the	the	DET
ejpam-3545	171	11	projectors	projector	NOUN
ejpam-3545	171	12	and	and	CCONJ
ejpam-3545	171	13	the	the	DET
ejpam-3545	171	14	mapping	mapping	NOUN
ejpam-3545	171	15	h	h	NOUN
ejpam-3545	171	16	is	be	AUX
ejpam-3545	171	17	called	call	VERB
ejpam-3545	171	18	the	the	DET
ejpam-3545	171	19	coprojector	coprojector	NOUN
ejpam-3545	171	20	for	for	ADP
ejpam-3545	171	21	the	the	DET
ejpam-3545	171	22	pair	pair	NOUN
ejpam-3545	171	23	(	(	PUNCT
ejpam-3545	171	24	+1,+2	+1,+2	NUM
ejpam-3545	171	25	)	)	PUNCT
ejpam-3545	171	26	.	.	PUNCT
ejpam-3545	172	1	c	c	X
ejpam-3545	172	2	)	)	PUNCT
ejpam-3545	172	3	in	in	ADP
ejpam-3545	172	4	this	this	DET
ejpam-3545	172	5	case	case	NOUN
ejpam-3545	172	6	,	,	PUNCT
ejpam-3545	172	7	we	we	PRON
ejpam-3545	172	8	say	say	VERB
ejpam-3545	172	9	that	that	SCONJ
ejpam-3545	172	10	addition	addition	NOUN
ejpam-3545	172	11	in	in	ADP
ejpam-3545	172	12	a2	a2	PROPN
ejpam-3545	172	13	is	be	AUX
ejpam-3545	172	14	weakly	weakly	ADV
ejpam-3545	172	15	projected	project	VERB
ejpam-3545	172	16	onto	onto	ADP
ejpam-3545	172	17	addition	addition	NOUN
ejpam-3545	172	18	in	in	ADP
ejpam-3545	172	19	a1	a1	NOUN
ejpam-3545	172	20	,	,	PUNCT
ejpam-3545	172	21	while	while	SCONJ
ejpam-3545	172	22	addition	addition	NOUN
ejpam-3545	172	23	in	in	ADP
ejpam-3545	172	24	a1	a1	NOUN
ejpam-3545	172	25	is	be	AUX
ejpam-3545	172	26	a	a	DET
ejpam-3545	172	27	weak	weak	ADJ
ejpam-3545	172	28	projection	projection	NOUN
ejpam-3545	172	29	of	of	ADP
ejpam-3545	172	30	addition	addition	NOUN
ejpam-3545	172	31	in	in	ADP
ejpam-3545	172	32	a2	a2	PROPN
ejpam-3545	172	33	.	.	PUNCT
ejpam-3545	173	1	we	we	PRON
ejpam-3545	173	2	also	also	ADV
ejpam-3545	173	3	say	say	VERB
ejpam-3545	173	4	that	that	SCONJ
ejpam-3545	173	5	there	there	PRON
ejpam-3545	173	6	is	be	VERB
ejpam-3545	173	7	a	a	DET
ejpam-3545	173	8	weak	weak	ADJ
ejpam-3545	173	9	projectivity	projectivity	NOUN
ejpam-3545	173	10	between	between	ADP
ejpam-3545	173	11	addition	addition	NOUN
ejpam-3545	173	12	in	in	ADP
ejpam-3545	173	13	the	the	DET
ejpam-3545	173	14	prearithmetic	prearithmetic	ADJ
ejpam-3545	173	15	a1	a1	NOUN
ejpam-3545	173	16	and	and	CCONJ
ejpam-3545	173	17	addition	addition	NOUN
ejpam-3545	173	18	in	in	ADP
ejpam-3545	173	19	the	the	DET
ejpam-3545	173	20	prearithmetic	prearithmetic	PROPN
ejpam-3545	173	21	a2	a2	PROPN
ejpam-3545	173	22	and	and	CCONJ
ejpam-3545	173	23	there	there	PRON
ejpam-3545	173	24	is	be	VERB
ejpam-3545	173	25	a	a	DET
ejpam-3545	173	26	weak	weak	ADJ
ejpam-3545	173	27	inverse	inverse	NOUN
ejpam-3545	173	28	projectivity	projectivity	NOUN
ejpam-3545	173	29	between	between	ADP
ejpam-3545	173	30	addition	addition	NOUN
ejpam-3545	173	31	in	in	ADP
ejpam-3545	173	32	the	the	DET
ejpam-3545	173	33	prearithmetic	prearithmetic	ADJ
ejpam-3545	173	34	a2	a2	PROPN
ejpam-3545	173	35	and	and	CCONJ
ejpam-3545	173	36	addition	addition	NOUN
ejpam-3545	173	37	in	in	ADP
ejpam-3545	173	38	the	the	DET
ejpam-3545	173	39	prearithmetic	prearithmetic	ADJ
ejpam-3545	173	40	a1	a1	NOUN
ejpam-3545	173	41	.	.	PUNCT
ejpam-3545	174	1	this	this	PRON
ejpam-3545	174	2	means	mean	VERB
ejpam-3545	174	3	that	that	SCONJ
ejpam-3545	174	4	there	there	PRON
ejpam-3545	174	5	is	be	VERB
ejpam-3545	174	6	partial	partial	ADJ
ejpam-3545	174	7	weak	weak	ADJ
ejpam-3545	174	8	projectivity	projectivity	NOUN
ejpam-3545	174	9	between	between	ADP
ejpam-3545	174	10	the	the	DET
ejpam-3545	174	11	prearithmetics	prearithmetic	NOUN
ejpam-3545	174	12	a1	a1	NOUN
ejpam-3545	174	13	and	and	CCONJ
ejpam-3545	174	14	a2	a2	PROPN
ejpam-3545	174	15	.	.	PUNCT
ejpam-3545	175	1	this	this	DET
ejpam-3545	175	2	type	type	NOUN
ejpam-3545	175	3	of	of	ADP
ejpam-3545	175	4	partial	partial	ADJ
ejpam-3545	175	5	weak	weak	ADJ
ejpam-3545	175	6	projectivity	projectivity	NOUN
ejpam-3545	175	7	is	be	AUX
ejpam-3545	175	8	calledadditive	calledadditive	ADJ
ejpam-3545	175	9	weak	weak	ADJ
ejpam-3545	175	10	projectivity	projectivity	NOUN
ejpam-3545	175	11	.	.	PUNCT
ejpam-3545	176	1	note	note	VERB
ejpam-3545	176	2	that	that	PRON
ejpam-3545	176	3	studied	study	VERB
ejpam-3545	176	4	in	in	ADP
ejpam-3545	176	5	[	[	X
ejpam-3545	176	6	5	5	NUM
ejpam-3545	176	7	,	,	PUNCT
ejpam-3545	176	8	7	7	NUM
ejpam-3545	176	9	,	,	PUNCT
ejpam-3545	176	10	11	11	NUM
ejpam-3545	176	11	]	]	SYM
ejpam-3545	176	12	weak	weak	ADJ
ejpam-3545	176	13	projectivity	projectivity	NOUN
ejpam-3545	176	14	connects	connect	VERB
ejpam-3545	176	15	both	both	DET
ejpam-3545	176	16	operations	operation	NOUN
ejpam-3545	176	17	in	in	ADP
ejpam-3545	176	18	prearithmetics	prearithmetic	NOUN
ejpam-3545	176	19	while	while	SCONJ
ejpam-3545	176	20	partial	partial	ADJ
ejpam-3545	176	21	weak	weak	ADJ
ejpam-3545	176	22	projectivity	projectivity	NOUN
ejpam-3545	176	23	connects	connect	VERB
ejpam-3545	176	24	only	only	ADV
ejpam-3545	176	25	one	one	NUM
ejpam-3545	176	26	operation	operation	NOUN
ejpam-3545	176	27	in	in	ADP
ejpam-3545	176	28	prearithmetics	prearithmetic	NOUN
ejpam-3545	176	29	.	.	PUNCT
ejpam-3545	177	1	m.	m.	NOUN
ejpam-3545	177	2	burgin	burgin	PROPN
ejpam-3545	177	3	/	/	SYM
ejpam-3545	177	4	eur	eur	PROPN
ejpam-3545	177	5	.	.	PUNCT
ejpam-3545	178	1	j.	j.	PROPN
ejpam-3545	178	2	pure	pure	PROPN
ejpam-3545	178	3	appl	appl	PROPN
ejpam-3545	178	4	.	.	PROPN
ejpam-3545	178	5	math	math	PROPN
ejpam-3545	178	6	,	,	PUNCT
ejpam-3545	178	7	12	12	NUM
ejpam-3545	178	8	(	(	PUNCT
ejpam-3545	178	9	4	4	NUM
ejpam-3545	178	10	)	)	PUNCT
ejpam-3545	178	11	(	(	PUNCT
ejpam-3545	178	12	2019	2019	NUM
ejpam-3545	178	13	)	)	PUNCT
ejpam-3545	178	14	,	,	PUNCT
ejpam-3545	178	15	1787	1787	NUM
ejpam-3545	178	16	-	-	SYM
ejpam-3545	178	17	1810	1810	NUM
ejpam-3545	178	18	1794	1794	NUM
ejpam-3545	178	19	example	example	NOUN
ejpam-3545	178	20	10	10	NUM
ejpam-3545	178	21	.	.	PUNCT
ejpam-3545	179	1	it	it	PRON
ejpam-3545	179	2	is	be	AUX
ejpam-3545	179	3	possible	possible	ADJ
ejpam-3545	179	4	to	to	PART
ejpam-3545	179	5	treat	treat	VERB
ejpam-3545	179	6	numerical	numerical	ADJ
ejpam-3545	179	7	average	average	NOUN
ejpam-3545	179	8	as	as	ADP
ejpam-3545	179	9	a	a	DET
ejpam-3545	179	10	projection	projection	NOUN
ejpam-3545	179	11	of	of	ADP
ejpam-3545	179	12	the	the	DET
ejpam-3545	179	13	conventional	conventional	ADJ
ejpam-3545	179	14	addition	addition	NOUN
ejpam-3545	179	15	of	of	ADP
ejpam-3545	179	16	numbers	number	NOUN
ejpam-3545	179	17	.	.	PUNCT
ejpam-3545	180	1	indeed	indeed	ADV
ejpam-3545	180	2	,	,	PUNCT
ejpam-3545	180	3	taking	take	VERB
ejpam-3545	180	4	g1(a	g1(a	PRON
ejpam-3545	180	5	)	)	PUNCT
ejpam-3545	180	6	=	=	SYM
ejpam-3545	180	7	g2(a	g2(a	NOUN
ejpam-3545	180	8	)	)	PUNCT
ejpam-3545	180	9	=	=	SYM
ejpam-3545	180	10	g(a	g(a	PROPN
ejpam-3545	180	11	)	)	PUNCT
ejpam-3545	180	12	=	=	PUNCT
ejpam-3545	180	13	a	a	PRON
ejpam-3545	180	14	and	and	CCONJ
ejpam-3545	180	15	h(x	h(x	PROPN
ejpam-3545	180	16	)	)	PUNCT
ejpam-3545	181	1	=	=	PUNCT
ejpam-3545	181	2	(	(	PUNCT
ejpam-3545	181	3	12)x	12)x	NUM
ejpam-3545	181	4	,	,	PUNCT
ejpam-3545	181	5	the	the	DET
ejpam-3545	181	6	average	average	NOUN
ejpam-3545	181	7	of	of	ADP
ejpam-3545	181	8	numbers	number	NOUN
ejpam-3545	181	9	a	a	PRON
ejpam-3545	181	10	and	and	CCONJ
ejpam-3545	181	11	b	b	NOUN
ejpam-3545	181	12	is	be	AUX
ejpam-3545	181	13	1	1	NUM
ejpam-3545	181	14	2	2	NUM
ejpam-3545	181	15	(	(	PUNCT
ejpam-3545	181	16	a	a	DET
ejpam-3545	181	17	+	+	NOUN
ejpam-3545	181	18	b	b	NOUN
ejpam-3545	181	19	)	)	PUNCT
ejpam-3545	181	20	=	=	SYM
ejpam-3545	181	21	h(g(a	h(g(a	PROPN
ejpam-3545	181	22	)	)	PUNCT
ejpam-3545	181	23	+	+	NUM
ejpam-3545	181	24	g(b	g(b	NOUN
ejpam-3545	181	25	)	)	PUNCT
ejpam-3545	181	26	)	)	PUNCT
ejpam-3545	182	1	=	=	PUNCT
ejpam-3545	183	1	a⊕	a⊕	X
ejpam-3545	183	2	b	b	NOUN
ejpam-3545	183	3	it	it	PRON
ejpam-3545	183	4	is	be	AUX
ejpam-3545	183	5	possible	possible	ADJ
ejpam-3545	183	6	to	to	PART
ejpam-3545	183	7	extend	extend	VERB
ejpam-3545	183	8	these	these	DET
ejpam-3545	183	9	projections	projection	NOUN
ejpam-3545	183	10	to	to	ADP
ejpam-3545	183	11	averages	average	NOUN
ejpam-3545	183	12	of	of	ADP
ejpam-3545	183	13	any	any	DET
ejpam-3545	183	14	quantity	quantity	NOUN
ejpam-3545	183	15	of	of	ADP
ejpam-3545	183	16	numbers	number	NOUN
ejpam-3545	183	17	,	,	PUNCT
ejpam-3545	183	18	i.e.	i.e.	X
ejpam-3545	183	19	,	,	PUNCT
ejpam-3545	183	20	(	(	PUNCT
ejpam-3545	183	21	1	1	NUM
ejpam-3545	183	22	/	/	SYM
ejpam-3545	183	23	n)(a1	n)(a1	NOUN
ejpam-3545	183	24	+	+	CCONJ
ejpam-3545	183	25	·	·	PUNCT
ejpam-3545	183	26	·	·	PUNCT
ejpam-3545	183	27	·	·	PUNCT
ejpam-3545	184	1	+	+	NUM
ejpam-3545	184	2	an	an	X
ejpam-3545	184	3	)	)	PUNCT
ejpam-3545	184	4	=	=	SYM
ejpam-3545	184	5	h(g(a1	h(g(a1	NOUN
ejpam-3545	184	6	)	)	PUNCT
ejpam-3545	184	7	+	+	CCONJ
ejpam-3545	184	8	·	·	PUNCT
ejpam-3545	184	9	·	·	PUNCT
ejpam-3545	184	10	·	·	PUNCT
ejpam-3545	184	11	+	+	NUM
ejpam-3545	184	12	g(an	g(an	NOUN
ejpam-3545	184	13	)	)	PUNCT
ejpam-3545	184	14	)	)	PUNCT
ejpam-3545	185	1	=	=	SYM
ejpam-3545	185	2	a1	a1	PROPN
ejpam-3545	185	3	⊕	⊕	PROPN
ejpam-3545	185	4	·	·	PUNCT
ejpam-3545	185	5	·	·	PUNCT
ejpam-3545	185	6	·	·	PUNCT
ejpam-3545	185	7	⊕	⊕	NOUN
ejpam-3545	185	8	an	an	DET
ejpam-3545	185	9	a	a	DET
ejpam-3545	185	10	special	special	ADJ
ejpam-3545	185	11	case	case	NOUN
ejpam-3545	185	12	of	of	ADP
ejpam-3545	185	13	this	this	DET
ejpam-3545	185	14	projection	projection	NOUN
ejpam-3545	185	15	,	,	PUNCT
ejpam-3545	185	16	i.e.	i.e.	X
ejpam-3545	185	17	,	,	PUNCT
ejpam-3545	185	18	when	when	SCONJ
ejpam-3545	185	19	g	g	PROPN
ejpam-3545	185	20	is	be	AUX
ejpam-3545	185	21	a	a	DET
ejpam-3545	185	22	bijection	bijection	NOUN
ejpam-3545	185	23	,	,	PUNCT
ejpam-3545	185	24	h(x	h(x	PROPN
ejpam-3545	185	25	)	)	PUNCT
ejpam-3545	185	26	=	=	SYM
ejpam-3545	186	1	g−1(1/2x	g−1(1/2x	NOUN
ejpam-3545	186	2	)	)	PUNCT
ejpam-3545	186	3	in	in	ADP
ejpam-3545	186	4	the	the	DET
ejpam-3545	186	5	binary	binary	ADJ
ejpam-3545	186	6	case	case	NOUN
ejpam-3545	186	7	and	and	CCONJ
ejpam-3545	186	8	h(x	h(x	PROPN
ejpam-3545	186	9	)	)	PUNCT
ejpam-3545	187	1	=	=	PUNCT
ejpam-3545	187	2	g−1((1	g−1((1	PROPN
ejpam-3545	187	3	/	/	SYM
ejpam-3545	187	4	n)x	n)x	ADJ
ejpam-3545	187	5	)	)	PUNCT
ejpam-3545	187	6	,	,	PUNCT
ejpam-3545	187	7	in	in	ADP
ejpam-3545	187	8	a	a	DET
ejpam-3545	187	9	general	general	ADJ
ejpam-3545	187	10	case	case	NOUN
ejpam-3545	187	11	,	,	PUNCT
ejpam-3545	187	12	was	be	AUX
ejpam-3545	187	13	introduced	introduce	VERB
ejpam-3545	187	14	and	and	CCONJ
ejpam-3545	187	15	studied	study	VERB
ejpam-3545	187	16	by	by	ADP
ejpam-3545	187	17	kolmogorov	kolmogorov	PROPN
ejpam-3545	187	18	,	,	PUNCT
ejpam-3545	187	19	nagumo	nagumo	ADJ
ejpam-3545	187	20	and	and	CCONJ
ejpam-3545	187	21	de	de	ADP
ejpam-3545	187	22	finetti	finetti	PROPN
ejpam-3545	187	23	[	[	X
ejpam-3545	187	24	23	23	NUM
ejpam-3545	187	25	,	,	PUNCT
ejpam-3545	187	26	43	43	NUM
ejpam-3545	187	27	,	,	PUNCT
ejpam-3545	187	28	61	61	NUM
ejpam-3545	187	29	]	]	PUNCT
ejpam-3545	187	30	.	.	PUNCT
ejpam-3545	188	1	it	it	PRON
ejpam-3545	188	2	is	be	AUX
ejpam-3545	188	3	also	also	ADV
ejpam-3545	188	4	used	use	VERB
ejpam-3545	188	5	in	in	ADP
ejpam-3545	188	6	the	the	DET
ejpam-3545	188	7	book	book	NOUN
ejpam-3545	188	8	[	[	X
ejpam-3545	188	9	35	35	NUM
ejpam-3545	188	10	]	]	PUNCT
ejpam-3545	188	11	.	.	PUNCT
ejpam-3545	189	1	example	example	NOUN
ejpam-3545	189	2	11	11	NUM
ejpam-3545	189	3	.	.	PUNCT
ejpam-3545	190	1	weighted	weight	VERB
ejpam-3545	190	2	sum	sum	NOUN
ejpam-3545	190	3	of	of	ADP
ejpam-3545	190	4	numbers	number	NOUN
ejpam-3545	190	5	is	be	AUX
ejpam-3545	190	6	a	a	DET
ejpam-3545	190	7	projection	projection	NOUN
ejpam-3545	190	8	of	of	ADP
ejpam-3545	190	9	the	the	DET
ejpam-3545	190	10	conventional	conventional	ADJ
ejpam-3545	190	11	addition	addition	NOUN
ejpam-3545	190	12	of	of	ADP
ejpam-3545	190	13	numbers	number	NOUN
ejpam-3545	190	14	.	.	PUNCT
ejpam-3545	191	1	indeed	indeed	ADV
ejpam-3545	191	2	,	,	PUNCT
ejpam-3545	191	3	with	with	ADP
ejpam-3545	191	4	the	the	DET
ejpam-3545	191	5	functions	function	NOUN
ejpam-3545	191	6	g1(a	g1(a	PRON
ejpam-3545	191	7	)	)	PUNCT
ejpam-3545	191	8	=	=	PUNCT
ejpam-3545	192	1	w1a	w1a	PROPN
ejpam-3545	192	2	,	,	PUNCT
ejpam-3545	192	3	g2(a	g2(a	NOUN
ejpam-3545	192	4	)	)	PUNCT
ejpam-3545	192	5	=	=	SYM
ejpam-3545	193	1	w2a	w2a	PROPN
ejpam-3545	193	2	as	as	ADP
ejpam-3545	193	3	projectors	projector	NOUN
ejpam-3545	193	4	and	and	CCONJ
ejpam-3545	193	5	h(x	h(x	PROPN
ejpam-3545	193	6	)	)	PUNCT
ejpam-3545	194	1	=	=	PUNCT
ejpam-3545	195	1	x	x	PUNCT
ejpam-3545	195	2	as	as	ADP
ejpam-3545	195	3	the	the	DET
ejpam-3545	195	4	coprojector	coprojector	NOUN
ejpam-3545	195	5	,	,	PUNCT
ejpam-3545	195	6	the	the	DET
ejpam-3545	195	7	weighted	weighted	ADJ
ejpam-3545	195	8	sum	sum	NOUN
ejpam-3545	195	9	of	of	ADP
ejpam-3545	195	10	numbers	number	NOUN
ejpam-3545	195	11	a	a	PRON
ejpam-3545	195	12	and	and	CCONJ
ejpam-3545	195	13	b	b	NOUN
ejpam-3545	195	14	is	be	AUX
ejpam-3545	195	15	presented	present	VERB
ejpam-3545	195	16	as	as	ADP
ejpam-3545	195	17	a⊕	a⊕	PROPN
ejpam-3545	195	18	b	b	PROPN
ejpam-3545	195	19	=	=	PUNCT
ejpam-3545	196	1	w1a	w1a	X
ejpam-3545	196	2	+	+	NUM
ejpam-3545	196	3	w2b	w2b	NOUN
ejpam-3545	196	4	example	example	VERB
ejpam-3545	196	5	12	12	NUM
ejpam-3545	196	6	.	.	PUNCT
ejpam-3545	197	1	weighted	weight	VERB
ejpam-3545	197	2	normalized	normalize	VERB
ejpam-3545	197	3	sum	sum	NOUN
ejpam-3545	197	4	of	of	ADP
ejpam-3545	197	5	numbers	number	NOUN
ejpam-3545	197	6	is	be	AUX
ejpam-3545	197	7	a	a	DET
ejpam-3545	197	8	projection	projection	NOUN
ejpam-3545	197	9	of	of	ADP
ejpam-3545	197	10	the	the	DET
ejpam-3545	197	11	conventional	conventional	ADJ
ejpam-3545	197	12	addition	addition	NOUN
ejpam-3545	197	13	of	of	ADP
ejpam-3545	197	14	numbers	number	NOUN
ejpam-3545	197	15	.	.	PUNCT
ejpam-3545	198	1	indeed	indeed	ADV
ejpam-3545	198	2	,	,	PUNCT
ejpam-3545	198	3	with	with	ADP
ejpam-3545	198	4	the	the	DET
ejpam-3545	198	5	functions	function	NOUN
ejpam-3545	198	6	g1(a	g1(a	PRON
ejpam-3545	198	7	)	)	PUNCT
ejpam-3545	198	8	=	=	PUNCT
ejpam-3545	199	1	w1a	w1a	PROPN
ejpam-3545	199	2	,	,	PUNCT
ejpam-3545	199	3	g2(a	g2(a	NOUN
ejpam-3545	199	4	)	)	PUNCT
ejpam-3545	199	5	=	=	SYM
ejpam-3545	200	1	w1a	w1a	PROPN
ejpam-3545	200	2	as	as	ADP
ejpam-3545	200	3	projectors	projector	NOUN
ejpam-3545	200	4	and	and	CCONJ
ejpam-3545	200	5	h(x	h(x	PROPN
ejpam-3545	200	6	)	)	PUNCT
ejpam-3545	200	7	=	=	PUNCT
ejpam-3545	200	8	x/(w1	x/(w1	PUNCT
ejpam-3545	201	1	+	+	NUM
ejpam-3545	201	2	w2	w2	NOUN
ejpam-3545	201	3	)	)	PUNCT
ejpam-3545	201	4	as	as	ADP
ejpam-3545	201	5	the	the	DET
ejpam-3545	201	6	coprojector	coprojector	NOUN
ejpam-3545	201	7	,	,	PUNCT
ejpam-3545	201	8	the	the	DET
ejpam-3545	201	9	weighted	weighted	ADJ
ejpam-3545	201	10	sum	sum	NOUN
ejpam-3545	201	11	of	of	ADP
ejpam-3545	201	12	numbers	number	NOUN
ejpam-3545	201	13	a	a	PRON
ejpam-3545	201	14	and	and	CCONJ
ejpam-3545	201	15	b	b	NOUN
ejpam-3545	201	16	is	be	AUX
ejpam-3545	201	17	presented	present	VERB
ejpam-3545	201	18	as	as	ADP
ejpam-3545	201	19	a⊕	a⊕	PROPN
ejpam-3545	201	20	b	b	PROPN
ejpam-3545	201	21	=	=	PRON
ejpam-3545	201	22	(	(	PUNCT
ejpam-3545	201	23	w1a	w1a	X
ejpam-3545	201	24	+	+	NUM
ejpam-3545	201	25	w2b)/(w1	w2b)/(w1	X
ejpam-3545	201	26	+	+	CCONJ
ejpam-3545	201	27	w2	w2	NOUN
ejpam-3545	201	28	)	)	PUNCT
ejpam-3545	201	29	it	it	PRON
ejpam-3545	201	30	is	be	AUX
ejpam-3545	201	31	necessary	necessary	ADJ
ejpam-3545	201	32	to	to	PART
ejpam-3545	201	33	remark	remark	VERB
ejpam-3545	201	34	that	that	SCONJ
ejpam-3545	201	35	weak	weak	ADJ
ejpam-3545	201	36	projectivity	projectivity	NOUN
ejpam-3545	201	37	is	be	AUX
ejpam-3545	201	38	intrinsically	intrinsically	ADV
ejpam-3545	201	39	related	relate	VERB
ejpam-3545	201	40	to	to	ADP
ejpam-3545	201	41	such	such	ADJ
ejpam-3545	201	42	mathematical	mathematical	ADJ
ejpam-3545	201	43	constructions	construction	NOUN
ejpam-3545	201	44	as	as	ADP
ejpam-3545	201	45	fiber	fiber	NOUN
ejpam-3545	201	46	bundles	bundle	NOUN
ejpam-3545	201	47	[	[	X
ejpam-3545	201	48	37	37	NUM
ejpam-3545	201	49	]	]	PUNCT
ejpam-3545	201	50	and	and	CCONJ
ejpam-3545	201	51	bidirectional	bidirectional	NOUN
ejpam-3545	201	52	named	name	VERB
ejpam-3545	201	53	sets	set	NOUN
ejpam-3545	201	54	[	[	X
ejpam-3545	201	55	8	8	NUM
ejpam-3545	201	56	]	]	PUNCT
ejpam-3545	201	57	as	as	ADV
ejpam-3545	201	58	well	well	ADV
ejpam-3545	201	59	as	as	ADP
ejpam-3545	201	60	to	to	ADP
ejpam-3545	201	61	information	information	NOUN
ejpam-3545	201	62	processes	process	NOUN
ejpam-3545	201	63	of	of	ADP
ejpam-3545	201	64	coding	code	VERB
ejpam-3545	201	65	and	and	CCONJ
ejpam-3545	201	66	decoding	decode	VERB
ejpam-3545	201	67	[	[	X
ejpam-3545	201	68	68	68	NUM
ejpam-3545	201	69	]	]	PUNCT
ejpam-3545	201	70	.	.	PUNCT
ejpam-3545	202	1	let	let	VERB
ejpam-3545	202	2	us	we	PRON
ejpam-3545	202	3	consider	consider	VERB
ejpam-3545	202	4	two	two	NUM
ejpam-3545	202	5	abstract	abstract	ADJ
ejpam-3545	202	6	prearithmetics	prearithmetic	NOUN
ejpam-3545	202	7	a1	a1	NOUN
ejpam-3545	202	8	=	=	SYM
ejpam-3545	202	9	(	(	PUNCT
ejpam-3545	202	10	a1	a1	PROPN
ejpam-3545	202	11	;	;	PUNCT
ejpam-3545	202	12	+1	+1	PROPN
ejpam-3545	202	13	,	,	PUNCT
ejpam-3545	202	14	◦	◦	NOUN
ejpam-3545	202	15	1,≤1	1,≤1	ADJ
ejpam-3545	202	16	)	)	PUNCT
ejpam-3545	202	17	and	and	CCONJ
ejpam-3545	202	18	a2	a2	PROPN
ejpam-3545	202	19	=	=	SYM
ejpam-3545	202	20	(	(	PUNCT
ejpam-3545	202	21	a2	a2	PROPN
ejpam-3545	202	22	;	;	PUNCT
ejpam-3545	202	23	+2	+2	PROPN
ejpam-3545	202	24	,	,	PUNCT
ejpam-3545	202	25	◦	◦	NOUN
ejpam-3545	202	26	2,≤2	2,≤2	NUM
ejpam-3545	202	27	)	)	PUNCT
ejpam-3545	202	28	.	.	PUNCT
ejpam-3545	203	1	proposition	proposition	NOUN
ejpam-3545	203	2	3.1	3.1	NUM
ejpam-3545	203	3	.	.	PUNCT
ejpam-3545	204	1	if	if	SCONJ
ejpam-3545	204	2	the	the	DET
ejpam-3545	204	3	operation	operation	NOUN
ejpam-3545	204	4	+1	+1	PROPN
ejpam-3545	204	5	is	be	AUX
ejpam-3545	204	6	commutative	commutative	ADJ
ejpam-3545	204	7	and	and	CCONJ
ejpam-3545	204	8	weakly	weakly	ADJ
ejpam-3545	204	9	projective	projective	NOUN
ejpam-3545	204	10	with	with	ADP
ejpam-3545	204	11	respect	respect	NOUN
ejpam-3545	204	12	to	to	ADP
ejpam-3545	204	13	the	the	DET
ejpam-3545	204	14	commutative	commutative	ADJ
ejpam-3545	204	15	operation	operation	NOUN
ejpam-3545	204	16	+2	+2	PROPN
ejpam-3545	204	17	with	with	ADP
ejpam-3545	204	18	the	the	DET
ejpam-3545	204	19	projectors	projector	NOUN
ejpam-3545	204	20	g1	g1	NOUN
ejpam-3545	204	21	and	and	CCONJ
ejpam-3545	204	22	g2	g2	PROPN
ejpam-3545	204	23	,	,	PUNCT
ejpam-3545	204	24	then	then	ADV
ejpam-3545	204	25	the	the	DET
ejpam-3545	204	26	operation	operation	NOUN
ejpam-3545	204	27	+1	+1	PROPN
ejpam-3545	204	28	is	be	AUX
ejpam-3545	204	29	commutative	commutative	ADJ
ejpam-3545	204	30	and	and	CCONJ
ejpam-3545	204	31	weakly	weakly	ADJ
ejpam-3545	204	32	projective	projective	NOUN
ejpam-3545	204	33	with	with	ADP
ejpam-3545	204	34	respect	respect	NOUN
ejpam-3545	204	35	to	to	ADP
ejpam-3545	204	36	the	the	DET
ejpam-3545	204	37	operation	operation	NOUN
ejpam-3545	204	38	+2	+2	PROPN
ejpam-3545	204	39	with	with	ADP
ejpam-3545	204	40	the	the	DET
ejpam-3545	204	41	projectors	projector	NOUN
ejpam-3545	204	42	g2	g2	PROPN
ejpam-3545	204	43	and	and	CCONJ
ejpam-3545	204	44	g1	g1	PROPN
ejpam-3545	204	45	.	.	PUNCT
ejpam-3545	205	1	indeed	indeed	ADV
ejpam-3545	205	2	,	,	PUNCT
ejpam-3545	205	3	for	for	ADP
ejpam-3545	205	4	any	any	DET
ejpam-3545	205	5	elements	element	NOUN
ejpam-3545	205	6	a	a	PRON
ejpam-3545	205	7	and	and	CCONJ
ejpam-3545	205	8	b	b	NOUN
ejpam-3545	205	9	from	from	ADP
ejpam-3545	205	10	a1	a1	NOUN
ejpam-3545	205	11	,	,	PUNCT
ejpam-3545	205	12	we	we	PRON
ejpam-3545	205	13	have	have	VERB
ejpam-3545	205	14	a	a	DET
ejpam-3545	205	15	+1	+1	PROPN
ejpam-3545	205	16	b	b	NOUN
ejpam-3545	205	17	=	=	SYM
ejpam-3545	205	18	h(g1(a	h(g1(a	PROPN
ejpam-3545	205	19	)	)	PUNCT
ejpam-3545	205	20	+2	+2	PROPN
ejpam-3545	205	21	g2(b	g2(b	PROPN
ejpam-3545	205	22	)	)	PUNCT
ejpam-3545	205	23	)	)	PUNCT
ejpam-3545	206	1	=	=	PUNCT
ejpam-3545	207	1	h(g2(b	h(g2(b	PROPN
ejpam-3545	207	2	)	)	PUNCT
ejpam-3545	207	3	+2	+2	PRON
ejpam-3545	207	4	g1(a	g1(a	NUM
ejpam-3545	207	5	)	)	PUNCT
ejpam-3545	207	6	)	)	PUNCT
ejpam-3545	208	1	=	=	PUNCT
ejpam-3545	209	1	b	b	X
ejpam-3545	209	2	+1	+1	NOUN
ejpam-3545	210	1	a	a	DET
ejpam-3545	210	2	this	this	PRON
ejpam-3545	210	3	implies	imply	VERB
ejpam-3545	210	4	b	b	X
ejpam-3545	210	5	+1	+1	NOUN
ejpam-3545	210	6	a	a	X
ejpam-3545	210	7	=	=	SYM
ejpam-3545	210	8	h(g2(b	h(g2(b	PROPN
ejpam-3545	210	9	)	)	PUNCT
ejpam-3545	210	10	+2	+2	PRON
ejpam-3545	210	11	g1(a	g1(a	NUM
ejpam-3545	210	12	)	)	PUNCT
ejpam-3545	210	13	)	)	PUNCT
ejpam-3545	211	1	i.e.	i.e.	ADV
ejpam-3545	211	2	,	,	PUNCT
ejpam-3545	211	3	the	the	DET
ejpam-3545	211	4	operation	operation	NOUN
ejpam-3545	211	5	+1	+1	PROPN
ejpam-3545	211	6	is	be	AUX
ejpam-3545	211	7	weakly	weakly	ADV
ejpam-3545	211	8	projective	projective	ADJ
ejpam-3545	211	9	with	with	ADP
ejpam-3545	211	10	respect	respect	NOUN
ejpam-3545	211	11	to	to	ADP
ejpam-3545	211	12	the	the	DET
ejpam-3545	211	13	operation	operation	NOUN
ejpam-3545	211	14	+2	+2	PROPN
ejpam-3545	211	15	with	with	ADP
ejpam-3545	211	16	the	the	DET
ejpam-3545	211	17	projectors	projector	NOUN
ejpam-3545	211	18	g2	g2	PROPN
ejpam-3545	211	19	and	and	CCONJ
ejpam-3545	211	20	g1	g1	PROPN
ejpam-3545	211	21	.	.	PUNCT
ejpam-3545	212	1	m.	m.	NOUN
ejpam-3545	212	2	burgin	burgin	PROPN
ejpam-3545	212	3	/	/	SYM
ejpam-3545	212	4	eur	eur	PROPN
ejpam-3545	212	5	.	.	PUNCT
ejpam-3545	213	1	j.	j.	PROPN
ejpam-3545	213	2	pure	pure	PROPN
ejpam-3545	213	3	appl	appl	PROPN
ejpam-3545	213	4	.	.	PROPN
ejpam-3545	213	5	math	math	PROPN
ejpam-3545	213	6	,	,	PUNCT
ejpam-3545	213	7	12	12	NUM
ejpam-3545	213	8	(	(	PUNCT
ejpam-3545	213	9	4	4	NUM
ejpam-3545	213	10	)	)	PUNCT
ejpam-3545	213	11	(	(	PUNCT
ejpam-3545	213	12	2019	2019	NUM
ejpam-3545	213	13	)	)	PUNCT
ejpam-3545	213	14	,	,	PUNCT
ejpam-3545	213	15	1787	1787	NUM
ejpam-3545	213	16	-	-	SYM
ejpam-3545	213	17	1810	1810	NUM
ejpam-3545	213	18	1795	1795	NUM
ejpam-3545	213	19	proposition	proposition	NOUN
ejpam-3545	213	20	3.1	3.1	NUM
ejpam-3545	213	21	allows	allow	VERB
ejpam-3545	213	22	to	to	PART
ejpam-3545	213	23	show	show	VERB
ejpam-3545	213	24	when	when	SCONJ
ejpam-3545	213	25	addition	addition	NOUN
ejpam-3545	213	26	in	in	ADP
ejpam-3545	213	27	one	one	NUM
ejpam-3545	213	28	abstract	abstract	ADJ
ejpam-3545	213	29	prearithmetic	prearithmetic	NOUN
ejpam-3545	213	30	is	be	AUX
ejpam-3545	213	31	not	not	PART
ejpam-3545	213	32	weakly	weakly	ADV
ejpam-3545	213	33	projective	projective	ADJ
ejpam-3545	213	34	with	with	ADP
ejpam-3545	213	35	respect	respect	NOUN
ejpam-3545	213	36	to	to	ADP
ejpam-3545	213	37	addition	addition	NOUN
ejpam-3545	213	38	in	in	ADP
ejpam-3545	213	39	another	another	DET
ejpam-3545	213	40	abstract	abstract	ADJ
ejpam-3545	213	41	prearithmetic	prearithmetic	NOUN
ejpam-3545	213	42	.	.	PUNCT
ejpam-3545	214	1	example	example	NOUN
ejpam-3545	214	2	13	13	NUM
ejpam-3545	214	3	.	.	PUNCT
ejpam-3545	215	1	let	let	VERB
ejpam-3545	215	2	us	we	PRON
ejpam-3545	215	3	consider	consider	VERB
ejpam-3545	215	4	the	the	DET
ejpam-3545	215	5	conventional	conventional	ADJ
ejpam-3545	215	6	diophantine	diophantine	NOUN
ejpam-3545	215	7	arithmetic	arithmetic	ADJ
ejpam-3545	215	8	n	n	PROPN
ejpam-3545	215	9	of	of	ADP
ejpam-3545	215	10	all	all	DET
ejpam-3545	215	11	natural	natural	ADJ
ejpam-3545	215	12	numbers	number	NOUN
ejpam-3545	215	13	and	and	CCONJ
ejpam-3545	215	14	the	the	DET
ejpam-3545	215	15	abstract	abstract	ADJ
ejpam-3545	215	16	prearithmetic	prearithmetic	NOUN
ejpam-3545	215	17	a	a	PRON
ejpam-3545	215	18	=	=	X
ejpam-3545	215	19	(	(	PUNCT
ejpam-3545	215	20	n	n	NOUN
ejpam-3545	215	21	;	;	PUNCT
ejpam-3545	215	22	⊕,⊗,≤	⊕,⊗,≤	X
ejpam-3545	215	23	)	)	PUNCT
ejpam-3545	215	24	where	where	SCONJ
ejpam-3545	215	25	n	n	PRON
ejpam-3545	215	26	is	be	AUX
ejpam-3545	215	27	the	the	DET
ejpam-3545	215	28	set	set	NOUN
ejpam-3545	215	29	of	of	ADP
ejpam-3545	215	30	all	all	DET
ejpam-3545	215	31	natural	natural	ADJ
ejpam-3545	215	32	numbers,≤	numbers,≤	PROPN
ejpam-3545	215	33	is	be	AUX
ejpam-3545	215	34	the	the	DET
ejpam-3545	215	35	natural	natural	ADJ
ejpam-3545	215	36	order	order	NOUN
ejpam-3545	215	37	on	on	ADP
ejpam-3545	215	38	the	the	DET
ejpam-3545	215	39	set	set	NOUN
ejpam-3545	215	40	of	of	ADP
ejpam-3545	215	41	all	all	DET
ejpam-3545	215	42	natural	natural	ADJ
ejpam-3545	215	43	numbers	number	NOUN
ejpam-3545	215	44	,	,	PUNCT
ejpam-3545	215	45	multiplication	multiplication	NOUN
ejpam-3545	215	46	⊗	⊗	PROPN
ejpam-3545	215	47	is	be	AUX
ejpam-3545	215	48	the	the	DET
ejpam-3545	215	49	same	same	ADJ
ejpam-3545	215	50	as	as	ADP
ejpam-3545	215	51	in	in	ADP
ejpam-3545	215	52	n	n	NUM
ejpam-3545	215	53	,	,	PUNCT
ejpam-3545	215	54	while	while	SCONJ
ejpam-3545	215	55	addition	addition	NOUN
ejpam-3545	215	56	is	be	AUX
ejpam-3545	215	57	defined	define	VERB
ejpam-3545	215	58	by	by	ADP
ejpam-3545	215	59	the	the	DET
ejpam-3545	215	60	following	follow	VERB
ejpam-3545	215	61	formula	formula	NOUN
ejpam-3545	216	1	a⊕	a⊕	PROPN
ejpam-3545	216	2	b	b	NOUN
ejpam-3545	216	3	=	=	PUNCT
ejpam-3545	216	4	a	a	DET
ejpam-3545	216	5	addition	addition	NOUN
ejpam-3545	216	6	⊕	⊕	PROPN
ejpam-3545	216	7	in	in	ADP
ejpam-3545	216	8	the	the	DET
ejpam-3545	216	9	abstract	abstract	ADJ
ejpam-3545	216	10	prearithmetic	prearithmetic	NOUN
ejpam-3545	216	11	a	a	PRON
ejpam-3545	216	12	is	be	AUX
ejpam-3545	216	13	not	not	PART
ejpam-3545	216	14	weakly	weakly	ADV
ejpam-3545	216	15	projective	projective	ADJ
ejpam-3545	216	16	with	with	ADP
ejpam-3545	216	17	respect	respect	NOUN
ejpam-3545	216	18	to	to	ADP
ejpam-3545	216	19	addition	addition	NOUN
ejpam-3545	216	20	in	in	ADP
ejpam-3545	216	21	n	n	NOUN
ejpam-3545	216	22	because	because	SCONJ
ejpam-3545	216	23	otherwise	otherwise	ADV
ejpam-3545	216	24	by	by	ADP
ejpam-3545	216	25	proposition	proposition	NOUN
ejpam-3545	216	26	3.1	3.1	NUM
ejpam-3545	216	27	,	,	PUNCT
ejpam-3545	216	28	it	it	PRON
ejpam-3545	216	29	would	would	AUX
ejpam-3545	216	30	be	be	AUX
ejpam-3545	216	31	commutative	commutative	ADJ
ejpam-3545	216	32	and	and	CCONJ
ejpam-3545	216	33	it	it	PRON
ejpam-3545	216	34	is	be	AUX
ejpam-3545	216	35	not	not	PART
ejpam-3545	216	36	commutative	commutative	ADJ
ejpam-3545	216	37	.	.	PUNCT
ejpam-3545	217	1	at	at	ADP
ejpam-3545	217	2	the	the	DET
ejpam-3545	217	3	same	same	ADJ
ejpam-3545	217	4	time	time	NOUN
ejpam-3545	217	5	,	,	PUNCT
ejpam-3545	217	6	as	as	SCONJ
ejpam-3545	217	7	we	we	PRON
ejpam-3545	217	8	will	will	AUX
ejpam-3545	217	9	see	see	VERB
ejpam-3545	217	10	later	later	ADV
ejpam-3545	217	11	,	,	PUNCT
ejpam-3545	217	12	multiplication	multiplication	NOUN
ejpam-3545	217	13	⊗	⊗	PROPN
ejpam-3545	217	14	in	in	ADP
ejpam-3545	217	15	the	the	DET
ejpam-3545	217	16	abstract	abstract	ADJ
ejpam-3545	217	17	prearithmetic	prearithmetic	NOUN
ejpam-3545	217	18	a	a	PRON
ejpam-3545	217	19	is	be	AUX
ejpam-3545	217	20	weakly	weakly	ADV
ejpam-3545	217	21	projective	projective	ADJ
ejpam-3545	217	22	with	with	ADP
ejpam-3545	217	23	respect	respect	NOUN
ejpam-3545	217	24	to	to	ADP
ejpam-3545	217	25	multiplication	multiplication	NOUN
ejpam-3545	217	26	in	in	ADP
ejpam-3545	217	27	n	n	PROPN
ejpam-3545	217	28	.	.	PUNCT
ejpam-3545	218	1	if	if	SCONJ
ejpam-3545	218	2	we	we	PRON
ejpam-3545	218	3	investigate	investigate	VERB
ejpam-3545	218	4	properties	property	NOUN
ejpam-3545	218	5	of	of	ADP
ejpam-3545	218	6	weak	weak	ADJ
ejpam-3545	218	7	projectivity	projectivity	NOUN
ejpam-3545	218	8	in	in	ADP
ejpam-3545	218	9	the	the	DET
ejpam-3545	218	10	class	class	NOUN
ejpam-3545	218	11	of	of	ADP
ejpam-3545	218	12	abstract	abstract	ADJ
ejpam-3545	218	13	prearithmetics	prearithmetic	NOUN
ejpam-3545	218	14	,	,	PUNCT
ejpam-3545	218	15	we	we	PRON
ejpam-3545	218	16	find	find	VERB
ejpam-3545	218	17	that	that	SCONJ
ejpam-3545	218	18	it	it	PRON
ejpam-3545	218	19	is	be	AUX
ejpam-3545	218	20	a	a	DET
ejpam-3545	218	21	transitive	transitive	ADJ
ejpam-3545	218	22	relation	relation	NOUN
ejpam-3545	218	23	.	.	PUNCT
ejpam-3545	219	1	let	let	VERB
ejpam-3545	219	2	us	we	PRON
ejpam-3545	219	3	consider	consider	VERB
ejpam-3545	219	4	three	three	NUM
ejpam-3545	219	5	abstract	abstract	ADJ
ejpam-3545	219	6	prearithmetics	prearithmetic	NOUN
ejpam-3545	219	7	a1	a1	NOUN
ejpam-3545	219	8	=	=	SYM
ejpam-3545	219	9	(	(	PUNCT
ejpam-3545	219	10	a1	a1	PROPN
ejpam-3545	219	11	;	;	PUNCT
ejpam-3545	219	12	+1	+1	PROPN
ejpam-3545	219	13	,	,	PUNCT
ejpam-3545	219	14	◦	◦	NOUN
ejpam-3545	219	15	1,≤1),a2	1,≤1),a2	NUM
ejpam-3545	219	16	=	=	SYM
ejpam-3545	219	17	(	(	PUNCT
ejpam-3545	219	18	a2	a2	PROPN
ejpam-3545	219	19	;	;	PUNCT
ejpam-3545	219	20	+2	+2	PROPN
ejpam-3545	219	21	,	,	PUNCT
ejpam-3545	219	22	◦	◦	NOUN
ejpam-3545	219	23	2,≤2	2,≤2	NOUN
ejpam-3545	219	24	)	)	PUNCT
ejpam-3545	219	25	and	and	CCONJ
ejpam-3545	219	26	a3	a3	NOUN
ejpam-3545	219	27	=	=	SYM
ejpam-3545	219	28	(	(	PUNCT
ejpam-3545	219	29	a3	a3	NOUN
ejpam-3545	219	30	;	;	PUNCT
ejpam-3545	219	31	+3	+3	PROPN
ejpam-3545	219	32	,	,	PUNCT
ejpam-3545	219	33	◦	◦	NOUN
ejpam-3545	219	34	3,≤3	3,≤3	NOUN
ejpam-3545	219	35	)	)	PUNCT
ejpam-3545	219	36	.	.	PUNCT
ejpam-3545	220	1	proposition	proposition	NOUN
ejpam-3545	220	2	3.2	3.2	NUM
ejpam-3545	220	3	.	.	PUNCT
ejpam-3545	221	1	if	if	SCONJ
ejpam-3545	221	2	the	the	DET
ejpam-3545	221	3	operation	operation	NOUN
ejpam-3545	221	4	+1	+1	PROPN
ejpam-3545	221	5	is	be	AUX
ejpam-3545	221	6	weakly	weakly	ADV
ejpam-3545	221	7	projective	projective	ADJ
ejpam-3545	221	8	with	with	ADP
ejpam-3545	221	9	respect	respect	NOUN
ejpam-3545	221	10	to	to	ADP
ejpam-3545	221	11	the	the	DET
ejpam-3545	221	12	operation	operation	NOUN
ejpam-3545	221	13	+2	+2	PROPN
ejpam-3545	221	14	and	and	CCONJ
ejpam-3545	221	15	the	the	DET
ejpam-3545	221	16	operation	operation	NOUN
ejpam-3545	221	17	+2	+2	PROPN
ejpam-3545	221	18	is	be	AUX
ejpam-3545	221	19	weakly	weakly	ADV
ejpam-3545	221	20	projective	projective	ADJ
ejpam-3545	221	21	with	with	ADP
ejpam-3545	221	22	respect	respect	NOUN
ejpam-3545	221	23	to	to	ADP
ejpam-3545	221	24	the	the	DET
ejpam-3545	221	25	operation	operation	NOUN
ejpam-3545	221	26	+3	+3	PROPN
ejpam-3545	221	27	,	,	PUNCT
ejpam-3545	221	28	then	then	ADV
ejpam-3545	221	29	the	the	DET
ejpam-3545	221	30	operation	operation	NOUN
ejpam-3545	221	31	+1	+1	PROPN
ejpam-3545	221	32	is	be	AUX
ejpam-3545	221	33	weakly	weakly	ADV
ejpam-3545	221	34	projective	projective	ADJ
ejpam-3545	221	35	with	with	ADP
ejpam-3545	221	36	respect	respect	NOUN
ejpam-3545	221	37	to	to	ADP
ejpam-3545	221	38	the	the	DET
ejpam-3545	221	39	operation	operation	NOUN
ejpam-3545	221	40	+3	+3	PROPN
ejpam-3545	221	41	.	.	PUNCT
ejpam-3545	222	1	proof	proof	NOUN
ejpam-3545	222	2	.	.	PUNCT
ejpam-3545	223	1	let	let	VERB
ejpam-3545	223	2	us	we	PRON
ejpam-3545	223	3	assume	assume	VERB
ejpam-3545	223	4	that	that	SCONJ
ejpam-3545	223	5	the	the	DET
ejpam-3545	223	6	operation	operation	NOUN
ejpam-3545	223	7	+1	+1	X
ejpam-3545	223	8	in	in	ADP
ejpam-3545	223	9	an	an	DET
ejpam-3545	223	10	abstract	abstract	ADJ
ejpam-3545	223	11	prearithmetic	prearithmetic	ADJ
ejpam-3545	223	12	a1	a1	NOUN
ejpam-3545	223	13	=	=	SYM
ejpam-3545	223	14	(	(	PUNCT
ejpam-3545	223	15	a1	a1	PROPN
ejpam-3545	223	16	;	;	PUNCT
ejpam-3545	223	17	+1	+1	PROPN
ejpam-3545	223	18	,	,	PUNCT
ejpam-3545	223	19	◦	◦	NOUN
ejpam-3545	223	20	1,≤1	1,≤1	ADJ
ejpam-3545	223	21	)	)	PUNCT
ejpam-3545	223	22	is	be	AUX
ejpam-3545	223	23	weakly	weakly	ADV
ejpam-3545	223	24	projective	projective	ADJ
ejpam-3545	223	25	with	with	ADP
ejpam-3545	223	26	respect	respect	NOUN
ejpam-3545	223	27	to	to	ADP
ejpam-3545	223	28	the	the	DET
ejpam-3545	223	29	operation	operation	NOUN
ejpam-3545	223	30	+2	+2	ADP
ejpam-3545	223	31	an	an	DET
ejpam-3545	223	32	abstract	abstract	ADJ
ejpam-3545	223	33	prearithmetic	prearithmetic	ADJ
ejpam-3545	223	34	a2	a2	PROPN
ejpam-3545	223	35	=	=	SYM
ejpam-3545	223	36	(	(	PUNCT
ejpam-3545	223	37	a2	a2	PROPN
ejpam-3545	223	38	;	;	PUNCT
ejpam-3545	223	39	+2	+2	PROPN
ejpam-3545	223	40	,	,	PUNCT
ejpam-3545	223	41	◦	◦	NOUN
ejpam-3545	223	42	2,≤2	2,≤2	NOUN
ejpam-3545	223	43	)	)	PUNCT
ejpam-3545	223	44	with	with	ADP
ejpam-3545	223	45	the	the	DET
ejpam-3545	223	46	projectors	projector	NOUN
ejpam-3545	223	47	g11	g11	NOUN
ejpam-3545	223	48	:	:	PUNCT
ejpam-3545	223	49	a1	a1	PROPN
ejpam-3545	223	50	→	→	SYM
ejpam-3545	223	51	a2	a2	PROPN
ejpam-3545	223	52	,	,	PUNCT
ejpam-3545	223	53	g12	g12	NOUN
ejpam-3545	223	54	:	:	PUNCT
ejpam-3545	223	55	a1	a1	PROPN
ejpam-3545	223	56	→	→	SYM
ejpam-3545	223	57	a2	a2	PROPN
ejpam-3545	223	58	,	,	PUNCT
ejpam-3545	223	59	and	and	CCONJ
ejpam-3545	223	60	the	the	DET
ejpam-3545	223	61	coprojector	coprojector	NOUN
ejpam-3545	223	62	h	h	NOUN
ejpam-3545	223	63	:	:	PUNCT
ejpam-3545	223	64	a2	a2	PROPN
ejpam-3545	223	65	→	→	SYM
ejpam-3545	223	66	a1	a1	NOUN
ejpam-3545	223	67	for	for	ADP
ejpam-3545	223	68	the	the	DET
ejpam-3545	223	69	pair	pair	NOUN
ejpam-3545	223	70	(	(	PUNCT
ejpam-3545	223	71	a1,a2	a1,a2	PROPN
ejpam-3545	223	72	)	)	PUNCT
ejpam-3545	223	73	and	and	CCONJ
ejpam-3545	223	74	the	the	DET
ejpam-3545	223	75	operation	operation	NOUN
ejpam-3545	223	76	+2	+2	PROPN
ejpam-3545	223	77	is	be	AUX
ejpam-3545	223	78	weakly	weakly	ADV
ejpam-3545	223	79	projective	projective	ADJ
ejpam-3545	223	80	with	with	ADP
ejpam-3545	223	81	respect	respect	NOUN
ejpam-3545	223	82	to	to	ADP
ejpam-3545	223	83	the	the	DET
ejpam-3545	223	84	operation	operation	NOUN
ejpam-3545	223	85	+3	+3	PROPN
ejpam-3545	223	86	in	in	ADP
ejpam-3545	223	87	an	an	DET
ejpam-3545	223	88	abstract	abstract	ADJ
ejpam-3545	223	89	prearithmetic	prearithmetic	ADJ
ejpam-3545	223	90	a3	a3	NOUN
ejpam-3545	223	91	=	=	SYM
ejpam-3545	223	92	(	(	PUNCT
ejpam-3545	223	93	a3	a3	NOUN
ejpam-3545	223	94	;	;	PUNCT
ejpam-3545	223	95	+3	+3	PROPN
ejpam-3545	223	96	,	,	PUNCT
ejpam-3545	223	97	◦	◦	NOUN
ejpam-3545	223	98	3,≤3	3,≤3	NOUN
ejpam-3545	223	99	)	)	PUNCT
ejpam-3545	223	100	with	with	ADP
ejpam-3545	223	101	the	the	DET
ejpam-3545	223	102	projectors	projector	NOUN
ejpam-3545	223	103	g21	g21	NOUN
ejpam-3545	223	104	:	:	PUNCT
ejpam-3545	223	105	a2	a2	PROPN
ejpam-3545	223	106	→	→	SYM
ejpam-3545	223	107	a3	a3	NOUN
ejpam-3545	223	108	,	,	PUNCT
ejpam-3545	223	109	g22	g22	NOUN
ejpam-3545	223	110	:	:	PUNCT
ejpam-3545	223	111	a2	a2	PROPN
ejpam-3545	223	112	→	→	SYM
ejpam-3545	223	113	a3	a3	NOUN
ejpam-3545	223	114	,	,	PUNCT
ejpam-3545	223	115	and	and	CCONJ
ejpam-3545	223	116	the	the	DET
ejpam-3545	223	117	coprojector	coprojector	NOUN
ejpam-3545	223	118	l	l	NOUN
ejpam-3545	223	119	:	:	PUNCT
ejpam-3545	223	120	a3	a3	PROPN
ejpam-3545	223	121	→	→	SYM
ejpam-3545	223	122	a2	a2	PROPN
ejpam-3545	223	123	for	for	ADP
ejpam-3545	223	124	the	the	DET
ejpam-3545	223	125	pair	pair	NOUN
ejpam-3545	223	126	(	(	PUNCT
ejpam-3545	223	127	a2,a3	a2,a3	PROPN
ejpam-3545	223	128	)	)	PUNCT
ejpam-3545	223	129	.	.	PUNCT
ejpam-3545	224	1	then	then	ADV
ejpam-3545	224	2	we	we	PRON
ejpam-3545	224	3	can	can	AUX
ejpam-3545	224	4	define	define	VERB
ejpam-3545	224	5	mappings	mapping	NOUN
ejpam-3545	224	6	qi	qi	PRON
ejpam-3545	224	7	=	=	NOUN
ejpam-3545	224	8	g1ig2i	g1ig2i	X
ejpam-3545	224	9	:	:	PUNCT
ejpam-3545	224	10	a1	a1	PROPN
ejpam-3545	224	11	→	→	SYM
ejpam-3545	224	12	a3(i	a3(i	PROPN
ejpam-3545	224	13	=	=	SYM
ejpam-3545	224	14	1	1	NUM
ejpam-3545	224	15	,	,	PUNCT
ejpam-3545	224	16	2	2	NUM
ejpam-3545	224	17	)	)	PUNCT
ejpam-3545	224	18	and	and	CCONJ
ejpam-3545	224	19	p	p	NOUN
ejpam-3545	224	20	=	=	NOUN
ejpam-3545	224	21	hl	hl	NOUN
ejpam-3545	224	22	:	:	PUNCT
ejpam-3545	224	23	a3	a3	PROPN
ejpam-3545	224	24	→	→	SYM
ejpam-3545	224	25	a1	a1	NOUN
ejpam-3545	224	26	.	.	PUNCT
ejpam-3545	225	1	let	let	VERB
ejpam-3545	225	2	us	we	PRON
ejpam-3545	225	3	consider	consider	VERB
ejpam-3545	225	4	relations	relation	NOUN
ejpam-3545	225	5	between	between	ADP
ejpam-3545	225	6	operations	operation	NOUN
ejpam-3545	225	7	+1	+1	NOUN
ejpam-3545	225	8	and	and	CCONJ
ejpam-3545	225	9	+3	+3	PROPN
ejpam-3545	225	10	.	.	PUNCT
ejpam-3545	226	1	a	a	DET
ejpam-3545	226	2	+1	+1	PROPN
ejpam-3545	226	3	b	b	X
ejpam-3545	226	4	=	=	SYM
ejpam-3545	226	5	h(g11(a	h(g11(a	PROPN
ejpam-3545	226	6	)	)	PUNCT
ejpam-3545	226	7	+2	+2	ADV
ejpam-3545	226	8	g12(b	g12(b	ADJ
ejpam-3545	226	9	)	)	PUNCT
ejpam-3545	226	10	)	)	PUNCT
ejpam-3545	227	1	=	=	PUNCT
ejpam-3545	227	2	h(l(g21(g11(a	h(l(g21(g11(a	NOUN
ejpam-3545	227	3	)	)	PUNCT
ejpam-3545	227	4	)	)	PUNCT
ejpam-3545	228	1	+3	+3	PROPN
ejpam-3545	228	2	g22(g12(b	g22(g12(b	ADJ
ejpam-3545	228	3	)	)	PUNCT
ejpam-3545	228	4	)	)	PUNCT
ejpam-3545	228	5	)	)	PUNCT
ejpam-3545	228	6	)	)	PUNCT
ejpam-3545	229	1	=	=	PUNCT
ejpam-3545	229	2	hl(g21g11(a	hl(g21g11(a	PROPN
ejpam-3545	229	3	)	)	PUNCT
ejpam-3545	229	4	+3	+3	PROPN
ejpam-3545	229	5	g22g12(b	g22g12(b	NOUN
ejpam-3545	229	6	)	)	PUNCT
ejpam-3545	229	7	)	)	PUNCT
ejpam-3545	230	1	=	=	SYM
ejpam-3545	230	2	p(q1(a	p(q1(a	PROPN
ejpam-3545	230	3	)	)	PUNCT
ejpam-3545	230	4	+3	+3	PROPN
ejpam-3545	230	5	q2(b	q2(b	ADJ
ejpam-3545	230	6	)	)	PUNCT
ejpam-3545	230	7	)	)	PUNCT
ejpam-3545	231	1	consequently	consequently	ADV
ejpam-3545	231	2	,	,	PUNCT
ejpam-3545	231	3	a	a	DET
ejpam-3545	231	4	+1	+1	PROPN
ejpam-3545	231	5	b	b	X
ejpam-3545	231	6	=	=	SYM
ejpam-3545	231	7	p(q1(a	p(q1(a	PROPN
ejpam-3545	231	8	)	)	PUNCT
ejpam-3545	231	9	+3	+3	PROPN
ejpam-3545	231	10	q2(b	q2(b	ADJ
ejpam-3545	231	11	)	)	PUNCT
ejpam-3545	231	12	)	)	PUNCT
ejpam-3545	231	13	for	for	ADP
ejpam-3545	231	14	any	any	DET
ejpam-3545	231	15	elements	element	NOUN
ejpam-3545	231	16	a	a	PRON
ejpam-3545	231	17	and	and	CCONJ
ejpam-3545	231	18	b	b	NOUN
ejpam-3545	231	19	from	from	ADP
ejpam-3545	231	20	a1	a1	PROPN
ejpam-3545	231	21	.	.	PUNCT
ejpam-3545	232	1	it	it	PRON
ejpam-3545	232	2	means	mean	VERB
ejpam-3545	232	3	the	the	DET
ejpam-3545	232	4	operation	operation	NOUN
ejpam-3545	232	5	+1	+1	PROPN
ejpam-3545	232	6	is	be	AUX
ejpam-3545	232	7	weakly	weakly	ADV
ejpam-3545	232	8	projective	projective	ADJ
ejpam-3545	232	9	with	with	ADP
ejpam-3545	232	10	respect	respect	NOUN
ejpam-3545	232	11	to	to	ADP
ejpam-3545	232	12	the	the	DET
ejpam-3545	232	13	operation	operation	NOUN
ejpam-3545	232	14	+3	+3	PROPN
ejpam-3545	232	15	.	.	PUNCT
ejpam-3545	233	1	proposition	proposition	NOUN
ejpam-3545	233	2	is	be	AUX
ejpam-3545	233	3	proved	prove	VERB
ejpam-3545	233	4	.	.	PUNCT
ejpam-3545	234	1	proposition	proposition	NOUN
ejpam-3545	234	2	3.2	3.2	NUM
ejpam-3545	234	3	allows	allow	VERB
ejpam-3545	234	4	proving	prove	VERB
ejpam-3545	234	5	the	the	DET
ejpam-3545	234	6	following	follow	VERB
ejpam-3545	234	7	result	result	NOUN
ejpam-3545	234	8	.	.	PUNCT
ejpam-3545	235	1	theorem	theorem	NOUN
ejpam-3545	235	2	1	1	NUM
ejpam-3545	235	3	.	.	PUNCT
ejpam-3545	236	1	abstract	abstract	ADJ
ejpam-3545	236	2	prearithmetics	prearithmetic	NOUN
ejpam-3545	236	3	with	with	ADP
ejpam-3545	236	4	weak	weak	ADJ
ejpam-3545	236	5	projectivity	projectivity	NOUN
ejpam-3545	236	6	relations	relation	NOUN
ejpam-3545	236	7	for	for	ADP
ejpam-3545	236	8	addition	addition	NOUN
ejpam-3545	236	9	form	form	NOUN
ejpam-3545	236	10	the	the	DET
ejpam-3545	236	11	category	category	NOUN
ejpam-3545	236	12	aawp	aawp	ADV
ejpam-3545	236	13	where	where	SCONJ
ejpam-3545	236	14	objects	object	NOUN
ejpam-3545	236	15	are	be	AUX
ejpam-3545	236	16	abstract	abstract	ADJ
ejpam-3545	236	17	prearithmetics	prearithmetic	NOUN
ejpam-3545	236	18	and	and	CCONJ
ejpam-3545	236	19	morphisms	morphism	NOUN
ejpam-3545	236	20	are	be	AUX
ejpam-3545	236	21	weak	weak	ADJ
ejpam-3545	236	22	projectivity	projectivity	NOUN
ejpam-3545	236	23	relations	relation	NOUN
ejpam-3545	236	24	between	between	ADP
ejpam-3545	236	25	additions	addition	NOUN
ejpam-3545	236	26	.	.	PUNCT
ejpam-3545	237	1	m.	m.	NOUN
ejpam-3545	237	2	burgin	burgin	PROPN
ejpam-3545	237	3	/	/	SYM
ejpam-3545	237	4	eur	eur	PROPN
ejpam-3545	237	5	.	.	PUNCT
ejpam-3545	238	1	j.	j.	PROPN
ejpam-3545	238	2	pure	pure	PROPN
ejpam-3545	238	3	appl	appl	PROPN
ejpam-3545	238	4	.	.	PROPN
ejpam-3545	238	5	math	math	PROPN
ejpam-3545	238	6	,	,	PUNCT
ejpam-3545	238	7	12	12	NUM
ejpam-3545	238	8	(	(	PUNCT
ejpam-3545	238	9	4	4	NUM
ejpam-3545	238	10	)	)	PUNCT
ejpam-3545	238	11	(	(	PUNCT
ejpam-3545	238	12	2019	2019	NUM
ejpam-3545	238	13	)	)	PUNCT
ejpam-3545	238	14	,	,	PUNCT
ejpam-3545	238	15	1787	1787	NUM
ejpam-3545	238	16	-	-	SYM
ejpam-3545	238	17	1810	1810	NUM
ejpam-3545	238	18	1796	1796	NUM
ejpam-3545	238	19	indeed	indeed	ADV
ejpam-3545	238	20	,	,	PUNCT
ejpam-3545	238	21	the	the	DET
ejpam-3545	238	22	identity	identity	NOUN
ejpam-3545	238	23	function	function	NOUN
ejpam-3545	238	24	defines	define	VERB
ejpam-3545	238	25	weak	weak	ADJ
ejpam-3545	238	26	projectivity	projectivity	NOUN
ejpam-3545	238	27	relations	relation	NOUN
ejpam-3545	238	28	for	for	ADP
ejpam-3545	238	29	addition	addition	NOUN
ejpam-3545	238	30	of	of	ADP
ejpam-3545	238	31	an	an	DET
ejpam-3545	238	32	abstract	abstract	ADJ
ejpam-3545	238	33	prearithmetic	prearithmetic	NOUN
ejpam-3545	238	34	with	with	ADP
ejpam-3545	238	35	itself	itself	PRON
ejpam-3545	238	36	and	and	CCONJ
ejpam-3545	238	37	by	by	ADP
ejpam-3545	238	38	proposition	proposition	NOUN
ejpam-3545	238	39	3.2	3.2	NUM
ejpam-3545	238	40	,	,	PUNCT
ejpam-3545	238	41	the	the	DET
ejpam-3545	238	42	sequential	sequential	ADJ
ejpam-3545	238	43	composition	composition	NOUN
ejpam-3545	238	44	of	of	ADP
ejpam-3545	238	45	weak	weak	ADJ
ejpam-3545	238	46	projectivity	projectivity	NOUN
ejpam-3545	238	47	relations	relation	NOUN
ejpam-3545	238	48	is	be	AUX
ejpam-3545	238	49	a	a	DET
ejpam-3545	238	50	weak	weak	ADJ
ejpam-3545	238	51	projectivity	projectivity	NOUN
ejpam-3545	238	52	relation	relation	NOUN
ejpam-3545	238	53	.	.	PUNCT
ejpam-3545	239	1	in	in	ADP
ejpam-3545	239	2	this	this	DET
ejpam-3545	239	3	category	category	NOUN
ejpam-3545	239	4	,	,	PUNCT
ejpam-3545	239	5	the	the	DET
ejpam-3545	239	6	identity	identity	NOUN
ejpam-3545	239	7	morphism	morphism	NOUN
ejpam-3545	239	8	of	of	ADP
ejpam-3545	239	9	an	an	DET
ejpam-3545	239	10	abstract	abstract	ADJ
ejpam-3545	239	11	prearithmetic	prearithmetic	NOUN
ejpam-3545	239	12	a	a	PRON
ejpam-3545	239	13	is	be	AUX
ejpam-3545	239	14	the	the	DET
ejpam-3545	239	15	weak	weak	ADJ
ejpam-3545	239	16	projectivity	projectivity	NOUN
ejpam-3545	239	17	in	in	ADP
ejpam-3545	239	18	which	which	PRON
ejpam-3545	239	19	both	both	DET
ejpam-3545	239	20	projectors	projector	NOUN
ejpam-3545	239	21	and	and	CCONJ
ejpam-3545	239	22	the	the	DET
ejpam-3545	239	23	coprojector	coprojector	NOUN
ejpam-3545	239	24	are	be	AUX
ejpam-3545	239	25	identity	identity	NOUN
ejpam-3545	239	26	mappings	mapping	NOUN
ejpam-3545	239	27	of	of	ADP
ejpam-3545	239	28	this	this	DET
ejpam-3545	239	29	prearithmetic	prearithmetic	NOUN
ejpam-3545	239	30	.	.	PUNCT
ejpam-3545	240	1	an	an	DET
ejpam-3545	240	2	important	important	ADJ
ejpam-3545	240	3	special	special	ADJ
ejpam-3545	240	4	case	case	NOUN
ejpam-3545	240	5	of	of	ADP
ejpam-3545	240	6	weak	weak	ADJ
ejpam-3545	240	7	projectivity	projectivity	NOUN
ejpam-3545	240	8	is	be	AUX
ejpam-3545	240	9	obtained	obtain	VERB
ejpam-3545	240	10	when	when	SCONJ
ejpam-3545	240	11	both	both	DET
ejpam-3545	240	12	projections	projection	NOUN
ejpam-3545	240	13	coincide	coincide	VERB
ejpam-3545	240	14	.	.	PUNCT
ejpam-3545	241	1	definition	definition	NOUN
ejpam-3545	241	2	2	2	NUM
ejpam-3545	241	3	.	.	PUNCT
ejpam-3545	242	1	a	a	X
ejpam-3545	242	2	)	)	PUNCT
ejpam-3545	242	3	addition	addition	NOUN
ejpam-3545	242	4	+1	+1	PRON
ejpam-3545	242	5	in	in	ADP
ejpam-3545	242	6	the	the	DET
ejpam-3545	242	7	abstract	abstract	ADJ
ejpam-3545	242	8	prearithmetic	prearithmetic	ADJ
ejpam-3545	242	9	a1	a1	NOUN
ejpam-3545	242	10	=	=	SYM
ejpam-3545	242	11	(	(	PUNCT
ejpam-3545	242	12	a1	a1	PROPN
ejpam-3545	242	13	;	;	PUNCT
ejpam-3545	242	14	+1	+1	PROPN
ejpam-3545	242	15	,	,	PUNCT
ejpam-3545	242	16	◦	◦	NOUN
ejpam-3545	242	17	1,≤1	1,≤1	ADJ
ejpam-3545	242	18	)	)	PUNCT
ejpam-3545	242	19	is	be	AUX
ejpam-3545	242	20	called	call	VERB
ejpam-3545	242	21	weakly	weakly	ADJ
ejpam-3545	242	22	monoprojective	monoprojective	NOUN
ejpam-3545	242	23	with	with	ADP
ejpam-3545	242	24	respect	respect	NOUN
ejpam-3545	242	25	to	to	ADP
ejpam-3545	242	26	addition	addition	NOUN
ejpam-3545	242	27	+2	+2	ADP
ejpam-3545	242	28	in	in	ADP
ejpam-3545	242	29	the	the	DET
ejpam-3545	242	30	abstract	abstract	ADJ
ejpam-3545	242	31	prearithmetic	prearithmetic	ADJ
ejpam-3545	242	32	a2	a2	PROPN
ejpam-3545	242	33	=	=	SYM
ejpam-3545	242	34	(	(	PUNCT
ejpam-3545	242	35	a2	a2	PROPN
ejpam-3545	242	36	;	;	PUNCT
ejpam-3545	242	37	+2	+2	PROPN
ejpam-3545	242	38	,	,	PUNCT
ejpam-3545	242	39	◦	◦	NOUN
ejpam-3545	242	40	2,≤2	2,≤2	NOUN
ejpam-3545	242	41	)	)	PUNCT
ejpam-3545	242	42	if	if	SCONJ
ejpam-3545	242	43	+1	+1	PROPN
ejpam-3545	242	44	is	be	AUX
ejpam-3545	242	45	weakly	weakly	ADV
ejpam-3545	242	46	projective	projective	ADJ
ejpam-3545	242	47	with	with	ADP
ejpam-3545	242	48	respect	respect	NOUN
ejpam-3545	242	49	to	to	ADP
ejpam-3545	242	50	addition	addition	NOUN
ejpam-3545	242	51	+2	+2	PRON
ejpam-3545	242	52	and	and	CCONJ
ejpam-3545	242	53	g1	g1	PROPN
ejpam-3545	242	54	=	=	PROPN
ejpam-3545	242	55	g2	g2	PROPN
ejpam-3545	242	56	,	,	PUNCT
ejpam-3545	242	57	i.e.	i.e.	X
ejpam-3545	242	58	,	,	PUNCT
ejpam-3545	242	59	there	there	PRON
ejpam-3545	242	60	is	be	VERB
ejpam-3545	242	61	only	only	ADV
ejpam-3545	242	62	one	one	NUM
ejpam-3545	242	63	projector	projector	NOUN
ejpam-3545	242	64	.	.	PUNCT
ejpam-3545	243	1	b	b	X
ejpam-3545	243	2	)	)	PUNCT
ejpam-3545	243	3	in	in	ADP
ejpam-3545	243	4	this	this	DET
ejpam-3545	243	5	case	case	NOUN
ejpam-3545	243	6	,	,	PUNCT
ejpam-3545	243	7	we	we	PRON
ejpam-3545	243	8	say	say	VERB
ejpam-3545	243	9	that	that	SCONJ
ejpam-3545	243	10	addition	addition	NOUN
ejpam-3545	243	11	in	in	ADP
ejpam-3545	243	12	a2	a2	PROPN
ejpam-3545	243	13	is	be	AUX
ejpam-3545	243	14	weakly	weakly	ADV
ejpam-3545	243	15	monoprojected	monoprojected	ADJ
ejpam-3545	243	16	onto	onto	ADP
ejpam-3545	243	17	addition	addition	NOUN
ejpam-3545	243	18	in	in	ADP
ejpam-3545	243	19	a1	a1	NOUN
ejpam-3545	243	20	while	while	SCONJ
ejpam-3545	243	21	addition	addition	NOUN
ejpam-3545	243	22	in	in	ADP
ejpam-3545	243	23	a1	a1	NOUN
ejpam-3545	243	24	is	be	AUX
ejpam-3545	243	25	a	a	DET
ejpam-3545	243	26	weak	weak	ADJ
ejpam-3545	243	27	monoprojection	monoprojection	NOUN
ejpam-3545	243	28	of	of	ADP
ejpam-3545	243	29	addition	addition	NOUN
ejpam-3545	243	30	in	in	ADP
ejpam-3545	243	31	a2	a2	PROPN
ejpam-3545	243	32	.	.	PUNCT
ejpam-3545	244	1	we	we	PRON
ejpam-3545	244	2	also	also	ADV
ejpam-3545	244	3	say	say	VERB
ejpam-3545	244	4	that	that	SCONJ
ejpam-3545	244	5	there	there	PRON
ejpam-3545	244	6	is	be	VERB
ejpam-3545	244	7	a	a	DET
ejpam-3545	244	8	weak	weak	ADJ
ejpam-3545	244	9	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	244	10	between	between	ADP
ejpam-3545	244	11	addition	addition	NOUN
ejpam-3545	244	12	in	in	ADP
ejpam-3545	244	13	the	the	DET
ejpam-3545	244	14	prearithmetic	prearithmetic	ADJ
ejpam-3545	244	15	a1	a1	NOUN
ejpam-3545	244	16	and	and	CCONJ
ejpam-3545	244	17	addition	addition	NOUN
ejpam-3545	244	18	in	in	ADP
ejpam-3545	244	19	the	the	DET
ejpam-3545	244	20	prearithmetic	prearithmetic	PROPN
ejpam-3545	244	21	a2	a2	PROPN
ejpam-3545	244	22	and	and	CCONJ
ejpam-3545	244	23	there	there	PRON
ejpam-3545	244	24	is	be	VERB
ejpam-3545	244	25	an	an	DET
ejpam-3545	244	26	inverse	inverse	NOUN
ejpam-3545	244	27	weak	weak	ADJ
ejpam-3545	244	28	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	244	29	between	between	ADP
ejpam-3545	244	30	addition	addition	NOUN
ejpam-3545	244	31	in	in	ADP
ejpam-3545	244	32	the	the	DET
ejpam-3545	244	33	prearithmetic	prearithmetic	ADJ
ejpam-3545	244	34	a2	a2	PROPN
ejpam-3545	244	35	and	and	CCONJ
ejpam-3545	244	36	addition	addition	NOUN
ejpam-3545	244	37	in	in	ADP
ejpam-3545	244	38	the	the	DET
ejpam-3545	244	39	prearithmetic	prearithmetic	ADJ
ejpam-3545	244	40	a1	a1	NOUN
ejpam-3545	244	41	.	.	PUNCT
ejpam-3545	245	1	this	this	DET
ejpam-3545	245	2	relation	relation	NOUN
ejpam-3545	245	3	is	be	AUX
ejpam-3545	245	4	also	also	ADV
ejpam-3545	245	5	calledadditive	calledadditive	VERB
ejpam-3545	245	6	weak	weak	ADJ
ejpam-3545	245	7	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	245	8	between	between	ADP
ejpam-3545	245	9	prearithmetics	prearithmetic	NOUN
ejpam-3545	245	10	a1	a1	NOUN
ejpam-3545	245	11	and	and	CCONJ
ejpam-3545	245	12	a2	a2	PROPN
ejpam-3545	245	13	.	.	PUNCT
ejpam-3545	245	14	example	example	NOUN
ejpam-3545	246	1	14	14	NUM
ejpam-3545	246	2	.	.	PUNCT
ejpam-3545	246	3	weak	weak	ADJ
ejpam-3545	246	4	projectivity	projectivity	NOUN
ejpam-3545	246	5	in	in	ADP
ejpam-3545	246	6	non	non	ADJ
ejpam-3545	246	7	-	-	ADJ
ejpam-3545	246	8	diophantine	diophantine	ADJ
ejpam-3545	246	9	arithmetics	arithmetic	NOUN
ejpam-3545	246	10	is	be	AUX
ejpam-3545	246	11	an	an	DET
ejpam-3545	246	12	example	example	NOUN
ejpam-3545	246	13	of	of	ADP
ejpam-3545	246	14	weak	weak	ADJ
ejpam-3545	246	15	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	246	16	between	between	ADP
ejpam-3545	246	17	addition	addition	NOUN
ejpam-3545	246	18	in	in	ADP
ejpam-3545	246	19	one	one	NUM
ejpam-3545	246	20	prearithmetic	prearithmetic	ADJ
ejpam-3545	246	21	and	and	CCONJ
ejpam-3545	246	22	addition	addition	NOUN
ejpam-3545	246	23	in	in	ADP
ejpam-3545	246	24	another	another	DET
ejpam-3545	246	25	prearithmetic	prearithmetic	ADJ
ejpam-3545	246	26	[	[	X
ejpam-3545	246	27	5	5	NUM
ejpam-3545	246	28	,	,	PUNCT
ejpam-3545	246	29	11	11	NUM
ejpam-3545	246	30	]	]	PUNCT
ejpam-3545	246	31	.	.	PUNCT
ejpam-3545	247	1	let	let	VERB
ejpam-3545	247	2	us	we	PRON
ejpam-3545	247	3	consider	consider	VERB
ejpam-3545	247	4	two	two	NUM
ejpam-3545	247	5	abstract	abstract	ADJ
ejpam-3545	247	6	prearithmeticsa1	prearithmeticsa1	NOUN
ejpam-3545	247	7	=	=	SYM
ejpam-3545	247	8	(	(	PUNCT
ejpam-3545	247	9	a1	a1	PROPN
ejpam-3545	247	10	;	;	PUNCT
ejpam-3545	247	11	+1	+1	PROPN
ejpam-3545	247	12	,	,	PUNCT
ejpam-3545	247	13	◦	◦	NOUN
ejpam-3545	247	14	1,≤1	1,≤1	ADJ
ejpam-3545	247	15	)	)	PUNCT
ejpam-3545	247	16	and	and	CCONJ
ejpam-3545	247	17	a2	a2	PROPN
ejpam-3545	247	18	=	=	SYM
ejpam-3545	247	19	(	(	PUNCT
ejpam-3545	247	20	a2	a2	PROPN
ejpam-3545	247	21	;	;	PUNCT
ejpam-3545	247	22	+2	+2	PROPN
ejpam-3545	247	23	,	,	PUNCT
ejpam-3545	247	24	◦	◦	NOUN
ejpam-3545	247	25	2,≤2	2,≤2	NUM
ejpam-3545	247	26	)	)	PUNCT
ejpam-3545	247	27	.	.	PUNCT
ejpam-3545	248	1	proposition	proposition	NOUN
ejpam-3545	248	2	3.3	3.3	NUM
ejpam-3545	248	3	.	.	PUNCT
ejpam-3545	249	1	if	if	SCONJ
ejpam-3545	249	2	the	the	DET
ejpam-3545	249	3	operation	operation	NOUN
ejpam-3545	249	4	+1	+1	PROPN
ejpam-3545	249	5	is	be	AUX
ejpam-3545	249	6	weakly	weakly	ADV
ejpam-3545	249	7	monoprojective	monoprojective	ADJ
ejpam-3545	249	8	with	with	ADP
ejpam-3545	249	9	respect	respect	NOUN
ejpam-3545	249	10	to	to	ADP
ejpam-3545	249	11	the	the	DET
ejpam-3545	249	12	operation	operation	NOUN
ejpam-3545	249	13	+2	+2	PROPN
ejpam-3545	249	14	with	with	ADP
ejpam-3545	249	15	the	the	DET
ejpam-3545	249	16	projector	projector	NOUN
ejpam-3545	249	17	g	g	NOUN
ejpam-3545	249	18	and	and	CCONJ
ejpam-3545	249	19	the	the	DET
ejpam-3545	249	20	operation	operation	NOUN
ejpam-3545	249	21	+2	+2	PROPN
ejpam-3545	249	22	is	be	AUX
ejpam-3545	249	23	commutative	commutative	ADJ
ejpam-3545	249	24	in	in	ADP
ejpam-3545	249	25	the	the	DET
ejpam-3545	249	26	prearithmetic	prearithmetic	PROPN
ejpam-3545	249	27	a2	a2	PROPN
ejpam-3545	249	28	,	,	PUNCT
ejpam-3545	249	29	then	then	ADV
ejpam-3545	249	30	the	the	DET
ejpam-3545	249	31	operation	operation	NOUN
ejpam-3545	249	32	+1	+1	PROPN
ejpam-3545	249	33	is	be	AUX
ejpam-3545	249	34	commutative	commutative	ADJ
ejpam-3545	249	35	in	in	ADP
ejpam-3545	249	36	the	the	DET
ejpam-3545	249	37	prearithmetic	prearithmetic	ADJ
ejpam-3545	249	38	a1	a1	NOUN
ejpam-3545	249	39	.	.	PUNCT
ejpam-3545	250	1	indeed	indeed	ADV
ejpam-3545	250	2	,	,	PUNCT
ejpam-3545	250	3	for	for	ADP
ejpam-3545	250	4	any	any	DET
ejpam-3545	250	5	elements	element	NOUN
ejpam-3545	250	6	a	a	PRON
ejpam-3545	250	7	and	and	CCONJ
ejpam-3545	250	8	b	b	NOUN
ejpam-3545	250	9	from	from	ADP
ejpam-3545	250	10	a1	a1	NOUN
ejpam-3545	250	11	,	,	PUNCT
ejpam-3545	250	12	we	we	PRON
ejpam-3545	250	13	have	have	VERB
ejpam-3545	250	14	a	a	DET
ejpam-3545	250	15	+1	+1	PROPN
ejpam-3545	250	16	b	b	NOUN
ejpam-3545	250	17	=	=	SYM
ejpam-3545	250	18	h(g(a	h(g(a	PROPN
ejpam-3545	250	19	)	)	PUNCT
ejpam-3545	250	20	+2	+2	PROPN
ejpam-3545	250	21	g(b	g(b	NOUN
ejpam-3545	250	22	)	)	PUNCT
ejpam-3545	250	23	)	)	PUNCT
ejpam-3545	251	1	=	=	SYM
ejpam-3545	251	2	h(g(b	h(g(b	NOUN
ejpam-3545	251	3	)	)	PUNCT
ejpam-3545	251	4	+2	+2	PROPN
ejpam-3545	251	5	g(a	g(a	PROPN
ejpam-3545	251	6	)	)	PUNCT
ejpam-3545	251	7	)	)	PUNCT
ejpam-3545	252	1	=	=	PUNCT
ejpam-3545	252	2	b	b	X
ejpam-3545	252	3	+1	+1	NOUN
ejpam-3545	252	4	a	a	PRON
ejpam-3545	252	5	this	this	DET
ejpam-3545	252	6	shows	show	NOUN
ejpam-3545	252	7	that	that	SCONJ
ejpam-3545	252	8	inverse	inverse	NOUN
ejpam-3545	252	9	weak	weak	ADJ
ejpam-3545	252	10	projectivity	projectivity	NOUN
ejpam-3545	252	11	preserves	preserve	VERB
ejpam-3545	252	12	commutativity	commutativity	NOUN
ejpam-3545	252	13	of	of	ADP
ejpam-3545	252	14	addition	addition	NOUN
ejpam-3545	252	15	.	.	PUNCT
ejpam-3545	253	1	to	to	PART
ejpam-3545	253	2	preserve	preserve	VERB
ejpam-3545	253	3	associativity	associativity	NOUN
ejpam-3545	253	4	of	of	ADP
ejpam-3545	253	5	addition	addition	NOUN
ejpam-3545	253	6	in	in	ADP
ejpam-3545	253	7	inverse	inverse	ADJ
ejpam-3545	253	8	weak	weak	ADJ
ejpam-3545	253	9	projectivity	projectivity	NOUN
ejpam-3545	253	10	,	,	PUNCT
ejpam-3545	253	11	we	we	PRON
ejpam-3545	253	12	need	need	VERB
ejpam-3545	253	13	stronger	strong	ADJ
ejpam-3545	253	14	conditions	condition	NOUN
ejpam-3545	253	15	.	.	PUNCT
ejpam-3545	254	1	proposition	proposition	NOUN
ejpam-3545	254	2	3.4	3.4	NUM
ejpam-3545	254	3	.	.	PUNCT
ejpam-3545	255	1	if	if	SCONJ
ejpam-3545	255	2	the	the	DET
ejpam-3545	255	3	operation	operation	NOUN
ejpam-3545	255	4	+1	+1	PROPN
ejpam-3545	255	5	is	be	AUX
ejpam-3545	255	6	weakly	weakly	ADV
ejpam-3545	255	7	monoprojective	monoprojective	ADJ
ejpam-3545	255	8	with	with	ADP
ejpam-3545	255	9	respect	respect	NOUN
ejpam-3545	255	10	to	to	ADP
ejpam-3545	255	11	the	the	DET
ejpam-3545	255	12	operation	operation	NOUN
ejpam-3545	255	13	+2	+2	PROPN
ejpam-3545	255	14	with	with	ADP
ejpam-3545	255	15	the	the	DET
ejpam-3545	255	16	coprojector	coprojector	NOUN
ejpam-3545	255	17	h	h	NOUN
ejpam-3545	255	18	and	and	CCONJ
ejpam-3545	255	19	the	the	DET
ejpam-3545	255	20	projector	projector	NOUN
ejpam-3545	255	21	g	g	NOUN
ejpam-3545	255	22	,	,	PUNCT
ejpam-3545	255	23	which	which	PRON
ejpam-3545	255	24	is	be	AUX
ejpam-3545	255	25	a	a	DET
ejpam-3545	255	26	homomorphism	homomorphism	NOUN
ejpam-3545	255	27	with	with	ADP
ejpam-3545	255	28	respect	respect	NOUN
ejpam-3545	255	29	to	to	ADP
ejpam-3545	255	30	addition	addition	NOUN
ejpam-3545	255	31	+1	+1	PRON
ejpam-3545	255	32	,	,	PUNCT
ejpam-3545	255	33	i.e.	i.e.	X
ejpam-3545	255	34	,	,	PUNCT
ejpam-3545	255	35	g(a	g(a	PROPN
ejpam-3545	255	36	+1	+1	PROPN
ejpam-3545	255	37	b	b	PROPN
ejpam-3545	255	38	)	)	PUNCT
ejpam-3545	255	39	=	=	SYM
ejpam-3545	255	40	g(a	g(a	PROPN
ejpam-3545	255	41	)	)	PUNCT
ejpam-3545	255	42	+2	+2	PROPN
ejpam-3545	255	43	g(b	g(b	PROPN
ejpam-3545	255	44	)	)	PUNCT
ejpam-3545	255	45	for	for	ADP
ejpam-3545	255	46	arbitrary	arbitrary	ADJ
ejpam-3545	255	47	elements	element	NOUN
ejpam-3545	255	48	a	a	PRON
ejpam-3545	255	49	and	and	CCONJ
ejpam-3545	255	50	b	b	NOUN
ejpam-3545	255	51	from	from	ADP
ejpam-3545	255	52	a1	a1	NOUN
ejpam-3545	255	53	,	,	PUNCT
ejpam-3545	255	54	and	and	CCONJ
ejpam-3545	255	55	the	the	DET
ejpam-3545	255	56	operation	operation	NOUN
ejpam-3545	255	57	+2	+2	PROPN
ejpam-3545	255	58	is	be	AUX
ejpam-3545	255	59	associative	associative	ADJ
ejpam-3545	255	60	in	in	ADP
ejpam-3545	255	61	the	the	DET
ejpam-3545	255	62	prearithmetic	prearithmetic	PROPN
ejpam-3545	255	63	a2	a2	PROPN
ejpam-3545	255	64	,	,	PUNCT
ejpam-3545	255	65	then	then	ADV
ejpam-3545	255	66	the	the	DET
ejpam-3545	255	67	operation	operation	NOUN
ejpam-3545	255	68	+1	+1	PROPN
ejpam-3545	255	69	is	be	AUX
ejpam-3545	255	70	associative	associative	ADJ
ejpam-3545	255	71	in	in	ADP
ejpam-3545	255	72	the	the	DET
ejpam-3545	255	73	prearithmetic	prearithmetic	ADJ
ejpam-3545	255	74	a1	a1	NOUN
ejpam-3545	255	75	.	.	PUNCT
ejpam-3545	256	1	proof	proof	NOUN
ejpam-3545	256	2	.	.	PUNCT
ejpam-3545	257	1	assuming	assume	VERB
ejpam-3545	257	2	that	that	SCONJ
ejpam-3545	257	3	g	g	PROPN
ejpam-3545	257	4	is	be	AUX
ejpam-3545	257	5	a	a	DET
ejpam-3545	257	6	homomorphism	homomorphism	NOUN
ejpam-3545	257	7	with	with	ADP
ejpam-3545	257	8	respect	respect	NOUN
ejpam-3545	257	9	to	to	ADP
ejpam-3545	257	10	addition	addition	NOUN
ejpam-3545	257	11	and	and	CCONJ
ejpam-3545	257	12	the	the	DET
ejpam-3545	257	13	operation	operation	NOUN
ejpam-3545	257	14	+2	+2	PROPN
ejpam-3545	257	15	is	be	AUX
ejpam-3545	257	16	associative	associative	ADJ
ejpam-3545	257	17	in	in	ADP
ejpam-3545	257	18	the	the	DET
ejpam-3545	257	19	prearithmetic	prearithmetic	PROPN
ejpam-3545	257	20	a2	a2	PROPN
ejpam-3545	257	21	,	,	PUNCT
ejpam-3545	257	22	let	let	VERB
ejpam-3545	257	23	us	we	PRON
ejpam-3545	257	24	take	take	VERB
ejpam-3545	257	25	arbitrary	arbitrary	ADJ
ejpam-3545	257	26	elements	element	NOUN
ejpam-3545	257	27	a	a	PRON
ejpam-3545	257	28	and	and	CCONJ
ejpam-3545	257	29	b	b	NOUN
ejpam-3545	257	30	from	from	ADP
ejpam-3545	257	31	a1	a1	PROPN
ejpam-3545	257	32	.	.	PUNCT
ejpam-3545	258	1	then	then	ADV
ejpam-3545	258	2	by	by	ADP
ejpam-3545	258	3	definition	definition	NOUN
ejpam-3545	258	4	,	,	PUNCT
ejpam-3545	258	5	we	we	PRON
ejpam-3545	258	6	have	have	VERB
ejpam-3545	258	7	m.	m.	NOUN
ejpam-3545	258	8	burgin	burgin	PROPN
ejpam-3545	258	9	/	/	SYM
ejpam-3545	258	10	eur	eur	PROPN
ejpam-3545	258	11	.	.	PUNCT
ejpam-3545	259	1	j.	j.	PROPN
ejpam-3545	259	2	pure	pure	PROPN
ejpam-3545	259	3	appl	appl	PROPN
ejpam-3545	259	4	.	.	PROPN
ejpam-3545	259	5	math	math	PROPN
ejpam-3545	259	6	,	,	PUNCT
ejpam-3545	259	7	12	12	NUM
ejpam-3545	259	8	(	(	PUNCT
ejpam-3545	259	9	4	4	NUM
ejpam-3545	259	10	)	)	PUNCT
ejpam-3545	259	11	(	(	PUNCT
ejpam-3545	259	12	2019	2019	NUM
ejpam-3545	259	13	)	)	PUNCT
ejpam-3545	259	14	,	,	PUNCT
ejpam-3545	259	15	1787	1787	NUM
ejpam-3545	259	16	-	-	SYM
ejpam-3545	259	17	1810	1810	NUM
ejpam-3545	259	18	1797	1797	NUM
ejpam-3545	259	19	g(a	g(a	PROPN
ejpam-3545	259	20	+1	+1	PROPN
ejpam-3545	259	21	b	b	PROPN
ejpam-3545	259	22	)	)	PUNCT
ejpam-3545	259	23	=	=	SYM
ejpam-3545	259	24	g(h(g(a	g(h(g(a	PROPN
ejpam-3545	259	25	)	)	PUNCT
ejpam-3545	260	1	+2	+2	PROPN
ejpam-3545	260	2	g(b	g(b	NOUN
ejpam-3545	260	3	)	)	PUNCT
ejpam-3545	260	4	)	)	PUNCT
ejpam-3545	260	5	)	)	PUNCT
ejpam-3545	261	1	=	=	SYM
ejpam-3545	261	2	g(a	g(a	PROPN
ejpam-3545	261	3	)	)	PUNCT
ejpam-3545	261	4	+2	+2	PROPN
ejpam-3545	261	5	g(b	g(b	PROPN
ejpam-3545	261	6	)	)	PUNCT
ejpam-3545	261	7	(	(	PUNCT
ejpam-3545	261	8	1	1	X
ejpam-3545	261	9	)	)	PUNCT
ejpam-3545	261	10	equality	equality	NOUN
ejpam-3545	261	11	(	(	PUNCT
ejpam-3545	261	12	1	1	NUM
ejpam-3545	261	13	)	)	PUNCT
ejpam-3545	261	14	implies	imply	VERB
ejpam-3545	261	15	the	the	DET
ejpam-3545	261	16	following	follow	VERB
ejpam-3545	261	17	equalities	equality	NOUN
ejpam-3545	261	18	for	for	ADP
ejpam-3545	261	19	arbitrary	arbitrary	ADJ
ejpam-3545	261	20	elements	element	NOUN
ejpam-3545	261	21	a	a	DET
ejpam-3545	261	22	,	,	PUNCT
ejpam-3545	261	23	b	b	PROPN
ejpam-3545	261	24	and	and	CCONJ
ejpam-3545	261	25	c	c	PROPN
ejpam-3545	261	26	from	from	ADP
ejpam-3545	261	27	a1	a1	NOUN
ejpam-3545	261	28	(	(	PUNCT
ejpam-3545	261	29	a	a	DET
ejpam-3545	261	30	+1	+1	PROPN
ejpam-3545	261	31	b	b	NOUN
ejpam-3545	261	32	)	)	PUNCT
ejpam-3545	261	33	+1	+1	PROPN
ejpam-3545	261	34	c	c	NOUN
ejpam-3545	261	35	=	=	SYM
ejpam-3545	261	36	h(g(h(g(a	h(g(h(g(a	PROPN
ejpam-3545	261	37	)	)	PUNCT
ejpam-3545	261	38	+2	+2	PROPN
ejpam-3545	261	39	g(b	g(b	NOUN
ejpam-3545	261	40	)	)	PUNCT
ejpam-3545	261	41	)	)	PUNCT
ejpam-3545	261	42	)	)	PUNCT
ejpam-3545	262	1	+2	+2	PRON
ejpam-3545	262	2	g(c	g(c	NOUN
ejpam-3545	262	3	)	)	PUNCT
ejpam-3545	262	4	)	)	PUNCT
ejpam-3545	263	1	=	=	SYM
ejpam-3545	263	2	h((g(a	h((g(a	X
ejpam-3545	263	3	)	)	PUNCT
ejpam-3545	263	4	+2	+2	PROPN
ejpam-3545	263	5	g(b	g(b	PROPN
ejpam-3545	263	6	)	)	PUNCT
ejpam-3545	263	7	)	)	PUNCT
ejpam-3545	263	8	)	)	PUNCT
ejpam-3545	264	1	+2	+2	PRON
ejpam-3545	264	2	g(c	g(c	NOUN
ejpam-3545	264	3	)	)	PUNCT
ejpam-3545	264	4	)	)	PUNCT
ejpam-3545	265	1	a	a	DET
ejpam-3545	265	2	+1	+1	PROPN
ejpam-3545	265	3	(	(	PUNCT
ejpam-3545	265	4	b	b	NOUN
ejpam-3545	265	5	+1	+1	NOUN
ejpam-3545	265	6	c	c	NOUN
ejpam-3545	265	7	)	)	PUNCT
ejpam-3545	265	8	=	=	SYM
ejpam-3545	265	9	h(g(a	h(g(a	PROPN
ejpam-3545	265	10	)	)	PUNCT
ejpam-3545	265	11	+2	+2	PROPN
ejpam-3545	265	12	g(h(g(b	g(h(g(b	NUM
ejpam-3545	265	13	)	)	PUNCT
ejpam-3545	265	14	+2	+2	PROPN
ejpam-3545	265	15	g(c	g(c	NOUN
ejpam-3545	265	16	)	)	PUNCT
ejpam-3545	265	17	)	)	PUNCT
ejpam-3545	265	18	)	)	PUNCT
ejpam-3545	265	19	)	)	PUNCT
ejpam-3545	266	1	=	=	PUNCT
ejpam-3545	266	2	h(g(a	h(g(a	PROPN
ejpam-3545	266	3	)	)	PUNCT
ejpam-3545	266	4	+2	+2	PROPN
ejpam-3545	266	5	(	(	PUNCT
ejpam-3545	266	6	g(b	g(b	X
ejpam-3545	266	7	)	)	PUNCT
ejpam-3545	266	8	+2	+2	PROPN
ejpam-3545	266	9	g(c	g(c	NOUN
ejpam-3545	266	10	)	)	PUNCT
ejpam-3545	266	11	)	)	PUNCT
ejpam-3545	266	12	)	)	PUNCT
ejpam-3545	266	13	)	)	PUNCT
ejpam-3545	267	1	as	as	ADP
ejpam-3545	267	2	the	the	DET
ejpam-3545	267	3	operation	operation	NOUN
ejpam-3545	267	4	+2	+2	PROPN
ejpam-3545	267	5	is	be	AUX
ejpam-3545	267	6	associative	associative	ADJ
ejpam-3545	267	7	in	in	ADP
ejpam-3545	267	8	the	the	DET
ejpam-3545	267	9	prearithmetic	prearithmetic	PROPN
ejpam-3545	267	10	a2	a2	PROPN
ejpam-3545	267	11	,	,	PUNCT
ejpam-3545	267	12	we	we	PRON
ejpam-3545	267	13	have	have	VERB
ejpam-3545	267	14	(	(	PUNCT
ejpam-3545	267	15	a	a	DET
ejpam-3545	267	16	+1	+1	PROPN
ejpam-3545	267	17	b	b	NOUN
ejpam-3545	267	18	)	)	PUNCT
ejpam-3545	268	1	+1	+1	PROPN
ejpam-3545	268	2	c	c	NOUN
ejpam-3545	268	3	=	=	SYM
ejpam-3545	268	4	h((g(a	h((g(a	PROPN
ejpam-3545	268	5	)	)	PUNCT
ejpam-3545	268	6	+2	+2	PROPN
ejpam-3545	268	7	g(b	g(b	PROPN
ejpam-3545	268	8	)	)	PUNCT
ejpam-3545	268	9	)	)	PUNCT
ejpam-3545	269	1	+2	+2	PROPN
ejpam-3545	269	2	g(c	g(c	NOUN
ejpam-3545	269	3	)	)	PUNCT
ejpam-3545	269	4	)	)	PUNCT
ejpam-3545	270	1	=	=	PUNCT
ejpam-3545	270	2	h(g(a	h(g(a	PROPN
ejpam-3545	270	3	)	)	PUNCT
ejpam-3545	270	4	+2	+2	PROPN
ejpam-3545	270	5	(	(	PUNCT
ejpam-3545	270	6	g(b	g(b	PROPN
ejpam-3545	270	7	)	)	PUNCT
ejpam-3545	270	8	)	)	PUNCT
ejpam-3545	271	1	+2	+2	PROPN
ejpam-3545	271	2	g(c	g(c	NOUN
ejpam-3545	271	3	)	)	PUNCT
ejpam-3545	271	4	)	)	PUNCT
ejpam-3545	271	5	)	)	PUNCT
ejpam-3545	272	1	=	=	PUNCT
ejpam-3545	272	2	a	a	DET
ejpam-3545	272	3	+1	+1	PROPN
ejpam-3545	272	4	(	(	PUNCT
ejpam-3545	272	5	b	b	NOUN
ejpam-3545	272	6	+1	+1	ADJ
ejpam-3545	272	7	c	c	NOUN
ejpam-3545	272	8	)	)	PUNCT
ejpam-3545	272	9	proposition	proposition	NOUN
ejpam-3545	272	10	is	be	AUX
ejpam-3545	272	11	proved	prove	VERB
ejpam-3545	272	12	.	.	PUNCT
ejpam-3545	273	1	proposition	proposition	NOUN
ejpam-3545	273	2	3.4	3.4	NUM
ejpam-3545	273	3	implies	imply	VERB
ejpam-3545	273	4	the	the	DET
ejpam-3545	273	5	following	follow	VERB
ejpam-3545	273	6	result	result	NOUN
ejpam-3545	273	7	.	.	PUNCT
ejpam-3545	274	1	let	let	VERB
ejpam-3545	274	2	us	we	PRON
ejpam-3545	274	3	consider	consider	VERB
ejpam-3545	274	4	three	three	NUM
ejpam-3545	274	5	abstract	abstract	ADJ
ejpam-3545	274	6	prearithmetics	prearithmetic	NOUN
ejpam-3545	274	7	a1	a1	NOUN
ejpam-3545	274	8	=	=	SYM
ejpam-3545	274	9	(	(	PUNCT
ejpam-3545	274	10	a1	a1	PROPN
ejpam-3545	274	11	;	;	PUNCT
ejpam-3545	274	12	+1	+1	PROPN
ejpam-3545	274	13	,	,	PUNCT
ejpam-3545	274	14	◦	◦	NOUN
ejpam-3545	274	15	1,≤1),a2	1,≤1),a2	NUM
ejpam-3545	274	16	=	=	SYM
ejpam-3545	274	17	(	(	PUNCT
ejpam-3545	274	18	a2	a2	PROPN
ejpam-3545	274	19	;	;	PUNCT
ejpam-3545	274	20	+2	+2	PROPN
ejpam-3545	274	21	,	,	PUNCT
ejpam-3545	274	22	◦	◦	NOUN
ejpam-3545	274	23	2,≤2	2,≤2	NOUN
ejpam-3545	274	24	)	)	PUNCT
ejpam-3545	274	25	and	and	CCONJ
ejpam-3545	274	26	a3	a3	NOUN
ejpam-3545	274	27	=	=	SYM
ejpam-3545	274	28	(	(	PUNCT
ejpam-3545	274	29	a3	a3	NOUN
ejpam-3545	274	30	;	;	PUNCT
ejpam-3545	274	31	+3	+3	PROPN
ejpam-3545	274	32	,	,	PUNCT
ejpam-3545	274	33	◦	◦	NOUN
ejpam-3545	274	34	3,≤3	3,≤3	NOUN
ejpam-3545	274	35	)	)	PUNCT
ejpam-3545	274	36	.	.	PUNCT
ejpam-3545	275	1	proposition	proposition	NOUN
ejpam-3545	275	2	3.5	3.5	NUM
ejpam-3545	275	3	.	.	PUNCT
ejpam-3545	276	1	if	if	SCONJ
ejpam-3545	276	2	the	the	DET
ejpam-3545	276	3	operation	operation	NOUN
ejpam-3545	276	4	+1	+1	PROPN
ejpam-3545	276	5	is	be	AUX
ejpam-3545	276	6	weakly	weakly	ADV
ejpam-3545	276	7	monoprojective	monoprojective	ADJ
ejpam-3545	276	8	with	with	ADP
ejpam-3545	276	9	respect	respect	NOUN
ejpam-3545	276	10	to	to	ADP
ejpam-3545	276	11	the	the	DET
ejpam-3545	276	12	operation	operation	NOUN
ejpam-3545	276	13	+2	+2	PROPN
ejpam-3545	276	14	and	and	CCONJ
ejpam-3545	276	15	the	the	DET
ejpam-3545	276	16	operation	operation	NOUN
ejpam-3545	276	17	+2	+2	PROPN
ejpam-3545	276	18	is	be	AUX
ejpam-3545	276	19	weakly	weakly	ADV
ejpam-3545	276	20	monoprojective	monoprojective	ADJ
ejpam-3545	276	21	with	with	ADP
ejpam-3545	276	22	respect	respect	NOUN
ejpam-3545	276	23	to	to	ADP
ejpam-3545	276	24	the	the	DET
ejpam-3545	276	25	operation	operation	NOUN
ejpam-3545	276	26	+3	+3	PROPN
ejpam-3545	276	27	,	,	PUNCT
ejpam-3545	276	28	then	then	ADV
ejpam-3545	276	29	the	the	DET
ejpam-3545	276	30	operation	operation	NOUN
ejpam-3545	276	31	+1	+1	PROPN
ejpam-3545	276	32	is	be	AUX
ejpam-3545	276	33	weakly	weakly	ADV
ejpam-3545	276	34	monoprojective	monoprojective	ADJ
ejpam-3545	276	35	with	with	ADP
ejpam-3545	276	36	respect	respect	NOUN
ejpam-3545	276	37	to	to	ADP
ejpam-3545	276	38	the	the	DET
ejpam-3545	276	39	operation	operation	NOUN
ejpam-3545	276	40	+3	+3	PROPN
ejpam-3545	276	41	.	.	PUNCT
ejpam-3545	277	1	proof	proof	NOUN
ejpam-3545	277	2	is	be	AUX
ejpam-3545	277	3	similar	similar	ADJ
ejpam-3545	277	4	to	to	ADP
ejpam-3545	277	5	the	the	DET
ejpam-3545	277	6	proof	proof	NOUN
ejpam-3545	277	7	of	of	ADP
ejpam-3545	277	8	proposition	proposition	NOUN
ejpam-3545	277	9	3.2	3.2	NUM
ejpam-3545	277	10	.	.	PUNCT
ejpam-3545	278	1	proposition	proposition	NOUN
ejpam-3545	278	2	3.5	3.5	NUM
ejpam-3545	278	3	allows	allow	VERB
ejpam-3545	278	4	proving	prove	VERB
ejpam-3545	278	5	the	the	DET
ejpam-3545	278	6	following	follow	VERB
ejpam-3545	278	7	result	result	NOUN
ejpam-3545	278	8	.	.	PUNCT
ejpam-3545	279	1	theorem	theorem	NOUN
ejpam-3545	279	2	2	2	NUM
ejpam-3545	279	3	.	.	PUNCT
ejpam-3545	279	4	abstract	abstract	ADJ
ejpam-3545	279	5	prearithmetics	prearithmetic	NOUN
ejpam-3545	279	6	with	with	ADP
ejpam-3545	279	7	weak	weak	ADJ
ejpam-3545	279	8	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	279	9	relations	relation	NOUN
ejpam-3545	279	10	for	for	ADP
ejpam-3545	279	11	addition	addition	NOUN
ejpam-3545	279	12	form	form	NOUN
ejpam-3545	279	13	the	the	DET
ejpam-3545	279	14	category	category	NOUN
ejpam-3545	279	15	aawmp	aawmp	VERB
ejpam-3545	279	16	where	where	SCONJ
ejpam-3545	279	17	objects	object	NOUN
ejpam-3545	279	18	are	be	AUX
ejpam-3545	279	19	abstract	abstract	ADJ
ejpam-3545	279	20	prearithmetics	prearithmetic	NOUN
ejpam-3545	279	21	and	and	CCONJ
ejpam-3545	279	22	morphisms	morphism	NOUN
ejpam-3545	279	23	are	be	AUX
ejpam-3545	279	24	weak	weak	ADJ
ejpam-3545	279	25	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	279	26	relations	relation	NOUN
ejpam-3545	279	27	between	between	ADP
ejpam-3545	279	28	additions	addition	NOUN
ejpam-3545	279	29	.	.	PUNCT
ejpam-3545	280	1	proof	proof	NOUN
ejpam-3545	280	2	is	be	AUX
ejpam-3545	280	3	similar	similar	ADJ
ejpam-3545	280	4	to	to	ADP
ejpam-3545	280	5	the	the	DET
ejpam-3545	280	6	proof	proof	NOUN
ejpam-3545	280	7	of	of	ADP
ejpam-3545	280	8	theorem	theorem	NOUN
ejpam-3545	280	9	1	1	NUM
ejpam-3545	280	10	.	.	PUNCT
ejpam-3545	280	11	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	280	12	allows	allow	VERB
ejpam-3545	280	13	turning	turn	VERB
ejpam-3545	280	14	a	a	DET
ejpam-3545	280	15	universal	universal	ADJ
ejpam-3545	280	16	algebra	algebra	NOUN
ejpam-3545	280	17	with	with	ADP
ejpam-3545	280	18	one	one	NUM
ejpam-3545	280	19	binary	binary	ADJ
ejpam-3545	280	20	operation	operation	NOUN
ejpam-3545	280	21	into	into	ADP
ejpam-3545	280	22	an	an	DET
ejpam-3545	280	23	abstract	abstract	ADJ
ejpam-3545	280	24	prearithmetic	prearithmetic	NOUN
ejpam-3545	280	25	.	.	PUNCT
ejpam-3545	281	1	let	let	VERB
ejpam-3545	281	2	us	we	PRON
ejpam-3545	281	3	consider	consider	VERB
ejpam-3545	281	4	a	a	DET
ejpam-3545	281	5	universal	universal	ADJ
ejpam-3545	281	6	algebra	algebra	NOUN
ejpam-3545	281	7	a	a	PRON
ejpam-3545	281	8	=	=	X
ejpam-3545	281	9	(	(	PUNCT
ejpam-3545	281	10	a	a	NOUN
ejpam-3545	281	11	;	;	PUNCT
ejpam-3545	281	12	•	•	NUM
ejpam-3545	281	13	)	)	PUNCT
ejpam-3545	281	14	and	and	CCONJ
ejpam-3545	281	15	with	with	ADP
ejpam-3545	281	16	one	one	NUM
ejpam-3545	281	17	binary	binary	ADJ
ejpam-3545	281	18	operation	operation	NOUN
ejpam-3545	281	19	•	•	ADP
ejpam-3545	281	20	,	,	PUNCT
ejpam-3545	281	21	i.e.	i.e.	X
ejpam-3545	281	22	,	,	PUNCT
ejpam-3545	281	23	a	a	DET
ejpam-3545	281	24	groupoid	groupoid	NOUN
ejpam-3545	281	25	,	,	PUNCT
ejpam-3545	281	26	and	and	CCONJ
ejpam-3545	281	27	an	an	DET
ejpam-3545	281	28	abstract	abstract	ADJ
ejpam-3545	281	29	prearithmetic	prearithmetic	ADJ
ejpam-3545	281	30	a2	a2	PROPN
ejpam-3545	281	31	=	=	SYM
ejpam-3545	281	32	(	(	PUNCT
ejpam-3545	281	33	a2	a2	PROPN
ejpam-3545	281	34	;	;	PUNCT
ejpam-3545	281	35	+2	+2	PROPN
ejpam-3545	281	36	,	,	PUNCT
ejpam-3545	281	37	◦	◦	NOUN
ejpam-3545	281	38	2,≤2	2,≤2	NUM
ejpam-3545	281	39	)	)	PUNCT
ejpam-3545	281	40	.	.	PUNCT
ejpam-3545	282	1	proposition	proposition	NOUN
ejpam-3545	282	2	3.6	3.6	NUM
ejpam-3545	282	3	.	.	PUNCT
ejpam-3545	283	1	for	for	ADP
ejpam-3545	283	2	any	any	DET
ejpam-3545	283	3	two	two	NUM
ejpam-3545	283	4	mappings	mapping	NOUN
ejpam-3545	283	5	g	g	NOUN
ejpam-3545	283	6	:	:	PUNCT
ejpam-3545	283	7	a	a	DET
ejpam-3545	283	8	→	→	SYM
ejpam-3545	283	9	a2	a2	PROPN
ejpam-3545	283	10	and	and	CCONJ
ejpam-3545	283	11	h	h	NOUN
ejpam-3545	283	12	:	:	PUNCT
ejpam-3545	283	13	a2	a2	PROPN
ejpam-3545	283	14	→	→	SYM
ejpam-3545	283	15	a	a	X
ejpam-3545	283	16	,	,	PUNCT
ejpam-3545	283	17	it	it	PRON
ejpam-3545	283	18	is	be	AUX
ejpam-3545	283	19	possible	possible	ADJ
ejpam-3545	283	20	to	to	PART
ejpam-3545	283	21	extend	extend	VERB
ejpam-3545	283	22	the	the	DET
ejpam-3545	283	23	algebra	algebra	NOUN
ejpam-3545	283	24	a	a	PRON
ejpam-3545	283	25	to	to	ADP
ejpam-3545	283	26	an	an	DET
ejpam-3545	283	27	abstract	abstract	ADJ
ejpam-3545	283	28	prearithmetic	prearithmetic	ADJ
ejpam-3545	283	29	a1	a1	NOUN
ejpam-3545	283	30	=	=	PUNCT
ejpam-3545	283	31	(	(	PUNCT
ejpam-3545	283	32	a	a	X
ejpam-3545	283	33	;	;	PUNCT
ejpam-3545	283	34	+	+	ADJ
ejpam-3545	283	35	,	,	PUNCT
ejpam-3545	283	36	•,≤	•,≤	NOUN
ejpam-3545	283	37	)	)	PUNCT
ejpam-3545	283	38	,	,	PUNCT
ejpam-3545	283	39	in	in	ADP
ejpam-3545	283	40	which	which	DET
ejpam-3545	283	41	addition	addition	NOUN
ejpam-3545	283	42	+	+	CCONJ
ejpam-3545	283	43	is	be	AUX
ejpam-3545	283	44	weakly	weakly	ADV
ejpam-3545	283	45	monoprojective	monoprojective	ADJ
ejpam-3545	283	46	with	with	ADP
ejpam-3545	283	47	respect	respect	NOUN
ejpam-3545	283	48	to	to	ADP
ejpam-3545	283	49	addition	addition	NOUN
ejpam-3545	283	50	+2	+2	PRON
ejpam-3545	283	51	.	.	PUNCT
ejpam-3545	284	1	indeed	indeed	ADV
ejpam-3545	284	2	,	,	PUNCT
ejpam-3545	284	3	it	it	PRON
ejpam-3545	284	4	is	be	AUX
ejpam-3545	284	5	possible	possible	ADJ
ejpam-3545	284	6	to	to	PART
ejpam-3545	284	7	take	take	VERB
ejpam-3545	284	8	the	the	DET
ejpam-3545	284	9	trivial	trivial	ADJ
ejpam-3545	284	10	partial	partial	ADJ
ejpam-3545	284	11	order	order	NOUN
ejpam-3545	284	12	on	on	ADP
ejpam-3545	284	13	a	a	PRON
ejpam-3545	284	14	and	and	CCONJ
ejpam-3545	284	15	define	define	VERB
ejpam-3545	284	16	addition	addition	NOUN
ejpam-3545	284	17	+	+	CCONJ
ejpam-3545	284	18	in	in	ADP
ejpam-3545	284	19	a	a	PRON
ejpam-3545	284	20	by	by	ADP
ejpam-3545	284	21	the	the	DET
ejpam-3545	284	22	following	follow	VERB
ejpam-3545	284	23	formula	formula	NOUN
ejpam-3545	284	24	a	a	DET
ejpam-3545	284	25	+	+	NOUN
ejpam-3545	284	26	b	b	NOUN
ejpam-3545	284	27	=	=	SYM
ejpam-3545	284	28	h(g(a	h(g(a	PROPN
ejpam-3545	284	29	)	)	PUNCT
ejpam-3545	284	30	+2	+2	PROPN
ejpam-3545	284	31	g(b	g(b	PROPN
ejpam-3545	284	32	)	)	PUNCT
ejpam-3545	284	33	)	)	PUNCT
ejpam-3545	285	1	the	the	DET
ejpam-3545	285	2	abstract	abstract	ADJ
ejpam-3545	285	3	prearithmetic	prearithmetic	ADJ
ejpam-3545	285	4	a1	a1	NOUN
ejpam-3545	285	5	=	=	PUNCT
ejpam-3545	285	6	(	(	PUNCT
ejpam-3545	285	7	a	a	X
ejpam-3545	285	8	;	;	PUNCT
ejpam-3545	285	9	+	+	ADJ
ejpam-3545	285	10	,	,	PUNCT
ejpam-3545	285	11	•,≤	•,≤	NOUN
ejpam-3545	285	12	)	)	PUNCT
ejpam-3545	285	13	is	be	AUX
ejpam-3545	285	14	called	call	VERB
ejpam-3545	285	15	the	the	DET
ejpam-3545	285	16	extension	extension	NOUN
ejpam-3545	285	17	of	of	ADP
ejpam-3545	285	18	a	a	PRON
ejpam-3545	285	19	by	by	ADP
ejpam-3545	285	20	the	the	DET
ejpam-3545	285	21	pair	pair	NOUN
ejpam-3545	285	22	(	(	PUNCT
ejpam-3545	285	23	g	g	NOUN
ejpam-3545	285	24	,	,	PUNCT
ejpam-3545	285	25	h	h	NOUN
ejpam-3545	285	26	)	)	PUNCT
ejpam-3545	285	27	.	.	PUNCT
ejpam-3545	286	1	the	the	DET
ejpam-3545	286	2	utilized	utilize	VERB
ejpam-3545	286	3	construction	construction	NOUN
ejpam-3545	286	4	implies	imply	VERB
ejpam-3545	286	5	the	the	DET
ejpam-3545	286	6	following	follow	VERB
ejpam-3545	286	7	result	result	NOUN
ejpam-3545	286	8	.	.	PUNCT
ejpam-3545	287	1	let	let	VERB
ejpam-3545	287	2	us	we	PRON
ejpam-3545	287	3	consider	consider	VERB
ejpam-3545	287	4	three	three	NUM
ejpam-3545	287	5	mappings	mapping	NOUN
ejpam-3545	287	6	g	g	NOUN
ejpam-3545	287	7	:	:	PUNCT
ejpam-3545	287	8	a→	a→	PROPN
ejpam-3545	287	9	a2	a2	PROPN
ejpam-3545	287	10	,	,	PUNCT
ejpam-3545	287	11	h	h	NOUN
ejpam-3545	287	12	:	:	PUNCT
ejpam-3545	287	13	a2	a2	PROPN
ejpam-3545	287	14	→	→	SYM
ejpam-3545	287	15	a	a	PROPN
ejpam-3545	287	16	and	and	CCONJ
ejpam-3545	287	17	f	f	NOUN
ejpam-3545	287	18	:	:	PUNCT
ejpam-3545	287	19	a2	a2	PROPN
ejpam-3545	287	20	→	→	SYM
ejpam-3545	287	21	a	a	DET
ejpam-3545	287	22	.	.	PUNCT
ejpam-3545	287	23	m.	m.	NOUN
ejpam-3545	287	24	burgin	burgin	PROPN
ejpam-3545	287	25	/	/	SYM
ejpam-3545	287	26	eur	eur	PROPN
ejpam-3545	287	27	.	.	PUNCT
ejpam-3545	288	1	j.	j.	PROPN
ejpam-3545	288	2	pure	pure	PROPN
ejpam-3545	288	3	appl	appl	PROPN
ejpam-3545	288	4	.	.	PROPN
ejpam-3545	288	5	math	math	PROPN
ejpam-3545	288	6	,	,	PUNCT
ejpam-3545	288	7	12	12	NUM
ejpam-3545	288	8	(	(	PUNCT
ejpam-3545	288	9	4	4	NUM
ejpam-3545	288	10	)	)	PUNCT
ejpam-3545	288	11	(	(	PUNCT
ejpam-3545	288	12	2019	2019	NUM
ejpam-3545	288	13	)	)	PUNCT
ejpam-3545	288	14	,	,	PUNCT
ejpam-3545	288	15	1787	1787	NUM
ejpam-3545	288	16	-	-	SYM
ejpam-3545	288	17	1810	1810	NUM
ejpam-3545	288	18	1798	1798	NUM
ejpam-3545	288	19	proposition	proposition	NOUN
ejpam-3545	288	20	3.7	3.7	NUM
ejpam-3545	288	21	.	.	PUNCT
ejpam-3545	289	1	if	if	SCONJ
ejpam-3545	289	2	mappings	mapping	NOUN
ejpam-3545	289	3	f	f	PROPN
ejpam-3545	289	4	and	and	CCONJ
ejpam-3545	289	5	h	h	PROPN
ejpam-3545	289	6	coincide	coincide	NOUN
ejpam-3545	289	7	on	on	ADP
ejpam-3545	289	8	the	the	DET
ejpam-3545	289	9	image	image	NOUN
ejpam-3545	289	10	g(a	g(a	PROPN
ejpam-3545	289	11	)	)	PUNCT
ejpam-3545	289	12	of	of	ADP
ejpam-3545	289	13	a	a	PRON
ejpam-3545	289	14	,	,	PUNCT
ejpam-3545	289	15	then	then	ADV
ejpam-3545	289	16	the	the	DET
ejpam-3545	289	17	extensions	extension	NOUN
ejpam-3545	289	18	of	of	ADP
ejpam-3545	289	19	a	a	PRON
ejpam-3545	289	20	by	by	ADP
ejpam-3545	289	21	the	the	DET
ejpam-3545	289	22	pairs	pair	NOUN
ejpam-3545	289	23	(	(	PUNCT
ejpam-3545	289	24	g	g	NOUN
ejpam-3545	289	25	,	,	PUNCT
ejpam-3545	289	26	h	h	NOUN
ejpam-3545	289	27	)	)	PUNCT
ejpam-3545	289	28	and	and	CCONJ
ejpam-3545	289	29	(	(	PUNCT
ejpam-3545	289	30	g	g	PROPN
ejpam-3545	289	31	,	,	PUNCT
ejpam-3545	289	32	f	f	NOUN
ejpam-3545	289	33	)	)	PUNCT
ejpam-3545	289	34	coincide	coincide	NOUN
ejpam-3545	289	35	.	.	PUNCT
ejpam-3545	290	1	proof	proof	NOUN
ejpam-3545	290	2	follows	follow	VERB
ejpam-3545	290	3	directly	directly	ADV
ejpam-3545	290	4	from	from	ADP
ejpam-3545	290	5	definitions	definition	NOUN
ejpam-3545	290	6	.	.	PUNCT
ejpam-3545	291	1	abstract	abstract	ADJ
ejpam-3545	291	2	prearithmetics	prearithmetic	NOUN
ejpam-3545	291	3	have	have	VERB
ejpam-3545	291	4	two	two	NUM
ejpam-3545	291	5	operations	operation	NOUN
ejpam-3545	291	6	.	.	PUNCT
ejpam-3545	292	1	this	this	PRON
ejpam-3545	292	2	gives	give	VERB
ejpam-3545	292	3	three	three	NUM
ejpam-3545	292	4	more	more	ADJ
ejpam-3545	292	5	concepts	concept	NOUN
ejpam-3545	292	6	of	of	ADP
ejpam-3545	292	7	weak	weak	ADJ
ejpam-3545	292	8	projectivity	projectivity	NOUN
ejpam-3545	292	9	and	and	CCONJ
ejpam-3545	292	10	three	three	NUM
ejpam-3545	292	11	more	more	ADJ
ejpam-3545	292	12	concepts	concept	NOUN
ejpam-3545	292	13	of	of	ADP
ejpam-3545	292	14	weak	weak	ADJ
ejpam-3545	292	15	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	292	16	.	.	PUNCT
ejpam-3545	293	1	definition	definition	NOUN
ejpam-3545	293	2	3	3	NUM
ejpam-3545	293	3	.	.	PUNCT
ejpam-3545	293	4	a	a	PRON
ejpam-3545	293	5	)	)	PUNCT
ejpam-3545	293	6	multiplication	multiplication	NOUN
ejpam-3545	293	7	◦	◦	NOUN
ejpam-3545	293	8	1	1	NUM
ejpam-3545	293	9	in	in	ADP
ejpam-3545	293	10	the	the	DET
ejpam-3545	293	11	abstract	abstract	ADJ
ejpam-3545	293	12	prearithmetic	prearithmetic	ADJ
ejpam-3545	293	13	a1	a1	NOUN
ejpam-3545	293	14	=	=	SYM
ejpam-3545	293	15	(	(	PUNCT
ejpam-3545	293	16	a1	a1	PROPN
ejpam-3545	293	17	;	;	PUNCT
ejpam-3545	293	18	+1	+1	PROPN
ejpam-3545	293	19	,	,	PUNCT
ejpam-3545	293	20	◦	◦	NOUN
ejpam-3545	293	21	1,≤1	1,≤1	ADJ
ejpam-3545	293	22	)	)	PUNCT
ejpam-3545	293	23	is	be	AUX
ejpam-3545	293	24	called	call	VERB
ejpam-3545	293	25	weakly	weakly	ADV
ejpam-3545	293	26	projective	projective	NOUN
ejpam-3545	293	27	with	with	ADP
ejpam-3545	293	28	respect	respect	NOUN
ejpam-3545	293	29	to	to	ADP
ejpam-3545	293	30	multiplication	multiplication	NOUN
ejpam-3545	293	31	◦	◦	NOUN
ejpam-3545	293	32	2	2	NUM
ejpam-3545	293	33	in	in	ADP
ejpam-3545	293	34	the	the	DET
ejpam-3545	293	35	abstract	abstract	ADJ
ejpam-3545	293	36	prearithmetic	prearithmetic	ADJ
ejpam-3545	293	37	a2	a2	PROPN
ejpam-3545	293	38	=	=	SYM
ejpam-3545	293	39	(	(	PUNCT
ejpam-3545	293	40	a2	a2	PROPN
ejpam-3545	293	41	;	;	PUNCT
ejpam-3545	293	42	+2	+2	PROPN
ejpam-3545	293	43	,	,	PUNCT
ejpam-3545	293	44	◦	◦	NOUN
ejpam-3545	293	45	2,≤2	2,≤2	NOUN
ejpam-3545	293	46	)	)	PUNCT
ejpam-3545	293	47	if	if	SCONJ
ejpam-3545	293	48	there	there	PRON
ejpam-3545	293	49	are	be	VERB
ejpam-3545	293	50	three	three	NUM
ejpam-3545	293	51	mappings	mapping	NOUN
ejpam-3545	293	52	g1	g1	NOUN
ejpam-3545	293	53	:	:	PUNCT
ejpam-3545	293	54	a1	a1	NOUN
ejpam-3545	293	55	→	→	SYM
ejpam-3545	293	56	a2	a2	PROPN
ejpam-3545	293	57	,	,	PUNCT
ejpam-3545	293	58	g2	g2	PROPN
ejpam-3545	293	59	:	:	PUNCT
ejpam-3545	293	60	a1	a1	PROPN
ejpam-3545	293	61	→	→	SYM
ejpam-3545	293	62	a2	a2	PROPN
ejpam-3545	293	63	and	and	CCONJ
ejpam-3545	293	64	h	h	NOUN
ejpam-3545	293	65	:	:	PUNCT
ejpam-3545	293	66	a2	a2	PROPN
ejpam-3545	293	67	→	→	SYM
ejpam-3545	293	68	a1	a1	NOUN
ejpam-3545	293	69	and	and	CCONJ
ejpam-3545	293	70	the	the	DET
ejpam-3545	293	71	following	follow	VERB
ejpam-3545	293	72	equality	equality	NOUN
ejpam-3545	293	73	is	be	AUX
ejpam-3545	293	74	valid	valid	ADJ
ejpam-3545	293	75	for	for	ADP
ejpam-3545	293	76	all	all	DET
ejpam-3545	293	77	elements	element	NOUN
ejpam-3545	293	78	a	a	PRON
ejpam-3545	293	79	and	and	CCONJ
ejpam-3545	293	80	b	b	NOUN
ejpam-3545	293	81	from	from	ADP
ejpam-3545	293	82	a1	a1	NOUN
ejpam-3545	293	83	:	:	PUNCT
ejpam-3545	293	84	a	a	DET
ejpam-3545	293	85	◦	◦	NOUN
ejpam-3545	293	86	1	1	NUM
ejpam-3545	293	87	b	b	NOUN
ejpam-3545	293	88	=	=	PUNCT
ejpam-3545	293	89	h(g1(a	h(g1(a	NOUN
ejpam-3545	293	90	)	)	PUNCT
ejpam-3545	293	91	◦	◦	NOUN
ejpam-3545	293	92	2	2	NUM
ejpam-3545	293	93	g2(b	g2(b	NOUN
ejpam-3545	293	94	)	)	PUNCT
ejpam-3545	293	95	)	)	PUNCT
ejpam-3545	294	1	b	b	X
ejpam-3545	294	2	)	)	PUNCT
ejpam-3545	294	3	the	the	DET
ejpam-3545	294	4	mappings	mapping	NOUN
ejpam-3545	294	5	g1	g1	NOUN
ejpam-3545	294	6	and	and	CCONJ
ejpam-3545	294	7	g2	g2	PROPN
ejpam-3545	294	8	are	be	AUX
ejpam-3545	294	9	called	call	VERB
ejpam-3545	294	10	the	the	DET
ejpam-3545	294	11	projectors	projector	NOUN
ejpam-3545	294	12	and	and	CCONJ
ejpam-3545	294	13	the	the	DET
ejpam-3545	294	14	mapping	mapping	NOUN
ejpam-3545	294	15	h	h	NOUN
ejpam-3545	294	16	is	be	AUX
ejpam-3545	294	17	called	call	VERB
ejpam-3545	294	18	the	the	DET
ejpam-3545	294	19	coprojector	coprojector	NOUN
ejpam-3545	294	20	for	for	ADP
ejpam-3545	294	21	the	the	DET
ejpam-3545	294	22	pair	pair	NOUN
ejpam-3545	294	23	(	(	PUNCT
ejpam-3545	294	24	◦	◦	NOUN
ejpam-3545	294	25	1	1	NUM
ejpam-3545	294	26	,	,	PUNCT
ejpam-3545	294	27	◦	◦	NOUN
ejpam-3545	294	28	2	2	NUM
ejpam-3545	294	29	)	)	PUNCT
ejpam-3545	294	30	.	.	PUNCT
ejpam-3545	295	1	c	c	X
ejpam-3545	295	2	)	)	PUNCT
ejpam-3545	295	3	in	in	ADP
ejpam-3545	295	4	this	this	DET
ejpam-3545	295	5	case	case	NOUN
ejpam-3545	295	6	,	,	PUNCT
ejpam-3545	295	7	we	we	PRON
ejpam-3545	295	8	say	say	VERB
ejpam-3545	295	9	that	that	DET
ejpam-3545	295	10	multiplication	multiplication	NOUN
ejpam-3545	295	11	in	in	ADP
ejpam-3545	295	12	a2	a2	PROPN
ejpam-3545	295	13	is	be	AUX
ejpam-3545	295	14	weakly	weakly	ADV
ejpam-3545	295	15	projected	project	VERB
ejpam-3545	295	16	onto	onto	ADP
ejpam-3545	295	17	addition	addition	NOUN
ejpam-3545	295	18	in	in	ADP
ejpam-3545	295	19	a1	a1	NOUN
ejpam-3545	295	20	while	while	SCONJ
ejpam-3545	295	21	multiplication	multiplication	NOUN
ejpam-3545	295	22	in	in	ADP
ejpam-3545	295	23	a1	a1	NOUN
ejpam-3545	295	24	is	be	AUX
ejpam-3545	295	25	a	a	DET
ejpam-3545	295	26	weak	weak	ADJ
ejpam-3545	295	27	projection	projection	NOUN
ejpam-3545	295	28	of	of	ADP
ejpam-3545	295	29	addition	addition	NOUN
ejpam-3545	295	30	in	in	ADP
ejpam-3545	295	31	a2	a2	PROPN
ejpam-3545	295	32	.	.	PUNCT
ejpam-3545	296	1	we	we	PRON
ejpam-3545	296	2	also	also	ADV
ejpam-3545	296	3	say	say	VERB
ejpam-3545	296	4	that	that	SCONJ
ejpam-3545	296	5	there	there	PRON
ejpam-3545	296	6	is	be	VERB
ejpam-3545	296	7	a	a	DET
ejpam-3545	296	8	weak	weak	ADJ
ejpam-3545	296	9	projectivity	projectivity	NOUN
ejpam-3545	296	10	between	between	ADP
ejpam-3545	296	11	multiplication	multiplication	NOUN
ejpam-3545	296	12	in	in	ADP
ejpam-3545	296	13	the	the	DET
ejpam-3545	296	14	prearithmetic	prearithmetic	ADJ
ejpam-3545	296	15	a1	a1	NOUN
ejpam-3545	296	16	and	and	CCONJ
ejpam-3545	296	17	multiplication	multiplication	NOUN
ejpam-3545	296	18	in	in	ADP
ejpam-3545	296	19	the	the	DET
ejpam-3545	296	20	prearithmetic	prearithmetic	PROPN
ejpam-3545	296	21	a2	a2	PROPN
ejpam-3545	296	22	and	and	CCONJ
ejpam-3545	296	23	there	there	PRON
ejpam-3545	296	24	is	be	VERB
ejpam-3545	296	25	a	a	DET
ejpam-3545	296	26	weak	weak	ADJ
ejpam-3545	296	27	inverse	inverse	NOUN
ejpam-3545	296	28	projectivity	projectivity	NOUN
ejpam-3545	296	29	between	between	ADP
ejpam-3545	296	30	multiplication	multiplication	NOUN
ejpam-3545	296	31	in	in	ADP
ejpam-3545	296	32	the	the	DET
ejpam-3545	296	33	prearithmetic	prearithmetic	ADJ
ejpam-3545	296	34	a2	a2	PROPN
ejpam-3545	296	35	and	and	CCONJ
ejpam-3545	296	36	multiplication	multiplication	NOUN
ejpam-3545	296	37	in	in	ADP
ejpam-3545	296	38	the	the	DET
ejpam-3545	296	39	prearithmetic	prearithmetic	ADJ
ejpam-3545	296	40	a1	a1	NOUN
ejpam-3545	296	41	.	.	PUNCT
ejpam-3545	297	1	this	this	PRON
ejpam-3545	297	2	means	mean	VERB
ejpam-3545	297	3	that	that	SCONJ
ejpam-3545	297	4	there	there	PRON
ejpam-3545	297	5	is	be	VERB
ejpam-3545	297	6	partial	partial	ADJ
ejpam-3545	297	7	weak	weak	ADJ
ejpam-3545	297	8	projectivity	projectivity	NOUN
ejpam-3545	297	9	between	between	ADP
ejpam-3545	297	10	the	the	DET
ejpam-3545	297	11	prearithmetics	prearithmetic	NOUN
ejpam-3545	297	12	a1	a1	NOUN
ejpam-3545	297	13	and	and	CCONJ
ejpam-3545	297	14	a2	a2	PROPN
ejpam-3545	297	15	.	.	PUNCT
ejpam-3545	298	1	this	this	DET
ejpam-3545	298	2	type	type	NOUN
ejpam-3545	298	3	of	of	ADP
ejpam-3545	298	4	partial	partial	ADJ
ejpam-3545	298	5	weak	weak	ADJ
ejpam-3545	298	6	projectivity	projectivity	NOUN
ejpam-3545	298	7	is	be	AUX
ejpam-3545	298	8	called	call	VERB
ejpam-3545	298	9	multiplicative	multiplicative	ADJ
ejpam-3545	298	10	weak	weak	ADJ
ejpam-3545	298	11	projectivity	projectivity	NOUN
ejpam-3545	298	12	.	.	PUNCT
ejpam-3545	299	1	let	let	VERB
ejpam-3545	299	2	us	we	PRON
ejpam-3545	299	3	consider	consider	VERB
ejpam-3545	299	4	two	two	NUM
ejpam-3545	299	5	abstract	abstract	ADJ
ejpam-3545	299	6	prearithmetics	prearithmetic	NOUN
ejpam-3545	299	7	a1	a1	NOUN
ejpam-3545	299	8	=	=	SYM
ejpam-3545	299	9	(	(	PUNCT
ejpam-3545	299	10	a1	a1	PROPN
ejpam-3545	299	11	;	;	PUNCT
ejpam-3545	299	12	+1	+1	PROPN
ejpam-3545	299	13	,	,	PUNCT
ejpam-3545	299	14	◦	◦	NOUN
ejpam-3545	299	15	1,≤1	1,≤1	ADJ
ejpam-3545	299	16	)	)	PUNCT
ejpam-3545	299	17	and	and	CCONJ
ejpam-3545	299	18	a2	a2	PROPN
ejpam-3545	299	19	=	=	SYM
ejpam-3545	299	20	(	(	PUNCT
ejpam-3545	299	21	a2	a2	PROPN
ejpam-3545	299	22	;	;	PUNCT
ejpam-3545	299	23	+2	+2	PROPN
ejpam-3545	299	24	,	,	PUNCT
ejpam-3545	299	25	◦	◦	NOUN
ejpam-3545	299	26	2,≤2	2,≤2	NUM
ejpam-3545	299	27	)	)	PUNCT
ejpam-3545	299	28	.	.	PUNCT
ejpam-3545	300	1	proposition	proposition	NOUN
ejpam-3545	300	2	3.8	3.8	NUM
ejpam-3545	300	3	.	.	PUNCT
ejpam-3545	301	1	if	if	SCONJ
ejpam-3545	301	2	multiplication	multiplication	NOUN
ejpam-3545	301	3	◦	◦	NOUN
ejpam-3545	301	4	1	1	NUM
ejpam-3545	301	5	is	be	AUX
ejpam-3545	301	6	commutative	commutative	ADJ
ejpam-3545	301	7	and	and	CCONJ
ejpam-3545	301	8	weakly	weakly	ADJ
ejpam-3545	301	9	projective	projective	NOUN
ejpam-3545	301	10	with	with	ADP
ejpam-3545	301	11	respect	respect	NOUN
ejpam-3545	301	12	to	to	ADP
ejpam-3545	301	13	the	the	DET
ejpam-3545	301	14	commutative	commutative	ADJ
ejpam-3545	301	15	multiplication	multiplication	NOUN
ejpam-3545	301	16	◦	◦	NOUN
ejpam-3545	301	17	2	2	NUM
ejpam-3545	301	18	with	with	ADP
ejpam-3545	301	19	the	the	DET
ejpam-3545	301	20	projectors	projector	NOUN
ejpam-3545	301	21	g1	g1	NOUN
ejpam-3545	301	22	and	and	CCONJ
ejpam-3545	301	23	g2	g2	PROPN
ejpam-3545	301	24	,	,	PUNCT
ejpam-3545	301	25	then	then	ADV
ejpam-3545	301	26	multiplication	multiplication	NOUN
ejpam-3545	301	27	◦	◦	NOUN
ejpam-3545	301	28	1	1	NUM
ejpam-3545	301	29	is	be	AUX
ejpam-3545	301	30	commutative	commutative	ADJ
ejpam-3545	301	31	and	and	CCONJ
ejpam-3545	301	32	weakly	weakly	ADJ
ejpam-3545	301	33	projective	projective	NOUN
ejpam-3545	301	34	with	with	ADP
ejpam-3545	301	35	respect	respect	NOUN
ejpam-3545	301	36	to	to	ADP
ejpam-3545	301	37	multiplication	multiplication	NOUN
ejpam-3545	301	38	◦	◦	NOUN
ejpam-3545	301	39	2	2	NUM
ejpam-3545	301	40	with	with	ADP
ejpam-3545	301	41	the	the	DET
ejpam-3545	301	42	projectors	projector	NOUN
ejpam-3545	301	43	g2	g2	PROPN
ejpam-3545	301	44	and	and	CCONJ
ejpam-3545	301	45	g1	g1	NOUN
ejpam-3545	301	46	.	.	PUNCT
ejpam-3545	302	1	proof	proof	NOUN
ejpam-3545	302	2	is	be	AUX
ejpam-3545	302	3	similar	similar	ADJ
ejpam-3545	302	4	to	to	ADP
ejpam-3545	302	5	the	the	DET
ejpam-3545	302	6	proof	proof	NOUN
ejpam-3545	302	7	of	of	ADP
ejpam-3545	302	8	proposition	proposition	NOUN
ejpam-3545	302	9	3.1	3.1	NUM
ejpam-3545	302	10	.	.	PUNCT
ejpam-3545	303	1	proposition	proposition	NOUN
ejpam-3545	303	2	3.8	3.8	NUM
ejpam-3545	303	3	allows	allow	VERB
ejpam-3545	303	4	to	to	PART
ejpam-3545	303	5	show	show	VERB
ejpam-3545	303	6	when	when	SCONJ
ejpam-3545	303	7	multiplication	multiplication	NOUN
ejpam-3545	303	8	in	in	ADP
ejpam-3545	303	9	one	one	NUM
ejpam-3545	303	10	abstract	abstract	ADJ
ejpam-3545	303	11	prearithmetic	prearithmetic	NOUN
ejpam-3545	303	12	is	be	AUX
ejpam-3545	303	13	not	not	PART
ejpam-3545	303	14	weakly	weakly	ADV
ejpam-3545	303	15	projective	projective	ADJ
ejpam-3545	303	16	with	with	ADP
ejpam-3545	303	17	respect	respect	NOUN
ejpam-3545	303	18	to	to	ADP
ejpam-3545	303	19	multiplication	multiplication	NOUN
ejpam-3545	303	20	in	in	ADP
ejpam-3545	303	21	another	another	DET
ejpam-3545	303	22	abstract	abstract	ADJ
ejpam-3545	303	23	prearithmetic	prearithmetic	NOUN
ejpam-3545	303	24	.	.	PUNCT
ejpam-3545	304	1	example	example	NOUN
ejpam-3545	305	1	15	15	NUM
ejpam-3545	305	2	.	.	PUNCT
ejpam-3545	306	1	let	let	VERB
ejpam-3545	306	2	us	we	PRON
ejpam-3545	306	3	consider	consider	VERB
ejpam-3545	306	4	the	the	DET
ejpam-3545	306	5	conventional	conventional	ADJ
ejpam-3545	306	6	diophantine	diophantine	NOUN
ejpam-3545	306	7	arithmetic	arithmetic	ADJ
ejpam-3545	306	8	n	n	PROPN
ejpam-3545	306	9	of	of	ADP
ejpam-3545	306	10	all	all	DET
ejpam-3545	306	11	natural	natural	ADJ
ejpam-3545	306	12	numbers	number	NOUN
ejpam-3545	306	13	and	and	CCONJ
ejpam-3545	306	14	the	the	DET
ejpam-3545	306	15	abstract	abstract	ADJ
ejpam-3545	306	16	prearithmetic	prearithmetic	NOUN
ejpam-3545	306	17	a	a	PRON
ejpam-3545	306	18	=	=	X
ejpam-3545	306	19	(	(	PUNCT
ejpam-3545	306	20	n	n	NOUN
ejpam-3545	306	21	;	;	PUNCT
ejpam-3545	306	22	⊕,⊗,≤	⊕,⊗,≤	X
ejpam-3545	306	23	)	)	PUNCT
ejpam-3545	306	24	where	where	SCONJ
ejpam-3545	306	25	n	n	PRON
ejpam-3545	306	26	is	be	AUX
ejpam-3545	306	27	the	the	DET
ejpam-3545	306	28	set	set	NOUN
ejpam-3545	306	29	of	of	ADP
ejpam-3545	306	30	all	all	DET
ejpam-3545	306	31	natural	natural	ADJ
ejpam-3545	306	32	numbers	number	NOUN
ejpam-3545	306	33	,	,	PUNCT
ejpam-3545	306	34	≤	≤	NUM
ejpam-3545	306	35	is	be	AUX
ejpam-3545	306	36	the	the	DET
ejpam-3545	306	37	natural	natural	ADJ
ejpam-3545	306	38	order	order	NOUN
ejpam-3545	306	39	on	on	ADP
ejpam-3545	306	40	the	the	DET
ejpam-3545	306	41	set	set	NOUN
ejpam-3545	306	42	of	of	ADP
ejpam-3545	306	43	all	all	DET
ejpam-3545	306	44	natural	natural	ADJ
ejpam-3545	306	45	numbers	number	NOUN
ejpam-3545	306	46	,	,	PUNCT
ejpam-3545	306	47	addition	addition	NOUN
ejpam-3545	306	48	⊕	⊕	PROPN
ejpam-3545	306	49	is	be	AUX
ejpam-3545	306	50	the	the	DET
ejpam-3545	306	51	same	same	ADJ
ejpam-3545	306	52	as	as	ADP
ejpam-3545	306	53	in	in	ADP
ejpam-3545	306	54	n	n	NOUN
ejpam-3545	306	55	,	,	PUNCT
ejpam-3545	306	56	while	while	SCONJ
ejpam-3545	306	57	multiplication	multiplication	NOUN
ejpam-3545	306	58	⊗	⊗	PROPN
ejpam-3545	306	59	is	be	AUX
ejpam-3545	306	60	defined	define	VERB
ejpam-3545	306	61	by	by	ADP
ejpam-3545	306	62	the	the	DET
ejpam-3545	306	63	following	follow	VERB
ejpam-3545	306	64	formula	formula	NOUN
ejpam-3545	306	65	a⊗	a⊗	NOUN
ejpam-3545	306	66	b	b	PROPN
ejpam-3545	306	67	=	=	SYM
ejpam-3545	306	68	b	b	PROPN
ejpam-3545	306	69	multiplication	multiplication	NOUN
ejpam-3545	306	70	⊗	⊗	NOUN
ejpam-3545	306	71	in	in	ADP
ejpam-3545	306	72	the	the	DET
ejpam-3545	306	73	abstract	abstract	ADJ
ejpam-3545	306	74	prearithmetic	prearithmetic	NOUN
ejpam-3545	306	75	a	a	PRON
ejpam-3545	306	76	is	be	AUX
ejpam-3545	306	77	not	not	PART
ejpam-3545	306	78	weakly	weakly	ADV
ejpam-3545	306	79	projective	projective	ADJ
ejpam-3545	306	80	with	with	ADP
ejpam-3545	306	81	respect	respect	NOUN
ejpam-3545	306	82	to	to	ADP
ejpam-3545	306	83	multiplication	multiplication	NOUN
ejpam-3545	306	84	in	in	ADP
ejpam-3545	306	85	n	n	NOUN
ejpam-3545	306	86	because	because	SCONJ
ejpam-3545	306	87	otherwise	otherwise	ADV
ejpam-3545	306	88	by	by	ADP
ejpam-3545	306	89	proposition	proposition	NOUN
ejpam-3545	306	90	3.8	3.8	NUM
ejpam-3545	306	91	,	,	PUNCT
ejpam-3545	306	92	it	it	PRON
ejpam-3545	306	93	would	would	AUX
ejpam-3545	306	94	be	be	AUX
ejpam-3545	306	95	commutative	commutative	ADJ
ejpam-3545	306	96	and	and	CCONJ
ejpam-3545	306	97	it	it	PRON
ejpam-3545	306	98	is	be	AUX
ejpam-3545	306	99	not	not	PART
ejpam-3545	306	100	commutative	commutative	ADJ
ejpam-3545	306	101	.	.	PUNCT
ejpam-3545	307	1	at	at	ADP
ejpam-3545	307	2	the	the	DET
ejpam-3545	307	3	same	same	ADJ
ejpam-3545	307	4	time	time	NOUN
ejpam-3545	307	5	,	,	PUNCT
ejpam-3545	307	6	addition	addition	NOUN
ejpam-3545	307	7	⊕	⊕	PROPN
ejpam-3545	307	8	in	in	ADP
ejpam-3545	307	9	the	the	DET
ejpam-3545	307	10	abstract	abstract	ADJ
ejpam-3545	307	11	prearithmetic	prearithmetic	NOUN
ejpam-3545	307	12	a	a	PRON
ejpam-3545	307	13	is	be	AUX
ejpam-3545	307	14	weakly	weakly	ADV
ejpam-3545	307	15	projective	projective	ADJ
ejpam-3545	307	16	with	with	ADP
ejpam-3545	307	17	respect	respect	NOUN
ejpam-3545	307	18	to	to	ADP
ejpam-3545	307	19	addition	addition	NOUN
ejpam-3545	307	20	in	in	ADP
ejpam-3545	307	21	n	n	PROPN
ejpam-3545	307	22	.	.	PUNCT
ejpam-3545	308	1	m.	m.	NOUN
ejpam-3545	308	2	burgin	burgin	PROPN
ejpam-3545	308	3	/	/	SYM
ejpam-3545	308	4	eur	eur	PROPN
ejpam-3545	308	5	.	.	PUNCT
ejpam-3545	309	1	j.	j.	PROPN
ejpam-3545	309	2	pure	pure	PROPN
ejpam-3545	309	3	appl	appl	PROPN
ejpam-3545	309	4	.	.	PROPN
ejpam-3545	309	5	math	math	PROPN
ejpam-3545	309	6	,	,	PUNCT
ejpam-3545	309	7	12	12	NUM
ejpam-3545	309	8	(	(	PUNCT
ejpam-3545	309	9	4	4	NUM
ejpam-3545	309	10	)	)	PUNCT
ejpam-3545	309	11	(	(	PUNCT
ejpam-3545	309	12	2019	2019	NUM
ejpam-3545	309	13	)	)	PUNCT
ejpam-3545	309	14	,	,	PUNCT
ejpam-3545	309	15	1787	1787	NUM
ejpam-3545	309	16	-	-	SYM
ejpam-3545	309	17	1810	1810	NUM
ejpam-3545	309	18	1799	1799	NUM
ejpam-3545	309	19	it	it	PRON
ejpam-3545	309	20	is	be	AUX
ejpam-3545	309	21	also	also	ADV
ejpam-3545	309	22	possible	possible	ADJ
ejpam-3545	309	23	that	that	SCONJ
ejpam-3545	309	24	both	both	DET
ejpam-3545	309	25	operations	operation	NOUN
ejpam-3545	309	26	in	in	ADP
ejpam-3545	309	27	two	two	NUM
ejpam-3545	309	28	abstract	abstract	ADJ
ejpam-3545	309	29	prearithmetics	prearithmetic	NOUN
ejpam-3545	309	30	are	be	AUX
ejpam-3545	309	31	not	not	PART
ejpam-3545	309	32	weakly	weakly	ADV
ejpam-3545	309	33	projective	projective	ADJ
ejpam-3545	309	34	with	with	ADP
ejpam-3545	309	35	respect	respect	NOUN
ejpam-3545	309	36	to	to	ADP
ejpam-3545	309	37	one	one	NUM
ejpam-3545	309	38	another	another	DET
ejpam-3545	309	39	.	.	PUNCT
ejpam-3545	310	1	example	example	NOUN
ejpam-3545	310	2	16	16	NUM
ejpam-3545	310	3	.	.	PUNCT
ejpam-3545	311	1	let	let	VERB
ejpam-3545	311	2	us	we	PRON
ejpam-3545	311	3	consider	consider	VERB
ejpam-3545	311	4	the	the	DET
ejpam-3545	311	5	conventional	conventional	ADJ
ejpam-3545	311	6	diophantine	diophantine	NOUN
ejpam-3545	311	7	arithmetic	arithmetic	ADJ
ejpam-3545	311	8	n	n	PROPN
ejpam-3545	311	9	of	of	ADP
ejpam-3545	311	10	all	all	DET
ejpam-3545	311	11	natural	natural	ADJ
ejpam-3545	311	12	numbers	number	NOUN
ejpam-3545	311	13	and	and	CCONJ
ejpam-3545	311	14	the	the	DET
ejpam-3545	311	15	abstract	abstract	ADJ
ejpam-3545	311	16	prearithmetic	prearithmetic	NOUN
ejpam-3545	311	17	a	a	PRON
ejpam-3545	311	18	=	=	X
ejpam-3545	311	19	(	(	PUNCT
ejpam-3545	311	20	n	n	NOUN
ejpam-3545	311	21	;	;	PUNCT
ejpam-3545	311	22	⊕,⊗,≤	⊕,⊗,≤	X
ejpam-3545	311	23	)	)	PUNCT
ejpam-3545	311	24	where	where	SCONJ
ejpam-3545	311	25	n	n	PRON
ejpam-3545	311	26	is	be	AUX
ejpam-3545	311	27	the	the	DET
ejpam-3545	311	28	set	set	NOUN
ejpam-3545	311	29	of	of	ADP
ejpam-3545	311	30	all	all	DET
ejpam-3545	311	31	natural	natural	ADJ
ejpam-3545	311	32	numbers	number	NOUN
ejpam-3545	311	33	and	and	CCONJ
ejpam-3545	311	34	≤	≤	NUM
ejpam-3545	311	35	is	be	AUX
ejpam-3545	311	36	the	the	DET
ejpam-3545	311	37	natural	natural	ADJ
ejpam-3545	311	38	order	order	NOUN
ejpam-3545	311	39	on	on	ADP
ejpam-3545	311	40	the	the	DET
ejpam-3545	311	41	set	set	NOUN
ejpam-3545	311	42	of	of	ADP
ejpam-3545	311	43	all	all	DET
ejpam-3545	311	44	natural	natural	ADJ
ejpam-3545	311	45	numbers	number	NOUN
ejpam-3545	311	46	,	,	PUNCT
ejpam-3545	311	47	while	while	SCONJ
ejpam-3545	311	48	addition	addition	NOUN
ejpam-3545	311	49	⊕	⊕	PROPN
ejpam-3545	311	50	and	and	CCONJ
ejpam-3545	311	51	multiplication	multiplication	NOUN
ejpam-3545	311	52	⊗	⊗	PROPN
ejpam-3545	311	53	are	be	AUX
ejpam-3545	311	54	defined	define	VERB
ejpam-3545	311	55	by	by	ADP
ejpam-3545	311	56	the	the	DET
ejpam-3545	311	57	following	follow	VERB
ejpam-3545	311	58	formulas	formula	NOUN
ejpam-3545	312	1	a⊕	a⊕	PROPN
ejpam-3545	312	2	b	b	X
ejpam-3545	312	3	=	=	PUNCT
ejpam-3545	312	4	a	a	DET
ejpam-3545	312	5	a⊗	a⊗	NOUN
ejpam-3545	312	6	b	b	PROPN
ejpam-3545	312	7	=	=	SYM
ejpam-3545	312	8	b	b	PROPN
ejpam-3545	312	9	multiplication	multiplication	NOUN
ejpam-3545	312	10	⊗	⊗	NOUN
ejpam-3545	312	11	in	in	ADP
ejpam-3545	312	12	the	the	DET
ejpam-3545	312	13	abstract	abstract	ADJ
ejpam-3545	312	14	prearithmetic	prearithmetic	NOUN
ejpam-3545	312	15	a	a	PRON
ejpam-3545	312	16	is	be	AUX
ejpam-3545	312	17	not	not	PART
ejpam-3545	312	18	weakly	weakly	ADV
ejpam-3545	312	19	projective	projective	ADJ
ejpam-3545	312	20	with	with	ADP
ejpam-3545	312	21	respect	respect	NOUN
ejpam-3545	312	22	to	to	ADP
ejpam-3545	312	23	multiplication	multiplication	NOUN
ejpam-3545	312	24	in	in	ADP
ejpam-3545	312	25	n	n	NOUN
ejpam-3545	312	26	because	because	SCONJ
ejpam-3545	312	27	otherwise	otherwise	ADV
ejpam-3545	312	28	by	by	ADP
ejpam-3545	312	29	proposition	proposition	NOUN
ejpam-3545	312	30	3.8	3.8	NUM
ejpam-3545	312	31	,	,	PUNCT
ejpam-3545	312	32	it	it	PRON
ejpam-3545	312	33	would	would	AUX
ejpam-3545	312	34	be	be	AUX
ejpam-3545	312	35	commutative	commutative	ADJ
ejpam-3545	312	36	and	and	CCONJ
ejpam-3545	312	37	it	it	PRON
ejpam-3545	312	38	is	be	AUX
ejpam-3545	312	39	not	not	PART
ejpam-3545	312	40	commutative	commutative	ADJ
ejpam-3545	312	41	.	.	PUNCT
ejpam-3545	313	1	addition	addition	NOUN
ejpam-3545	313	2	⊕	⊕	PROPN
ejpam-3545	313	3	in	in	ADP
ejpam-3545	313	4	the	the	DET
ejpam-3545	313	5	abstract	abstract	ADJ
ejpam-3545	313	6	prearithmetic	prearithmetic	NOUN
ejpam-3545	313	7	a	a	PRON
ejpam-3545	313	8	is	be	AUX
ejpam-3545	313	9	not	not	PART
ejpam-3545	313	10	weakly	weakly	ADV
ejpam-3545	313	11	projective	projective	ADJ
ejpam-3545	313	12	with	with	ADP
ejpam-3545	313	13	respect	respect	NOUN
ejpam-3545	313	14	to	to	ADP
ejpam-3545	313	15	addition	addition	NOUN
ejpam-3545	313	16	in	in	ADP
ejpam-3545	313	17	n	n	NOUN
ejpam-3545	313	18	because	because	SCONJ
ejpam-3545	313	19	otherwise	otherwise	ADV
ejpam-3545	313	20	by	by	ADP
ejpam-3545	313	21	proposition	proposition	NOUN
ejpam-3545	313	22	3.1	3.1	NUM
ejpam-3545	313	23	,	,	PUNCT
ejpam-3545	313	24	it	it	PRON
ejpam-3545	313	25	would	would	AUX
ejpam-3545	313	26	be	be	AUX
ejpam-3545	313	27	commutative	commutative	ADJ
ejpam-3545	313	28	and	and	CCONJ
ejpam-3545	313	29	it	it	PRON
ejpam-3545	313	30	is	be	AUX
ejpam-3545	313	31	not	not	PART
ejpam-3545	313	32	commutative	commutative	ADJ
ejpam-3545	313	33	.	.	PUNCT
ejpam-3545	314	1	similarly	similarly	ADV
ejpam-3545	314	2	to	to	ADP
ejpam-3545	314	3	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	314	4	of	of	ADP
ejpam-3545	314	5	addition	addition	NOUN
ejpam-3545	314	6	,	,	PUNCT
ejpam-3545	314	7	we	we	PRON
ejpam-3545	314	8	define	define	VERB
ejpam-3545	314	9	weak	weak	ADJ
ejpam-3545	314	10	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	314	11	of	of	ADP
ejpam-3545	314	12	multiplication	multiplication	NOUN
ejpam-3545	314	13	.	.	PUNCT
ejpam-3545	315	1	definition	definition	NOUN
ejpam-3545	315	2	4	4	NUM
ejpam-3545	315	3	.	.	PUNCT
ejpam-3545	316	1	a	a	DET
ejpam-3545	316	2	)	)	PUNCT
ejpam-3545	316	3	multiplication	multiplication	NOUN
ejpam-3545	316	4	◦	◦	NOUN
ejpam-3545	316	5	1	1	NUM
ejpam-3545	316	6	in	in	ADP
ejpam-3545	316	7	the	the	DET
ejpam-3545	316	8	abstract	abstract	ADJ
ejpam-3545	316	9	prearithmetic	prearithmetic	ADJ
ejpam-3545	316	10	a1	a1	NOUN
ejpam-3545	316	11	=	=	SYM
ejpam-3545	316	12	(	(	PUNCT
ejpam-3545	316	13	a1	a1	PROPN
ejpam-3545	316	14	;	;	PUNCT
ejpam-3545	316	15	+1	+1	PROPN
ejpam-3545	316	16	,	,	PUNCT
ejpam-3545	316	17	◦	◦	NOUN
ejpam-3545	316	18	1,≤1	1,≤1	ADJ
ejpam-3545	316	19	)	)	PUNCT
ejpam-3545	316	20	is	be	AUX
ejpam-3545	316	21	called	call	VERB
ejpam-3545	316	22	weakly	weakly	ADJ
ejpam-3545	316	23	monoprojective	monoprojective	NOUN
ejpam-3545	316	24	with	with	ADP
ejpam-3545	316	25	respect	respect	NOUN
ejpam-3545	316	26	to	to	ADP
ejpam-3545	316	27	multiplication	multiplication	NOUN
ejpam-3545	316	28	◦	◦	NOUN
ejpam-3545	316	29	2	2	NUM
ejpam-3545	316	30	in	in	ADP
ejpam-3545	316	31	the	the	DET
ejpam-3545	316	32	abstract	abstract	ADJ
ejpam-3545	316	33	prearithmetic	prearithmetic	ADJ
ejpam-3545	316	34	a2	a2	PROPN
ejpam-3545	316	35	=	=	SYM
ejpam-3545	316	36	(	(	PUNCT
ejpam-3545	316	37	a2	a2	PROPN
ejpam-3545	316	38	;	;	PUNCT
ejpam-3545	316	39	+2	+2	PROPN
ejpam-3545	316	40	,	,	PUNCT
ejpam-3545	316	41	◦	◦	NOUN
ejpam-3545	316	42	2,≤2	2,≤2	NOUN
ejpam-3545	316	43	)	)	PUNCT
ejpam-3545	316	44	if	if	SCONJ
ejpam-3545	316	45	◦	◦	NOUN
ejpam-3545	316	46	1	1	NUM
ejpam-3545	316	47	is	be	AUX
ejpam-3545	316	48	weakly	weakly	ADV
ejpam-3545	316	49	projective	projective	ADJ
ejpam-3545	316	50	with	with	ADP
ejpam-3545	316	51	respect	respect	NOUN
ejpam-3545	316	52	to	to	ADP
ejpam-3545	316	53	◦	◦	NOUN
ejpam-3545	316	54	2	2	NUM
ejpam-3545	316	55	and	and	CCONJ
ejpam-3545	316	56	g1	g1	NOUN
ejpam-3545	316	57	=	=	SYM
ejpam-3545	316	58	g2	g2	PROPN
ejpam-3545	316	59	,	,	PUNCT
ejpam-3545	316	60	i.e.	i.e.	X
ejpam-3545	316	61	,	,	PUNCT
ejpam-3545	316	62	there	there	PRON
ejpam-3545	316	63	is	be	VERB
ejpam-3545	316	64	only	only	ADV
ejpam-3545	316	65	one	one	NUM
ejpam-3545	316	66	projector	projector	NOUN
ejpam-3545	316	67	.	.	PUNCT
ejpam-3545	317	1	b	b	X
ejpam-3545	317	2	)	)	PUNCT
ejpam-3545	317	3	in	in	ADP
ejpam-3545	317	4	this	this	DET
ejpam-3545	317	5	case	case	NOUN
ejpam-3545	317	6	,	,	PUNCT
ejpam-3545	317	7	we	we	PRON
ejpam-3545	317	8	say	say	VERB
ejpam-3545	317	9	that	that	DET
ejpam-3545	317	10	multiplication	multiplication	NOUN
ejpam-3545	317	11	in	in	ADP
ejpam-3545	317	12	a2	a2	PROPN
ejpam-3545	317	13	is	be	AUX
ejpam-3545	317	14	weakly	weakly	ADV
ejpam-3545	317	15	monoprojected	monoprojected	ADJ
ejpam-3545	317	16	onto	onto	ADP
ejpam-3545	317	17	multiplication	multiplication	NOUN
ejpam-3545	317	18	in	in	ADP
ejpam-3545	317	19	a1	a1	NOUN
ejpam-3545	317	20	while	while	SCONJ
ejpam-3545	317	21	multiplication	multiplication	NOUN
ejpam-3545	317	22	in	in	ADP
ejpam-3545	317	23	a1	a1	NOUN
ejpam-3545	317	24	is	be	AUX
ejpam-3545	317	25	a	a	DET
ejpam-3545	317	26	weak	weak	ADJ
ejpam-3545	317	27	monoprojection	monoprojection	NOUN
ejpam-3545	317	28	of	of	ADP
ejpam-3545	317	29	multiplication	multiplication	NOUN
ejpam-3545	317	30	in	in	ADP
ejpam-3545	317	31	a2	a2	PROPN
ejpam-3545	317	32	.	.	PUNCT
ejpam-3545	318	1	we	we	PRON
ejpam-3545	318	2	also	also	ADV
ejpam-3545	318	3	say	say	VERB
ejpam-3545	318	4	that	that	SCONJ
ejpam-3545	318	5	there	there	PRON
ejpam-3545	318	6	is	be	VERB
ejpam-3545	318	7	a	a	DET
ejpam-3545	318	8	weak	weak	ADJ
ejpam-3545	318	9	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	318	10	between	between	ADP
ejpam-3545	318	11	multiplication	multiplication	NOUN
ejpam-3545	318	12	in	in	ADP
ejpam-3545	318	13	the	the	DET
ejpam-3545	318	14	prearithmetic	prearithmetic	ADJ
ejpam-3545	318	15	a1	a1	NOUN
ejpam-3545	318	16	and	and	CCONJ
ejpam-3545	318	17	multiplication	multiplication	NOUN
ejpam-3545	318	18	in	in	ADP
ejpam-3545	318	19	the	the	DET
ejpam-3545	318	20	prearithmetic	prearithmetic	PROPN
ejpam-3545	318	21	a2	a2	PROPN
ejpam-3545	318	22	and	and	CCONJ
ejpam-3545	318	23	there	there	PRON
ejpam-3545	318	24	is	be	VERB
ejpam-3545	318	25	an	an	DET
ejpam-3545	318	26	inverse	inverse	NOUN
ejpam-3545	318	27	weak	weak	ADJ
ejpam-3545	318	28	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	318	29	between	between	ADP
ejpam-3545	318	30	multiplication	multiplication	NOUN
ejpam-3545	318	31	in	in	ADP
ejpam-3545	318	32	the	the	DET
ejpam-3545	318	33	prearithmetic	prearithmetic	ADJ
ejpam-3545	318	34	a2	a2	PROPN
ejpam-3545	318	35	and	and	CCONJ
ejpam-3545	318	36	multiplication	multiplication	NOUN
ejpam-3545	318	37	in	in	ADP
ejpam-3545	318	38	the	the	DET
ejpam-3545	318	39	prearithmetic	prearithmetic	ADJ
ejpam-3545	318	40	a1	a1	NOUN
ejpam-3545	318	41	.	.	PUNCT
ejpam-3545	319	1	this	this	DET
ejpam-3545	319	2	relation	relation	NOUN
ejpam-3545	319	3	is	be	AUX
ejpam-3545	319	4	also	also	ADV
ejpam-3545	319	5	called	call	VERB
ejpam-3545	319	6	multiplicative	multiplicative	ADJ
ejpam-3545	319	7	weak	weak	ADJ
ejpam-3545	319	8	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	319	9	between	between	ADP
ejpam-3545	319	10	prearithmetics	prearithmetic	NOUN
ejpam-3545	319	11	a1	a1	NOUN
ejpam-3545	319	12	and	and	CCONJ
ejpam-3545	319	13	a2	a2	PROPN
ejpam-3545	319	14	.	.	PUNCT
ejpam-3545	319	15	example	example	NOUN
ejpam-3545	320	1	17	17	NUM
ejpam-3545	320	2	.	.	PUNCT
ejpam-3545	320	3	weak	weak	ADJ
ejpam-3545	320	4	projectivity	projectivity	NOUN
ejpam-3545	320	5	in	in	ADP
ejpam-3545	320	6	non	non	ADJ
ejpam-3545	320	7	-	-	ADJ
ejpam-3545	320	8	diophantine	diophantine	ADJ
ejpam-3545	320	9	arithmetics	arithmetic	NOUN
ejpam-3545	320	10	is	be	AUX
ejpam-3545	320	11	an	an	DET
ejpam-3545	320	12	example	example	NOUN
ejpam-3545	320	13	of	of	ADP
ejpam-3545	320	14	weak	weak	ADJ
ejpam-3545	320	15	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	320	16	between	between	ADP
ejpam-3545	320	17	multiplication	multiplication	NOUN
ejpam-3545	320	18	in	in	ADP
ejpam-3545	320	19	one	one	NUM
ejpam-3545	320	20	prearithmetic	prearithmetic	ADJ
ejpam-3545	320	21	and	and	CCONJ
ejpam-3545	320	22	multiplication	multiplication	NOUN
ejpam-3545	320	23	in	in	ADP
ejpam-3545	320	24	another	another	DET
ejpam-3545	320	25	prearithmetic	prearithmetic	ADJ
ejpam-3545	320	26	[	[	X
ejpam-3545	320	27	5	5	NUM
ejpam-3545	320	28	,	,	PUNCT
ejpam-3545	320	29	11	11	NUM
ejpam-3545	320	30	]	]	PUNCT
ejpam-3545	320	31	.	.	PUNCT
ejpam-3545	321	1	note	note	VERB
ejpam-3545	321	2	that	that	SCONJ
ejpam-3545	321	3	in	in	ADP
ejpam-3545	321	4	a	a	DET
ejpam-3545	321	5	general	general	ADJ
ejpam-3545	321	6	case	case	NOUN
ejpam-3545	321	7	,	,	PUNCT
ejpam-3545	321	8	addition	addition	NOUN
ejpam-3545	321	9	and	and	CCONJ
ejpam-3545	321	10	multiplication	multiplication	NOUN
ejpam-3545	321	11	in	in	ADP
ejpam-3545	321	12	an	an	DET
ejpam-3545	321	13	abstract	abstract	ADJ
ejpam-3545	321	14	prearithmetic	prearithmetic	NOUN
ejpam-3545	321	15	are	be	AUX
ejpam-3545	321	16	simply	simply	ADV
ejpam-3545	321	17	names	name	NOUN
ejpam-3545	321	18	of	of	ADP
ejpam-3545	321	19	two	two	NUM
ejpam-3545	321	20	operations	operation	NOUN
ejpam-3545	321	21	without	without	ADP
ejpam-3545	321	22	any	any	DET
ejpam-3545	321	23	additional	additional	ADJ
ejpam-3545	321	24	properties	property	NOUN
ejpam-3545	321	25	.	.	PUNCT
ejpam-3545	322	1	that	that	PRON
ejpam-3545	322	2	is	be	AUX
ejpam-3545	322	3	why	why	SCONJ
ejpam-3545	322	4	it	it	PRON
ejpam-3545	322	5	is	be	AUX
ejpam-3545	322	6	possible	possible	ADJ
ejpam-3545	322	7	to	to	PART
ejpam-3545	322	8	directly	directly	ADV
ejpam-3545	322	9	convert	convert	VERB
ejpam-3545	322	10	addition	addition	NOUN
ejpam-3545	322	11	to	to	ADP
ejpam-3545	322	12	multiplication	multiplication	NOUN
ejpam-3545	322	13	or	or	CCONJ
ejpam-3545	322	14	multiplication	multiplication	NOUN
ejpam-3545	322	15	to	to	PART
ejpam-3545	322	16	addition	addition	NOUN
ejpam-3545	322	17	by	by	ADP
ejpam-3545	322	18	renaming	rename	VERB
ejpam-3545	322	19	.	.	PUNCT
ejpam-3545	323	1	as	as	ADP
ejpam-3545	323	2	a	a	DET
ejpam-3545	323	3	result	result	NOUN
ejpam-3545	323	4	,	,	PUNCT
ejpam-3545	323	5	it	it	PRON
ejpam-3545	323	6	is	be	AUX
ejpam-3545	323	7	possible	possible	ADJ
ejpam-3545	323	8	to	to	PART
ejpam-3545	323	9	deduce	deduce	VERB
ejpam-3545	323	10	properties	property	NOUN
ejpam-3545	323	11	of	of	ADP
ejpam-3545	323	12	weak	weak	ADJ
ejpam-3545	323	13	projectivity	projectivity	NOUN
ejpam-3545	323	14	or	or	CCONJ
ejpam-3545	323	15	weak	weak	ADJ
ejpam-3545	323	16	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	323	17	between	between	ADP
ejpam-3545	323	18	multiplication	multiplication	NOUN
ejpam-3545	323	19	and	and	CCONJ
ejpam-3545	323	20	multiplication	multiplication	NOUN
ejpam-3545	323	21	from	from	ADP
ejpam-3545	323	22	the	the	DET
ejpam-3545	323	23	properties	property	NOUN
ejpam-3545	323	24	of	of	ADP
ejpam-3545	323	25	weak	weak	ADJ
ejpam-3545	323	26	projectivity	projectivity	NOUN
ejpam-3545	323	27	or	or	CCONJ
ejpam-3545	323	28	weak	weak	ADJ
ejpam-3545	323	29	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	323	30	between	between	ADP
ejpam-3545	323	31	addition	addition	NOUN
ejpam-3545	323	32	and	and	CCONJ
ejpam-3545	323	33	addition	addition	NOUN
ejpam-3545	323	34	.	.	PUNCT
ejpam-3545	324	1	for	for	ADP
ejpam-3545	324	2	instance	instance	NOUN
ejpam-3545	324	3	,	,	PUNCT
ejpam-3545	324	4	we	we	PRON
ejpam-3545	324	5	have	have	VERB
ejpam-3545	324	6	the	the	DET
ejpam-3545	324	7	following	follow	VERB
ejpam-3545	324	8	results	result	NOUN
ejpam-3545	324	9	.	.	PUNCT
ejpam-3545	325	1	m.	m.	NOUN
ejpam-3545	325	2	burgin	burgin	PROPN
ejpam-3545	325	3	/	/	SYM
ejpam-3545	325	4	eur	eur	PROPN
ejpam-3545	325	5	.	.	PUNCT
ejpam-3545	326	1	j.	j.	PROPN
ejpam-3545	326	2	pure	pure	PROPN
ejpam-3545	326	3	appl	appl	PROPN
ejpam-3545	326	4	.	.	PROPN
ejpam-3545	326	5	math	math	PROPN
ejpam-3545	326	6	,	,	PUNCT
ejpam-3545	326	7	12	12	NUM
ejpam-3545	326	8	(	(	PUNCT
ejpam-3545	326	9	4	4	NUM
ejpam-3545	326	10	)	)	PUNCT
ejpam-3545	326	11	(	(	PUNCT
ejpam-3545	326	12	2019	2019	NUM
ejpam-3545	326	13	)	)	PUNCT
ejpam-3545	326	14	,	,	PUNCT
ejpam-3545	326	15	1787	1787	NUM
ejpam-3545	326	16	-	-	SYM
ejpam-3545	326	17	1810	1810	NUM
ejpam-3545	326	18	1800	1800	NUM
ejpam-3545	326	19	let	let	VERB
ejpam-3545	326	20	us	we	PRON
ejpam-3545	326	21	consider	consider	VERB
ejpam-3545	326	22	three	three	NUM
ejpam-3545	326	23	abstract	abstract	ADJ
ejpam-3545	326	24	prearithmetics	prearithmetic	NOUN
ejpam-3545	326	25	a1	a1	NOUN
ejpam-3545	326	26	=	=	SYM
ejpam-3545	326	27	(	(	PUNCT
ejpam-3545	326	28	a1	a1	PROPN
ejpam-3545	326	29	;	;	PUNCT
ejpam-3545	326	30	+1	+1	PROPN
ejpam-3545	326	31	,	,	PUNCT
ejpam-3545	326	32	◦	◦	NOUN
ejpam-3545	326	33	1,≤1),a2	1,≤1),a2	NUM
ejpam-3545	326	34	=	=	SYM
ejpam-3545	326	35	(	(	PUNCT
ejpam-3545	326	36	a2	a2	PROPN
ejpam-3545	326	37	;	;	PUNCT
ejpam-3545	326	38	+2	+2	PROPN
ejpam-3545	326	39	,	,	PUNCT
ejpam-3545	326	40	◦	◦	NOUN
ejpam-3545	326	41	2,≤2	2,≤2	NOUN
ejpam-3545	326	42	)	)	PUNCT
ejpam-3545	326	43	and	and	CCONJ
ejpam-3545	326	44	a3	a3	NOUN
ejpam-3545	326	45	=	=	SYM
ejpam-3545	326	46	(	(	PUNCT
ejpam-3545	326	47	a3	a3	NOUN
ejpam-3545	326	48	;	;	PUNCT
ejpam-3545	326	49	+3	+3	PROPN
ejpam-3545	326	50	,	,	PUNCT
ejpam-3545	326	51	◦	◦	NOUN
ejpam-3545	326	52	3,≤3	3,≤3	NOUN
ejpam-3545	326	53	)	)	PUNCT
ejpam-3545	326	54	.	.	PUNCT
ejpam-3545	327	1	proposition	proposition	NOUN
ejpam-3545	327	2	3.9	3.9	NUM
ejpam-3545	327	3	.	.	PUNCT
ejpam-3545	328	1	if	if	SCONJ
ejpam-3545	328	2	the	the	DET
ejpam-3545	328	3	operation	operation	NOUN
ejpam-3545	328	4	◦	◦	NOUN
ejpam-3545	328	5	1	1	NUM
ejpam-3545	328	6	is	be	AUX
ejpam-3545	328	7	weakly	weakly	ADV
ejpam-3545	328	8	projective	projective	ADJ
ejpam-3545	328	9	(	(	PUNCT
ejpam-3545	328	10	monoprojective	monoprojective	NOUN
ejpam-3545	328	11	)	)	PUNCT
ejpam-3545	328	12	with	with	ADP
ejpam-3545	328	13	respect	respect	NOUN
ejpam-3545	328	14	to	to	ADP
ejpam-3545	328	15	the	the	DET
ejpam-3545	328	16	operation	operation	NOUN
ejpam-3545	328	17	◦	◦	NOUN
ejpam-3545	328	18	2	2	NUM
ejpam-3545	328	19	and	and	CCONJ
ejpam-3545	328	20	the	the	DET
ejpam-3545	328	21	operation	operation	NOUN
ejpam-3545	328	22	◦	◦	NOUN
ejpam-3545	328	23	2	2	NUM
ejpam-3545	328	24	is	be	AUX
ejpam-3545	328	25	weakly	weakly	ADV
ejpam-3545	328	26	projective	projective	ADJ
ejpam-3545	328	27	(	(	PUNCT
ejpam-3545	328	28	monoprojective	monoprojective	NOUN
ejpam-3545	328	29	)	)	PUNCT
ejpam-3545	328	30	with	with	ADP
ejpam-3545	328	31	respect	respect	NOUN
ejpam-3545	328	32	to	to	ADP
ejpam-3545	328	33	the	the	DET
ejpam-3545	328	34	operation	operation	NOUN
ejpam-3545	328	35	◦	◦	NOUN
ejpam-3545	328	36	3	3	NUM
ejpam-3545	328	37	,	,	PUNCT
ejpam-3545	328	38	then	then	ADV
ejpam-3545	328	39	the	the	DET
ejpam-3545	328	40	operation	operation	NOUN
ejpam-3545	328	41	◦	◦	NOUN
ejpam-3545	328	42	1	1	NUM
ejpam-3545	328	43	is	be	AUX
ejpam-3545	328	44	weakly	weakly	ADV
ejpam-3545	328	45	projective	projective	ADJ
ejpam-3545	328	46	(	(	PUNCT
ejpam-3545	328	47	monoprojective	monoprojective	NOUN
ejpam-3545	328	48	)	)	PUNCT
ejpam-3545	328	49	with	with	ADP
ejpam-3545	328	50	respect	respect	NOUN
ejpam-3545	328	51	to	to	ADP
ejpam-3545	328	52	the	the	DET
ejpam-3545	328	53	operation	operation	NOUN
ejpam-3545	328	54	◦	◦	NOUN
ejpam-3545	328	55	3	3	NUM
ejpam-3545	328	56	.	.	PUNCT
ejpam-3545	329	1	proof	proof	NOUN
ejpam-3545	329	2	is	be	AUX
ejpam-3545	329	3	similar	similar	ADJ
ejpam-3545	329	4	to	to	ADP
ejpam-3545	329	5	the	the	DET
ejpam-3545	329	6	proof	proof	NOUN
ejpam-3545	329	7	of	of	ADP
ejpam-3545	329	8	proposition	proposition	NOUN
ejpam-3545	329	9	3.2	3.2	NUM
ejpam-3545	329	10	.	.	PUNCT
ejpam-3545	330	1	proposition	proposition	NOUN
ejpam-3545	330	2	3.9	3.9	NUM
ejpam-3545	330	3	allows	allow	VERB
ejpam-3545	330	4	proving	prove	VERB
ejpam-3545	330	5	the	the	DET
ejpam-3545	330	6	following	follow	VERB
ejpam-3545	330	7	result	result	NOUN
ejpam-3545	330	8	.	.	PUNCT
ejpam-3545	331	1	theorem	theorem	NOUN
ejpam-3545	331	2	3	3	NUM
ejpam-3545	331	3	.	.	PUNCT
ejpam-3545	331	4	abstract	abstract	ADJ
ejpam-3545	331	5	prearithmetics	prearithmetic	NOUN
ejpam-3545	331	6	with	with	ADP
ejpam-3545	331	7	weak	weak	ADJ
ejpam-3545	331	8	projectivity	projectivity	NOUN
ejpam-3545	331	9	relations	relation	NOUN
ejpam-3545	331	10	for	for	ADP
ejpam-3545	331	11	multiplication	multiplication	NOUN
ejpam-3545	331	12	form	form	NOUN
ejpam-3545	331	13	the	the	DET
ejpam-3545	331	14	category	category	NOUN
ejpam-3545	331	15	amwp	amwp	NOUN
ejpam-3545	331	16	(	(	PUNCT
ejpam-3545	331	17	category	category	NOUN
ejpam-3545	331	18	amwmp	amwmp	NOUN
ejpam-3545	331	19	)	)	PUNCT
ejpam-3545	331	20	where	where	SCONJ
ejpam-3545	331	21	objects	object	NOUN
ejpam-3545	331	22	are	be	AUX
ejpam-3545	331	23	abstract	abstract	ADJ
ejpam-3545	331	24	prearithmetics	prearithmetic	NOUN
ejpam-3545	331	25	and	and	CCONJ
ejpam-3545	331	26	morphisms	morphism	NOUN
ejpam-3545	331	27	are	be	AUX
ejpam-3545	331	28	weak	weak	ADJ
ejpam-3545	331	29	projectivity	projectivity	NOUN
ejpam-3545	331	30	(	(	PUNCT
ejpam-3545	331	31	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	331	32	)	)	PUNCT
ejpam-3545	331	33	relations	relation	NOUN
ejpam-3545	331	34	between	between	ADP
ejpam-3545	331	35	multiplications	multiplication	NOUN
ejpam-3545	331	36	.	.	PUNCT
ejpam-3545	332	1	proof	proof	NOUN
ejpam-3545	332	2	is	be	AUX
ejpam-3545	332	3	similar	similar	ADJ
ejpam-3545	332	4	to	to	ADP
ejpam-3545	332	5	the	the	DET
ejpam-3545	332	6	proof	proof	NOUN
ejpam-3545	332	7	of	of	ADP
ejpam-3545	332	8	theorem	theorem	NOUN
ejpam-3545	332	9	1	1	NUM
ejpam-3545	332	10	.	.	X
ejpam-3545	332	11	taking	take	VERB
ejpam-3545	332	12	addition	addition	NOUN
ejpam-3545	332	13	and	and	CCONJ
ejpam-3545	332	14	multiplication	multiplication	NOUN
ejpam-3545	332	15	,	,	PUNCT
ejpam-3545	332	16	we	we	PRON
ejpam-3545	332	17	obtain	obtain	VERB
ejpam-3545	332	18	two	two	NUM
ejpam-3545	332	19	new	new	ADJ
ejpam-3545	332	20	concepts	concept	NOUN
ejpam-3545	332	21	.	.	PUNCT
ejpam-3545	333	1	definition	definition	NOUN
ejpam-3545	333	2	5	5	NUM
ejpam-3545	333	3	.	.	PUNCT
ejpam-3545	334	1	addition	addition	NOUN
ejpam-3545	334	2	+1	+1	PRON
ejpam-3545	334	3	in	in	ADP
ejpam-3545	334	4	the	the	DET
ejpam-3545	334	5	abstract	abstract	ADJ
ejpam-3545	334	6	prearithmetic	prearithmetic	ADJ
ejpam-3545	334	7	a1	a1	NOUN
ejpam-3545	334	8	=	=	SYM
ejpam-3545	334	9	(	(	PUNCT
ejpam-3545	334	10	a1	a1	PROPN
ejpam-3545	334	11	;	;	PUNCT
ejpam-3545	334	12	+1	+1	PROPN
ejpam-3545	334	13	,	,	PUNCT
ejpam-3545	334	14	◦	◦	NOUN
ejpam-3545	334	15	1,≤1	1,≤1	ADJ
ejpam-3545	334	16	)	)	PUNCT
ejpam-3545	334	17	is	be	AUX
ejpam-3545	334	18	called	call	VERB
ejpam-3545	334	19	weakly	weakly	ADV
ejpam-3545	334	20	projective	projective	NOUN
ejpam-3545	334	21	with	with	ADP
ejpam-3545	334	22	respect	respect	NOUN
ejpam-3545	334	23	to	to	ADP
ejpam-3545	334	24	multiplication	multiplication	NOUN
ejpam-3545	334	25	◦	◦	NOUN
ejpam-3545	334	26	2	2	NUM
ejpam-3545	334	27	in	in	ADP
ejpam-3545	334	28	the	the	DET
ejpam-3545	334	29	abstract	abstract	ADJ
ejpam-3545	334	30	prearithmetic	prearithmetic	ADJ
ejpam-3545	334	31	a2	a2	PROPN
ejpam-3545	334	32	=	=	SYM
ejpam-3545	334	33	(	(	PUNCT
ejpam-3545	334	34	a2	a2	PROPN
ejpam-3545	334	35	;	;	PUNCT
ejpam-3545	334	36	+2	+2	PROPN
ejpam-3545	334	37	,	,	PUNCT
ejpam-3545	334	38	◦	◦	NOUN
ejpam-3545	334	39	2,≤2	2,≤2	NOUN
ejpam-3545	334	40	)	)	PUNCT
ejpam-3545	334	41	if	if	SCONJ
ejpam-3545	334	42	there	there	PRON
ejpam-3545	334	43	are	be	VERB
ejpam-3545	334	44	three	three	NUM
ejpam-3545	334	45	mappings	mapping	NOUN
ejpam-3545	334	46	g1	g1	NOUN
ejpam-3545	334	47	:	:	PUNCT
ejpam-3545	334	48	a1	a1	NOUN
ejpam-3545	334	49	→	→	SYM
ejpam-3545	334	50	a2	a2	PROPN
ejpam-3545	334	51	,	,	PUNCT
ejpam-3545	334	52	g2	g2	PROPN
ejpam-3545	334	53	:	:	PUNCT
ejpam-3545	334	54	a1	a1	PROPN
ejpam-3545	334	55	→	→	SYM
ejpam-3545	334	56	a2	a2	PROPN
ejpam-3545	334	57	and	and	CCONJ
ejpam-3545	334	58	h	h	NOUN
ejpam-3545	334	59	:	:	PUNCT
ejpam-3545	334	60	a2	a2	PROPN
ejpam-3545	334	61	→	→	SYM
ejpam-3545	334	62	a1	a1	NOUN
ejpam-3545	334	63	and	and	CCONJ
ejpam-3545	334	64	the	the	DET
ejpam-3545	334	65	following	follow	VERB
ejpam-3545	334	66	equality	equality	NOUN
ejpam-3545	334	67	is	be	AUX
ejpam-3545	334	68	valid	valid	ADJ
ejpam-3545	334	69	for	for	ADP
ejpam-3545	334	70	all	all	DET
ejpam-3545	334	71	elements	element	NOUN
ejpam-3545	334	72	a	a	PRON
ejpam-3545	334	73	and	and	CCONJ
ejpam-3545	334	74	b	b	NOUN
ejpam-3545	334	75	from	from	ADP
ejpam-3545	334	76	a1	a1	NOUN
ejpam-3545	334	77	:	:	PUNCT
ejpam-3545	334	78	a	a	DET
ejpam-3545	334	79	+1	+1	PROPN
ejpam-3545	334	80	b	b	X
ejpam-3545	334	81	=	=	SYM
ejpam-3545	334	82	h(g1(a	h(g1(a	NOUN
ejpam-3545	334	83	)	)	PUNCT
ejpam-3545	334	84	◦	◦	NOUN
ejpam-3545	334	85	2	2	NUM
ejpam-3545	334	86	g2(b	g2(b	NOUN
ejpam-3545	334	87	)	)	PUNCT
ejpam-3545	334	88	)	)	PUNCT
ejpam-3545	335	1	b	b	X
ejpam-3545	335	2	)	)	PUNCT
ejpam-3545	335	3	the	the	DET
ejpam-3545	335	4	mappings	mapping	NOUN
ejpam-3545	335	5	g1	g1	NOUN
ejpam-3545	335	6	and	and	CCONJ
ejpam-3545	335	7	g2	g2	PROPN
ejpam-3545	335	8	are	be	AUX
ejpam-3545	335	9	called	call	VERB
ejpam-3545	335	10	the	the	DET
ejpam-3545	335	11	projectors	projector	NOUN
ejpam-3545	335	12	and	and	CCONJ
ejpam-3545	335	13	the	the	DET
ejpam-3545	335	14	mapping	mapping	NOUN
ejpam-3545	335	15	h	h	NOUN
ejpam-3545	335	16	is	be	AUX
ejpam-3545	335	17	called	call	VERB
ejpam-3545	335	18	the	the	DET
ejpam-3545	335	19	coprojector	coprojector	NOUN
ejpam-3545	335	20	for	for	ADP
ejpam-3545	335	21	the	the	DET
ejpam-3545	335	22	pair	pair	NOUN
ejpam-3545	335	23	(	(	PUNCT
ejpam-3545	335	24	+1	+1	INTJ
ejpam-3545	335	25	,	,	PUNCT
ejpam-3545	335	26	◦	◦	NOUN
ejpam-3545	335	27	2	2	NUM
ejpam-3545	335	28	)	)	PUNCT
ejpam-3545	335	29	.	.	PUNCT
ejpam-3545	336	1	c	c	X
ejpam-3545	336	2	)	)	PUNCT
ejpam-3545	336	3	in	in	ADP
ejpam-3545	336	4	this	this	DET
ejpam-3545	336	5	case	case	NOUN
ejpam-3545	336	6	,	,	PUNCT
ejpam-3545	336	7	we	we	PRON
ejpam-3545	336	8	say	say	VERB
ejpam-3545	336	9	that	that	DET
ejpam-3545	336	10	multiplication	multiplication	NOUN
ejpam-3545	336	11	in	in	ADP
ejpam-3545	336	12	a2	a2	PROPN
ejpam-3545	336	13	is	be	AUX
ejpam-3545	336	14	weakly	weakly	ADV
ejpam-3545	336	15	projected	project	VERB
ejpam-3545	336	16	onto	onto	ADP
ejpam-3545	336	17	addition	addition	NOUN
ejpam-3545	336	18	in	in	ADP
ejpam-3545	336	19	a1	a1	NOUN
ejpam-3545	336	20	while	while	SCONJ
ejpam-3545	336	21	addition	addition	NOUN
ejpam-3545	336	22	in	in	ADP
ejpam-3545	336	23	a1	a1	NOUN
ejpam-3545	336	24	is	be	AUX
ejpam-3545	336	25	a	a	DET
ejpam-3545	336	26	weak	weak	ADJ
ejpam-3545	336	27	projection	projection	NOUN
ejpam-3545	336	28	of	of	ADP
ejpam-3545	336	29	multiplication	multiplication	NOUN
ejpam-3545	336	30	in	in	ADP
ejpam-3545	336	31	a2	a2	PROPN
ejpam-3545	336	32	.	.	PUNCT
ejpam-3545	337	1	we	we	PRON
ejpam-3545	337	2	also	also	ADV
ejpam-3545	337	3	say	say	VERB
ejpam-3545	337	4	that	that	SCONJ
ejpam-3545	337	5	there	there	PRON
ejpam-3545	337	6	is	be	VERB
ejpam-3545	337	7	a	a	DET
ejpam-3545	337	8	weak	weak	ADJ
ejpam-3545	337	9	projectivity	projectivity	NOUN
ejpam-3545	337	10	between	between	ADP
ejpam-3545	337	11	addition	addition	NOUN
ejpam-3545	337	12	in	in	ADP
ejpam-3545	337	13	the	the	DET
ejpam-3545	337	14	prearithmetic	prearithmetic	ADJ
ejpam-3545	337	15	a1	a1	NOUN
ejpam-3545	337	16	and	and	CCONJ
ejpam-3545	337	17	multiplication	multiplication	NOUN
ejpam-3545	337	18	in	in	ADP
ejpam-3545	337	19	the	the	DET
ejpam-3545	337	20	prearithmetic	prearithmetic	PROPN
ejpam-3545	337	21	a2	a2	PROPN
ejpam-3545	337	22	and	and	CCONJ
ejpam-3545	337	23	there	there	PRON
ejpam-3545	337	24	is	be	VERB
ejpam-3545	337	25	a	a	DET
ejpam-3545	337	26	weak	weak	ADJ
ejpam-3545	337	27	inverse	inverse	NOUN
ejpam-3545	337	28	projectivity	projectivity	NOUN
ejpam-3545	337	29	between	between	ADP
ejpam-3545	337	30	multiplication	multiplication	NOUN
ejpam-3545	337	31	in	in	ADP
ejpam-3545	337	32	the	the	DET
ejpam-3545	337	33	prearithmetic	prearithmetic	ADJ
ejpam-3545	337	34	a2	a2	PROPN
ejpam-3545	337	35	and	and	CCONJ
ejpam-3545	337	36	addition	addition	NOUN
ejpam-3545	337	37	in	in	ADP
ejpam-3545	337	38	the	the	DET
ejpam-3545	337	39	prearithmetic	prearithmetic	ADJ
ejpam-3545	337	40	a1	a1	NOUN
ejpam-3545	337	41	.	.	PUNCT
ejpam-3545	338	1	in	in	ADP
ejpam-3545	338	2	a	a	DET
ejpam-3545	338	3	similar	similar	ADJ
ejpam-3545	338	4	way	way	NOUN
ejpam-3545	338	5	,	,	PUNCT
ejpam-3545	338	6	we	we	PRON
ejpam-3545	338	7	define	define	VERB
ejpam-3545	338	8	weak	weak	ADJ
ejpam-3545	338	9	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	338	10	.	.	PUNCT
ejpam-3545	339	1	definition	definition	NOUN
ejpam-3545	339	2	6	6	NUM
ejpam-3545	339	3	.	.	PUNCT
ejpam-3545	340	1	a	a	X
ejpam-3545	340	2	)	)	PUNCT
ejpam-3545	340	3	addition	addition	NOUN
ejpam-3545	340	4	+1	+1	PRON
ejpam-3545	340	5	in	in	ADP
ejpam-3545	340	6	the	the	DET
ejpam-3545	340	7	abstract	abstract	ADJ
ejpam-3545	340	8	prearithmetic	prearithmetic	ADJ
ejpam-3545	340	9	a1	a1	NOUN
ejpam-3545	340	10	=	=	SYM
ejpam-3545	340	11	(	(	PUNCT
ejpam-3545	340	12	a1	a1	PROPN
ejpam-3545	340	13	;	;	PUNCT
ejpam-3545	340	14	+1	+1	PROPN
ejpam-3545	340	15	,	,	PUNCT
ejpam-3545	340	16	◦	◦	NOUN
ejpam-3545	340	17	1,≤1	1,≤1	ADJ
ejpam-3545	340	18	)	)	PUNCT
ejpam-3545	340	19	is	be	AUX
ejpam-3545	340	20	called	call	VERB
ejpam-3545	340	21	weakly	weakly	ADJ
ejpam-3545	340	22	monoprojective	monoprojective	NOUN
ejpam-3545	340	23	with	with	ADP
ejpam-3545	340	24	respect	respect	NOUN
ejpam-3545	340	25	to	to	ADP
ejpam-3545	340	26	multiplication	multiplication	NOUN
ejpam-3545	340	27	◦	◦	NOUN
ejpam-3545	340	28	2	2	NUM
ejpam-3545	340	29	in	in	ADP
ejpam-3545	340	30	the	the	DET
ejpam-3545	340	31	abstract	abstract	ADJ
ejpam-3545	340	32	prearithmetic	prearithmetic	ADJ
ejpam-3545	340	33	a2	a2	PROPN
ejpam-3545	340	34	=	=	SYM
ejpam-3545	340	35	(	(	PUNCT
ejpam-3545	340	36	a2	a2	PROPN
ejpam-3545	340	37	;	;	PUNCT
ejpam-3545	340	38	+2	+2	PROPN
ejpam-3545	340	39	,	,	PUNCT
ejpam-3545	340	40	◦	◦	NOUN
ejpam-3545	340	41	2,≤2)if	2,≤2)if	NOUN
ejpam-3545	340	42	+1	+1	NOUN
ejpam-3545	340	43	is	be	AUX
ejpam-3545	340	44	weakly	weakly	ADV
ejpam-3545	340	45	projective	projective	ADJ
ejpam-3545	340	46	with	with	ADP
ejpam-3545	340	47	respect	respect	NOUN
ejpam-3545	340	48	to	to	ADP
ejpam-3545	340	49	◦	◦	NOUN
ejpam-3545	340	50	2	2	NUM
ejpam-3545	340	51	and	and	CCONJ
ejpam-3545	340	52	g1	g1	NOUN
ejpam-3545	340	53	=	=	SYM
ejpam-3545	340	54	g2	g2	PROPN
ejpam-3545	340	55	,	,	PUNCT
ejpam-3545	340	56	i.e.	i.e.	X
ejpam-3545	340	57	,	,	PUNCT
ejpam-3545	340	58	there	there	PRON
ejpam-3545	340	59	is	be	VERB
ejpam-3545	340	60	only	only	ADV
ejpam-3545	340	61	one	one	NUM
ejpam-3545	340	62	projector	projector	NOUN
ejpam-3545	340	63	.	.	PUNCT
ejpam-3545	341	1	b	b	X
ejpam-3545	341	2	)	)	PUNCT
ejpam-3545	341	3	in	in	ADP
ejpam-3545	341	4	this	this	DET
ejpam-3545	341	5	case	case	NOUN
ejpam-3545	341	6	,	,	PUNCT
ejpam-3545	341	7	we	we	PRON
ejpam-3545	341	8	say	say	VERB
ejpam-3545	341	9	that	that	DET
ejpam-3545	341	10	multiplication	multiplication	NOUN
ejpam-3545	341	11	in	in	ADP
ejpam-3545	341	12	a2	a2	PROPN
ejpam-3545	341	13	is	be	AUX
ejpam-3545	341	14	weakly	weakly	ADV
ejpam-3545	341	15	monoprojected	monoprojected	ADJ
ejpam-3545	341	16	onto	onto	ADP
ejpam-3545	341	17	addition	addition	NOUN
ejpam-3545	341	18	in	in	ADP
ejpam-3545	341	19	a1	a1	NOUN
ejpam-3545	341	20	while	while	SCONJ
ejpam-3545	341	21	addition	addition	NOUN
ejpam-3545	341	22	in	in	ADP
ejpam-3545	341	23	a1	a1	NOUN
ejpam-3545	341	24	is	be	AUX
ejpam-3545	341	25	a	a	DET
ejpam-3545	341	26	weak	weak	ADJ
ejpam-3545	341	27	monoprojection	monoprojection	NOUN
ejpam-3545	341	28	of	of	ADP
ejpam-3545	341	29	multiplication	multiplication	NOUN
ejpam-3545	341	30	in	in	ADP
ejpam-3545	341	31	a2	a2	PROPN
ejpam-3545	341	32	.	.	PUNCT
ejpam-3545	342	1	in	in	ADP
ejpam-3545	342	2	this	this	DET
ejpam-3545	342	3	case	case	NOUN
ejpam-3545	342	4	,	,	PUNCT
ejpam-3545	342	5	we	we	PRON
ejpam-3545	342	6	also	also	ADV
ejpam-3545	342	7	say	say	VERB
ejpam-3545	342	8	that	that	SCONJ
ejpam-3545	342	9	there	there	PRON
ejpam-3545	342	10	is	be	VERB
ejpam-3545	342	11	a	a	DET
ejpam-3545	342	12	weak	weak	ADJ
ejpam-3545	342	13	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	342	14	between	between	ADP
ejpam-3545	342	15	addition	addition	NOUN
ejpam-3545	342	16	in	in	ADP
ejpam-3545	342	17	the	the	DET
ejpam-3545	342	18	prearithmetic	prearithmetic	ADJ
ejpam-3545	342	19	a1	a1	NOUN
ejpam-3545	342	20	and	and	CCONJ
ejpam-3545	342	21	multiplication	multiplication	NOUN
ejpam-3545	342	22	in	in	ADP
ejpam-3545	342	23	the	the	DET
ejpam-3545	342	24	prearithmetic	prearithmetic	PROPN
ejpam-3545	342	25	a2	a2	PROPN
ejpam-3545	342	26	and	and	CCONJ
ejpam-3545	342	27	there	there	PRON
ejpam-3545	342	28	is	be	VERB
ejpam-3545	342	29	an	an	DET
ejpam-3545	342	30	inverse	inverse	NOUN
ejpam-3545	342	31	weak	weak	ADJ
ejpam-3545	342	32	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	342	33	between	between	ADP
ejpam-3545	342	34	multiplication	multiplication	NOUN
ejpam-3545	342	35	in	in	ADP
ejpam-3545	342	36	the	the	DET
ejpam-3545	342	37	prearithmetic	prearithmetic	ADJ
ejpam-3545	342	38	a2	a2	PROPN
ejpam-3545	342	39	and	and	CCONJ
ejpam-3545	342	40	addition	addition	NOUN
ejpam-3545	342	41	in	in	ADP
ejpam-3545	342	42	the	the	DET
ejpam-3545	342	43	prearithmetic	prearithmetic	ADJ
ejpam-3545	342	44	a1	a1	NOUN
ejpam-3545	342	45	.	.	PUNCT
ejpam-3545	343	1	renaming	rename	VERB
ejpam-3545	343	2	of	of	ADP
ejpam-3545	343	3	operations	operation	NOUN
ejpam-3545	343	4	in	in	ADP
ejpam-3545	343	5	abstract	abstract	ADJ
ejpam-3545	343	6	prearithmetics	prearithmetic	NOUN
ejpam-3545	343	7	allows	allow	VERB
ejpam-3545	343	8	obtaining	obtain	VERB
ejpam-3545	343	9	properties	property	NOUN
ejpam-3545	343	10	of	of	ADP
ejpam-3545	343	11	weak	weak	ADJ
ejpam-3545	343	12	projectivity	projectivity	NOUN
ejpam-3545	343	13	or	or	CCONJ
ejpam-3545	343	14	weak	weak	ADJ
ejpam-3545	343	15	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	343	16	between	between	ADP
ejpam-3545	343	17	addition	addition	NOUN
ejpam-3545	343	18	and	and	CCONJ
ejpam-3545	343	19	multiplication	multiplication	NOUN
ejpam-3545	343	20	from	from	ADP
ejpam-3545	343	21	the	the	DET
ejpam-3545	343	22	properties	property	NOUN
ejpam-3545	343	23	of	of	ADP
ejpam-3545	343	24	weak	weak	ADJ
ejpam-3545	343	25	projectivity	projectivity	NOUN
ejpam-3545	343	26	or	or	CCONJ
ejpam-3545	343	27	weak	weak	ADJ
ejpam-3545	343	28	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	343	29	between	between	ADP
ejpam-3545	343	30	addition	addition	NOUN
ejpam-3545	343	31	and	and	CCONJ
ejpam-3545	343	32	addition	addition	NOUN
ejpam-3545	343	33	.	.	PUNCT
ejpam-3545	344	1	m.	m.	NOUN
ejpam-3545	344	2	burgin	burgin	PROPN
ejpam-3545	344	3	/	/	SYM
ejpam-3545	344	4	eur	eur	PROPN
ejpam-3545	344	5	.	.	PUNCT
ejpam-3545	345	1	j.	j.	PROPN
ejpam-3545	345	2	pure	pure	PROPN
ejpam-3545	345	3	appl	appl	PROPN
ejpam-3545	345	4	.	.	PROPN
ejpam-3545	345	5	math	math	PROPN
ejpam-3545	345	6	,	,	PUNCT
ejpam-3545	345	7	12	12	NUM
ejpam-3545	345	8	(	(	PUNCT
ejpam-3545	345	9	4	4	NUM
ejpam-3545	345	10	)	)	PUNCT
ejpam-3545	345	11	(	(	PUNCT
ejpam-3545	345	12	2019	2019	NUM
ejpam-3545	345	13	)	)	PUNCT
ejpam-3545	345	14	,	,	PUNCT
ejpam-3545	345	15	1787	1787	NUM
ejpam-3545	345	16	-	-	SYM
ejpam-3545	345	17	1810	1810	NUM
ejpam-3545	345	18	1801	1801	NUM
ejpam-3545	345	19	taking	take	VERB
ejpam-3545	345	20	multiplication	multiplication	NOUN
ejpam-3545	345	21	and	and	CCONJ
ejpam-3545	345	22	addition	addition	NOUN
ejpam-3545	345	23	,	,	PUNCT
ejpam-3545	345	24	we	we	PRON
ejpam-3545	345	25	obtain	obtain	VERB
ejpam-3545	345	26	the	the	DET
ejpam-3545	345	27	following	follow	VERB
ejpam-3545	345	28	concepts	concept	NOUN
ejpam-3545	345	29	.	.	PUNCT
ejpam-3545	346	1	definition	definition	NOUN
ejpam-3545	346	2	7	7	NUM
ejpam-3545	346	3	.	.	PUNCT
ejpam-3545	346	4	multiplication	multiplication	NOUN
ejpam-3545	346	5	◦	◦	NOUN
ejpam-3545	346	6	1	1	NUM
ejpam-3545	346	7	in	in	ADP
ejpam-3545	346	8	the	the	DET
ejpam-3545	346	9	abstract	abstract	ADJ
ejpam-3545	346	10	prearithmetic	prearithmetic	ADJ
ejpam-3545	346	11	a1	a1	NOUN
ejpam-3545	346	12	=	=	SYM
ejpam-3545	346	13	(	(	PUNCT
ejpam-3545	346	14	a1	a1	PROPN
ejpam-3545	346	15	;	;	PUNCT
ejpam-3545	346	16	+1	+1	PROPN
ejpam-3545	346	17	,	,	PUNCT
ejpam-3545	346	18	◦	◦	NOUN
ejpam-3545	346	19	1,≤1	1,≤1	ADJ
ejpam-3545	346	20	)	)	PUNCT
ejpam-3545	346	21	is	be	AUX
ejpam-3545	346	22	called	call	VERB
ejpam-3545	346	23	weakly	weakly	ADV
ejpam-3545	346	24	projective	projective	NOUN
ejpam-3545	346	25	with	with	ADP
ejpam-3545	346	26	respect	respect	NOUN
ejpam-3545	346	27	to	to	ADP
ejpam-3545	346	28	addition	addition	NOUN
ejpam-3545	346	29	+2	+2	ADP
ejpam-3545	346	30	in	in	ADP
ejpam-3545	346	31	the	the	DET
ejpam-3545	346	32	abstract	abstract	ADJ
ejpam-3545	346	33	prearithmetic	prearithmetic	ADJ
ejpam-3545	346	34	a2	a2	PROPN
ejpam-3545	346	35	=	=	SYM
ejpam-3545	346	36	(	(	PUNCT
ejpam-3545	346	37	a2	a2	PROPN
ejpam-3545	346	38	;	;	PUNCT
ejpam-3545	346	39	+2	+2	PROPN
ejpam-3545	346	40	,	,	PUNCT
ejpam-3545	346	41	◦	◦	NOUN
ejpam-3545	346	42	2,≤2	2,≤2	NOUN
ejpam-3545	346	43	)	)	PUNCT
ejpam-3545	346	44	if	if	SCONJ
ejpam-3545	346	45	there	there	PRON
ejpam-3545	346	46	are	be	VERB
ejpam-3545	346	47	three	three	NUM
ejpam-3545	346	48	mappings	mapping	NOUN
ejpam-3545	346	49	g1	g1	NOUN
ejpam-3545	346	50	:	:	PUNCT
ejpam-3545	346	51	a1	a1	NOUN
ejpam-3545	346	52	→	→	SYM
ejpam-3545	346	53	a2	a2	PROPN
ejpam-3545	346	54	,	,	PUNCT
ejpam-3545	346	55	g2	g2	PROPN
ejpam-3545	346	56	:	:	PUNCT
ejpam-3545	346	57	a1	a1	PROPN
ejpam-3545	346	58	→	→	SYM
ejpam-3545	346	59	a2	a2	PROPN
ejpam-3545	346	60	and	and	CCONJ
ejpam-3545	346	61	h	h	NOUN
ejpam-3545	346	62	:	:	PUNCT
ejpam-3545	346	63	a2	a2	PROPN
ejpam-3545	346	64	→	→	SYM
ejpam-3545	346	65	a1	a1	NOUN
ejpam-3545	346	66	and	and	CCONJ
ejpam-3545	346	67	the	the	DET
ejpam-3545	346	68	following	follow	VERB
ejpam-3545	346	69	equality	equality	NOUN
ejpam-3545	346	70	is	be	AUX
ejpam-3545	346	71	valid	valid	ADJ
ejpam-3545	346	72	for	for	ADP
ejpam-3545	346	73	all	all	DET
ejpam-3545	346	74	elements	element	NOUN
ejpam-3545	346	75	a	a	PRON
ejpam-3545	346	76	and	and	CCONJ
ejpam-3545	346	77	b	b	NOUN
ejpam-3545	346	78	from	from	ADP
ejpam-3545	346	79	a1	a1	NOUN
ejpam-3545	346	80	:	:	PUNCT
ejpam-3545	346	81	a	a	DET
ejpam-3545	346	82	◦	◦	NOUN
ejpam-3545	346	83	1	1	NUM
ejpam-3545	346	84	b	b	NOUN
ejpam-3545	346	85	=	=	PUNCT
ejpam-3545	346	86	h(g1(a	h(g1(a	PROPN
ejpam-3545	346	87	)	)	PUNCT
ejpam-3545	346	88	+2	+2	PROPN
ejpam-3545	346	89	g2(b	g2(b	PROPN
ejpam-3545	346	90	)	)	PUNCT
ejpam-3545	346	91	)	)	PUNCT
ejpam-3545	347	1	b	b	X
ejpam-3545	347	2	)	)	PUNCT
ejpam-3545	347	3	the	the	DET
ejpam-3545	347	4	mappings	mapping	NOUN
ejpam-3545	347	5	g1	g1	NOUN
ejpam-3545	347	6	and	and	CCONJ
ejpam-3545	347	7	g2	g2	PROPN
ejpam-3545	347	8	are	be	AUX
ejpam-3545	347	9	called	call	VERB
ejpam-3545	347	10	the	the	DET
ejpam-3545	347	11	projectors	projector	NOUN
ejpam-3545	347	12	and	and	CCONJ
ejpam-3545	347	13	the	the	DET
ejpam-3545	347	14	mapping	mapping	NOUN
ejpam-3545	347	15	h	h	NOUN
ejpam-3545	347	16	is	be	AUX
ejpam-3545	347	17	called	call	VERB
ejpam-3545	347	18	the	the	DET
ejpam-3545	347	19	coprojector	coprojector	NOUN
ejpam-3545	347	20	for	for	ADP
ejpam-3545	347	21	the	the	DET
ejpam-3545	347	22	pair	pair	NOUN
ejpam-3545	347	23	(	(	PUNCT
ejpam-3545	347	24	◦	◦	NOUN
ejpam-3545	347	25	1,+2	1,+2	NUM
ejpam-3545	347	26	)	)	PUNCT
ejpam-3545	347	27	.	.	PUNCT
ejpam-3545	348	1	c	c	X
ejpam-3545	348	2	)	)	PUNCT
ejpam-3545	348	3	in	in	ADP
ejpam-3545	348	4	this	this	DET
ejpam-3545	348	5	case	case	NOUN
ejpam-3545	348	6	,	,	PUNCT
ejpam-3545	348	7	we	we	PRON
ejpam-3545	348	8	say	say	VERB
ejpam-3545	348	9	that	that	SCONJ
ejpam-3545	348	10	addition	addition	NOUN
ejpam-3545	348	11	in	in	ADP
ejpam-3545	348	12	a2	a2	PROPN
ejpam-3545	348	13	is	be	AUX
ejpam-3545	348	14	weakly	weakly	ADV
ejpam-3545	348	15	projected	project	VERB
ejpam-3545	348	16	onto	onto	ADP
ejpam-3545	348	17	multiplication	multiplication	NOUN
ejpam-3545	348	18	in	in	ADP
ejpam-3545	348	19	a1	a1	NOUN
ejpam-3545	348	20	while	while	SCONJ
ejpam-3545	348	21	multiplication	multiplication	NOUN
ejpam-3545	348	22	in	in	ADP
ejpam-3545	348	23	a1	a1	NOUN
ejpam-3545	348	24	is	be	AUX
ejpam-3545	348	25	a	a	DET
ejpam-3545	348	26	weak	weak	ADJ
ejpam-3545	348	27	projection	projection	NOUN
ejpam-3545	348	28	of	of	ADP
ejpam-3545	348	29	addition	addition	NOUN
ejpam-3545	348	30	in	in	ADP
ejpam-3545	348	31	a2	a2	PROPN
ejpam-3545	348	32	.	.	PUNCT
ejpam-3545	349	1	we	we	PRON
ejpam-3545	349	2	also	also	ADV
ejpam-3545	349	3	say	say	VERB
ejpam-3545	349	4	that	that	SCONJ
ejpam-3545	349	5	there	there	PRON
ejpam-3545	349	6	is	be	VERB
ejpam-3545	349	7	a	a	DET
ejpam-3545	349	8	weak	weak	ADJ
ejpam-3545	349	9	projectivity	projectivity	NOUN
ejpam-3545	349	10	between	between	ADP
ejpam-3545	349	11	multiplication	multiplication	NOUN
ejpam-3545	349	12	in	in	ADP
ejpam-3545	349	13	the	the	DET
ejpam-3545	349	14	prearithmetic	prearithmetic	ADJ
ejpam-3545	349	15	a1	a1	NOUN
ejpam-3545	349	16	and	and	CCONJ
ejpam-3545	349	17	addition	addition	NOUN
ejpam-3545	349	18	in	in	ADP
ejpam-3545	349	19	the	the	DET
ejpam-3545	349	20	prearithmetic	prearithmetic	PROPN
ejpam-3545	349	21	a2	a2	PROPN
ejpam-3545	349	22	and	and	CCONJ
ejpam-3545	349	23	there	there	PRON
ejpam-3545	349	24	is	be	VERB
ejpam-3545	349	25	a	a	DET
ejpam-3545	349	26	weak	weak	ADJ
ejpam-3545	349	27	inverse	inverse	NOUN
ejpam-3545	349	28	projectivity	projectivity	NOUN
ejpam-3545	349	29	between	between	ADP
ejpam-3545	349	30	addition	addition	NOUN
ejpam-3545	349	31	in	in	ADP
ejpam-3545	349	32	the	the	DET
ejpam-3545	349	33	prearithmetic	prearithmetic	PROPN
ejpam-3545	349	34	a2	a2	PROPN
ejpam-3545	349	35	and	and	CCONJ
ejpam-3545	349	36	multiplication	multiplication	NOUN
ejpam-3545	349	37	in	in	ADP
ejpam-3545	349	38	the	the	DET
ejpam-3545	349	39	prearithmetic	prearithmetic	ADJ
ejpam-3545	349	40	a1	a1	NOUN
ejpam-3545	349	41	.	.	PUNCT
ejpam-3545	350	1	in	in	ADP
ejpam-3545	350	2	a	a	DET
ejpam-3545	350	3	similar	similar	ADJ
ejpam-3545	350	4	way	way	NOUN
ejpam-3545	350	5	,	,	PUNCT
ejpam-3545	350	6	we	we	PRON
ejpam-3545	350	7	define	define	VERB
ejpam-3545	350	8	weak	weak	ADJ
ejpam-3545	350	9	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	350	10	.	.	PUNCT
ejpam-3545	351	1	definition	definition	NOUN
ejpam-3545	351	2	8	8	NUM
ejpam-3545	351	3	.	.	PUNCT
ejpam-3545	352	1	a	a	DET
ejpam-3545	352	2	)	)	PUNCT
ejpam-3545	352	3	multiplication	multiplication	NOUN
ejpam-3545	352	4	◦	◦	NOUN
ejpam-3545	352	5	1	1	NUM
ejpam-3545	352	6	in	in	ADP
ejpam-3545	352	7	the	the	DET
ejpam-3545	352	8	abstract	abstract	ADJ
ejpam-3545	352	9	prearithmetic	prearithmetic	ADJ
ejpam-3545	352	10	a1	a1	NOUN
ejpam-3545	352	11	=	=	SYM
ejpam-3545	352	12	(	(	PUNCT
ejpam-3545	352	13	a1	a1	PROPN
ejpam-3545	352	14	;	;	PUNCT
ejpam-3545	352	15	+1	+1	PROPN
ejpam-3545	352	16	,	,	PUNCT
ejpam-3545	352	17	◦	◦	NOUN
ejpam-3545	352	18	1,≤1	1,≤1	ADJ
ejpam-3545	352	19	)	)	PUNCT
ejpam-3545	352	20	is	be	AUX
ejpam-3545	352	21	called	call	VERB
ejpam-3545	352	22	weakly	weakly	ADJ
ejpam-3545	352	23	monoprojective	monoprojective	NOUN
ejpam-3545	352	24	with	with	ADP
ejpam-3545	352	25	respect	respect	NOUN
ejpam-3545	352	26	to	to	ADP
ejpam-3545	352	27	addition	addition	NOUN
ejpam-3545	352	28	+2	+2	ADP
ejpam-3545	352	29	in	in	ADP
ejpam-3545	352	30	the	the	DET
ejpam-3545	352	31	abstract	abstract	ADJ
ejpam-3545	352	32	prearithmetic	prearithmetic	ADJ
ejpam-3545	352	33	a2	a2	PROPN
ejpam-3545	352	34	=	=	SYM
ejpam-3545	352	35	(	(	PUNCT
ejpam-3545	352	36	a2	a2	PROPN
ejpam-3545	352	37	;	;	PUNCT
ejpam-3545	352	38	+2	+2	PROPN
ejpam-3545	352	39	,	,	PUNCT
ejpam-3545	352	40	◦	◦	NOUN
ejpam-3545	352	41	2,≤2	2,≤2	NOUN
ejpam-3545	352	42	)	)	PUNCT
ejpam-3545	352	43	if	if	SCONJ
ejpam-3545	352	44	◦	◦	NOUN
ejpam-3545	352	45	1	1	NUM
ejpam-3545	352	46	is	be	AUX
ejpam-3545	352	47	weakly	weakly	ADV
ejpam-3545	352	48	projective	projective	ADJ
ejpam-3545	352	49	with	with	ADP
ejpam-3545	352	50	respect	respect	NOUN
ejpam-3545	352	51	to	to	ADP
ejpam-3545	352	52	+2	+2	PROPN
ejpam-3545	352	53	and	and	CCONJ
ejpam-3545	352	54	g1	g1	PROPN
ejpam-3545	352	55	=	=	PROPN
ejpam-3545	352	56	g2	g2	PROPN
ejpam-3545	352	57	,	,	PUNCT
ejpam-3545	352	58	i.e.	i.e.	X
ejpam-3545	352	59	,	,	PUNCT
ejpam-3545	352	60	there	there	PRON
ejpam-3545	352	61	is	be	VERB
ejpam-3545	352	62	only	only	ADV
ejpam-3545	352	63	one	one	NUM
ejpam-3545	352	64	projector	projector	NOUN
ejpam-3545	352	65	.	.	PUNCT
ejpam-3545	353	1	b	b	X
ejpam-3545	353	2	)	)	PUNCT
ejpam-3545	353	3	in	in	ADP
ejpam-3545	353	4	this	this	DET
ejpam-3545	353	5	case	case	NOUN
ejpam-3545	353	6	,	,	PUNCT
ejpam-3545	353	7	we	we	PRON
ejpam-3545	353	8	say	say	VERB
ejpam-3545	353	9	that	that	SCONJ
ejpam-3545	353	10	addition	addition	NOUN
ejpam-3545	353	11	in	in	ADP
ejpam-3545	353	12	a2	a2	PROPN
ejpam-3545	353	13	is	be	AUX
ejpam-3545	353	14	weakly	weakly	ADV
ejpam-3545	353	15	monoprojected	monoprojected	ADJ
ejpam-3545	353	16	onto	onto	ADP
ejpam-3545	353	17	multiplication	multiplication	NOUN
ejpam-3545	353	18	in	in	ADP
ejpam-3545	353	19	a1	a1	NOUN
ejpam-3545	353	20	while	while	SCONJ
ejpam-3545	353	21	multiplication	multiplication	NOUN
ejpam-3545	353	22	in	in	ADP
ejpam-3545	353	23	a1	a1	NOUN
ejpam-3545	353	24	is	be	AUX
ejpam-3545	353	25	a	a	DET
ejpam-3545	353	26	weak	weak	ADJ
ejpam-3545	353	27	monoprojection	monoprojection	NOUN
ejpam-3545	353	28	of	of	ADP
ejpam-3545	353	29	addition	addition	NOUN
ejpam-3545	353	30	in	in	ADP
ejpam-3545	353	31	a2	a2	PROPN
ejpam-3545	353	32	.	.	PUNCT
ejpam-3545	354	1	we	we	PRON
ejpam-3545	354	2	also	also	ADV
ejpam-3545	354	3	say	say	VERB
ejpam-3545	354	4	that	that	SCONJ
ejpam-3545	354	5	there	there	PRON
ejpam-3545	354	6	is	be	VERB
ejpam-3545	354	7	a	a	DET
ejpam-3545	354	8	weak	weak	ADJ
ejpam-3545	354	9	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	354	10	between	between	ADP
ejpam-3545	354	11	multiplication	multiplication	NOUN
ejpam-3545	354	12	in	in	ADP
ejpam-3545	354	13	the	the	DET
ejpam-3545	354	14	prearithmetic	prearithmetic	ADJ
ejpam-3545	354	15	a1	a1	NOUN
ejpam-3545	354	16	and	and	CCONJ
ejpam-3545	354	17	addition	addition	NOUN
ejpam-3545	354	18	in	in	ADP
ejpam-3545	354	19	the	the	DET
ejpam-3545	354	20	prearithmetic	prearithmetic	PROPN
ejpam-3545	354	21	a2	a2	PROPN
ejpam-3545	354	22	and	and	CCONJ
ejpam-3545	354	23	there	there	PRON
ejpam-3545	354	24	is	be	VERB
ejpam-3545	354	25	an	an	DET
ejpam-3545	354	26	inverse	inverse	NOUN
ejpam-3545	354	27	weak	weak	ADJ
ejpam-3545	354	28	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	354	29	between	between	ADP
ejpam-3545	354	30	addition	addition	NOUN
ejpam-3545	354	31	in	in	ADP
ejpam-3545	354	32	the	the	DET
ejpam-3545	354	33	prearithmetic	prearithmetic	PROPN
ejpam-3545	354	34	a2	a2	PROPN
ejpam-3545	354	35	and	and	CCONJ
ejpam-3545	354	36	multiplication	multiplication	NOUN
ejpam-3545	354	37	in	in	ADP
ejpam-3545	354	38	the	the	DET
ejpam-3545	354	39	prearithmetic	prearithmetic	ADJ
ejpam-3545	354	40	a1	a1	NOUN
ejpam-3545	354	41	.	.	PROPN
ejpam-3545	354	42	example	example	NOUN
ejpam-3545	354	43	18	18	NUM
ejpam-3545	354	44	.	.	PUNCT
ejpam-3545	355	1	implicitly	implicitly	ADV
ejpam-3545	355	2	people	people	NOUN
ejpam-3545	355	3	started	start	VERB
ejpam-3545	355	4	using	use	VERB
ejpam-3545	355	5	weak	weak	ADJ
ejpam-3545	355	6	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	355	7	between	between	ADP
ejpam-3545	355	8	multiplication	multiplication	NOUN
ejpam-3545	355	9	and	and	CCONJ
ejpam-3545	355	10	addition	addition	NOUN
ejpam-3545	355	11	with	with	ADP
ejpam-3545	355	12	the	the	DET
ejpam-3545	355	13	invention	invention	NOUN
ejpam-3545	355	14	(	(	PUNCT
ejpam-3545	355	15	discovery	discovery	NOUN
ejpam-3545	355	16	)	)	PUNCT
ejpam-3545	355	17	of	of	ADP
ejpam-3545	355	18	logarithms	logarithm	NOUN
ejpam-3545	355	19	in	in	ADP
ejpam-3545	355	20	the	the	DET
ejpam-3545	355	21	early	early	ADJ
ejpam-3545	355	22	17th	17th	ADJ
ejpam-3545	355	23	century	century	NOUN
ejpam-3545	355	24	.	.	PUNCT
ejpam-3545	356	1	indeed	indeed	ADV
ejpam-3545	356	2	,	,	PUNCT
ejpam-3545	356	3	the	the	DET
ejpam-3545	356	4	logarithmic	logarithmic	ADJ
ejpam-3545	356	5	weak	weak	ADJ
ejpam-3545	356	6	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	356	7	is	be	AUX
ejpam-3545	356	8	defined	define	VERB
ejpam-3545	356	9	by	by	ADP
ejpam-3545	356	10	the	the	DET
ejpam-3545	356	11	projector	projector	NOUN
ejpam-3545	356	12	g1(a	g1(a	NOUN
ejpam-3545	356	13	)	)	PUNCT
ejpam-3545	357	1	=	=	SYM
ejpam-3545	357	2	g2(a	g2(a	NOUN
ejpam-3545	357	3	)	)	PUNCT
ejpam-3545	357	4	=	=	PRON
ejpam-3545	357	5	log	log	VERB
ejpam-3545	357	6	a	a	PRON
ejpam-3545	357	7	and	and	CCONJ
ejpam-3545	357	8	coprojector	coprojector	VERB
ejpam-3545	357	9	h(x	h(x	PROPN
ejpam-3545	357	10	)	)	PUNCT
ejpam-3545	358	1	=	=	PRON
ejpam-3545	358	2	expx	expx	ADJ
ejpam-3545	358	3	of	of	ADP
ejpam-3545	358	4	the	the	DET
ejpam-3545	358	5	arithmetic	arithmetic	ADJ
ejpam-3545	358	6	r	r	NOUN
ejpam-3545	358	7	of	of	ADP
ejpam-3545	358	8	real	real	ADJ
ejpam-3545	358	9	numbers	number	NOUN
ejpam-3545	358	10	into	into	ADP
ejpam-3545	358	11	itself	itself	PRON
ejpam-3545	358	12	.	.	PUNCT
ejpam-3545	359	1	namely	namely	ADV
ejpam-3545	359	2	,	,	PUNCT
ejpam-3545	359	3	we	we	PRON
ejpam-3545	359	4	have	have	VERB
ejpam-3545	359	5	a⊗	a⊗	NOUN
ejpam-3545	359	6	b	b	NOUN
ejpam-3545	359	7	=	=	SYM
ejpam-3545	359	8	2log2	2log2	NUM
ejpam-3545	359	9	a+log2	a+log2	NOUN
ejpam-3545	359	10	b	b	NOUN
ejpam-3545	359	11	=	=	SYM
ejpam-3545	359	12	2log−2a·b	2log−2a·b	PROPN
ejpam-3545	359	13	=	=	SYM
ejpam-3545	359	14	a	a	DET
ejpam-3545	359	15	·	·	SYM
ejpam-3545	359	16	b	b	NOUN
ejpam-3545	359	17	or	or	CCONJ
ejpam-3545	359	18	a⊗	a⊗	NOUN
ejpam-3545	359	19	b	b	PROPN
ejpam-3545	359	20	=	=	SYM
ejpam-3545	359	21	10log10	10log10	NUM
ejpam-3545	359	22	a+log10	a+log10	NOUN
ejpam-3545	359	23	b	b	PROPN
ejpam-3545	359	24	=	=	SYM
ejpam-3545	359	25	10log10	10log10	NUM
ejpam-3545	359	26	a·b	a·b	NOUN
ejpam-3545	359	27	=	=	PUNCT
ejpam-3545	359	28	a	a	DET
ejpam-3545	359	29	·	·	PUNCT
ejpam-3545	359	30	b	b	NOUN
ejpam-3545	359	31	renaming	renaming	NOUN
ejpam-3545	359	32	of	of	ADP
ejpam-3545	359	33	operations	operation	NOUN
ejpam-3545	359	34	in	in	ADP
ejpam-3545	359	35	abstract	abstract	ADJ
ejpam-3545	359	36	prearithmetics	prearithmetic	NOUN
ejpam-3545	359	37	allows	allow	VERB
ejpam-3545	359	38	obtaining	obtain	VERB
ejpam-3545	359	39	properties	property	NOUN
ejpam-3545	359	40	of	of	ADP
ejpam-3545	359	41	weak	weak	ADJ
ejpam-3545	359	42	projectivity	projectivity	NOUN
ejpam-3545	359	43	or	or	CCONJ
ejpam-3545	359	44	weak	weak	ADJ
ejpam-3545	359	45	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	359	46	between	between	ADP
ejpam-3545	359	47	multiplication	multiplication	NOUN
ejpam-3545	359	48	and	and	CCONJ
ejpam-3545	359	49	addition	addition	NOUN
ejpam-3545	359	50	from	from	ADP
ejpam-3545	359	51	the	the	DET
ejpam-3545	359	52	properties	property	NOUN
ejpam-3545	359	53	of	of	ADP
ejpam-3545	359	54	weak	weak	ADJ
ejpam-3545	359	55	projectivity	projectivity	NOUN
ejpam-3545	359	56	or	or	CCONJ
ejpam-3545	359	57	weak	weak	ADJ
ejpam-3545	359	58	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	359	59	between	between	ADP
ejpam-3545	359	60	addition	addition	NOUN
ejpam-3545	359	61	and	and	CCONJ
ejpam-3545	359	62	addition	addition	NOUN
ejpam-3545	359	63	.	.	PUNCT
ejpam-3545	360	1	while	while	SCONJ
ejpam-3545	360	2	weak	weak	ADJ
ejpam-3545	360	3	projectivity	projectivity	NOUN
ejpam-3545	360	4	connects	connect	VERB
ejpam-3545	360	5	two	two	NUM
ejpam-3545	360	6	operations	operation	NOUN
ejpam-3545	360	7	,	,	PUNCT
ejpam-3545	360	8	biprojectivity	biprojectivity	NOUN
ejpam-3545	360	9	connects	connect	VERB
ejpam-3545	360	10	all	all	DET
ejpam-3545	360	11	operations	operation	NOUN
ejpam-3545	360	12	from	from	ADP
ejpam-3545	360	13	two	two	NUM
ejpam-3545	360	14	abstract	abstract	ADJ
ejpam-3545	360	15	prearithmetics	prearithmetic	NOUN
ejpam-3545	360	16	.	.	PUNCT
ejpam-3545	361	1	m.	m.	NOUN
ejpam-3545	361	2	burgin	burgin	PROPN
ejpam-3545	361	3	/	/	SYM
ejpam-3545	361	4	eur	eur	PROPN
ejpam-3545	361	5	.	.	PUNCT
ejpam-3545	362	1	j.	j.	PROPN
ejpam-3545	362	2	pure	pure	PROPN
ejpam-3545	362	3	appl	appl	PROPN
ejpam-3545	362	4	.	.	PROPN
ejpam-3545	362	5	math	math	PROPN
ejpam-3545	362	6	,	,	PUNCT
ejpam-3545	362	7	12	12	NUM
ejpam-3545	362	8	(	(	PUNCT
ejpam-3545	362	9	4	4	NUM
ejpam-3545	362	10	)	)	PUNCT
ejpam-3545	362	11	(	(	PUNCT
ejpam-3545	362	12	2019	2019	NUM
ejpam-3545	362	13	)	)	PUNCT
ejpam-3545	362	14	,	,	PUNCT
ejpam-3545	362	15	1787	1787	NUM
ejpam-3545	362	16	-	-	SYM
ejpam-3545	362	17	1810	1810	NUM
ejpam-3545	362	18	1802	1802	NUM
ejpam-3545	362	19	let	let	VERB
ejpam-3545	362	20	us	we	PRON
ejpam-3545	362	21	take	take	VERB
ejpam-3545	362	22	two	two	NUM
ejpam-3545	362	23	abstract	abstract	ADJ
ejpam-3545	362	24	prearithmetics	prearithmetic	NOUN
ejpam-3545	362	25	a1	a1	NOUN
ejpam-3545	362	26	=	=	SYM
ejpam-3545	362	27	(	(	PUNCT
ejpam-3545	362	28	a1	a1	PROPN
ejpam-3545	362	29	;	;	PUNCT
ejpam-3545	362	30	+1	+1	PROPN
ejpam-3545	362	31	,	,	PUNCT
ejpam-3545	362	32	◦	◦	NOUN
ejpam-3545	362	33	1,≤1	1,≤1	ADJ
ejpam-3545	362	34	)	)	PUNCT
ejpam-3545	362	35	and	and	CCONJ
ejpam-3545	362	36	a2	a2	PROPN
ejpam-3545	362	37	=	=	SYM
ejpam-3545	362	38	(	(	PUNCT
ejpam-3545	362	39	a2	a2	PROPN
ejpam-3545	362	40	;	;	PUNCT
ejpam-3545	362	41	+2	+2	PROPN
ejpam-3545	362	42	,	,	PUNCT
ejpam-3545	362	43	◦	◦	NOUN
ejpam-3545	362	44	2,≤2	2,≤2	NUM
ejpam-3545	362	45	)	)	PUNCT
ejpam-3545	362	46	and	and	CCONJ
ejpam-3545	362	47	consider	consider	VERB
ejpam-3545	362	48	six	six	NUM
ejpam-3545	362	49	mappings	mapping	NOUN
ejpam-3545	362	50	g1	g1	NOUN
ejpam-3545	362	51	:	:	PUNCT
ejpam-3545	362	52	a1	a1	NOUN
ejpam-3545	362	53	→	→	SYM
ejpam-3545	362	54	a2	a2	PROPN
ejpam-3545	362	55	,	,	PUNCT
ejpam-3545	362	56	g2	g2	PROPN
ejpam-3545	362	57	:	:	PUNCT
ejpam-3545	362	58	a1	a1	PROPN
ejpam-3545	362	59	→	→	SYM
ejpam-3545	362	60	a2	a2	PROPN
ejpam-3545	362	61	,	,	PUNCT
ejpam-3545	362	62	g3	g3	PROPN
ejpam-3545	362	63	:	:	PUNCT
ejpam-3545	362	64	a1	a1	PROPN
ejpam-3545	362	65	→	→	SYM
ejpam-3545	362	66	a2	a2	PROPN
ejpam-3545	362	67	,	,	PUNCT
ejpam-3545	362	68	g4	g4	NOUN
ejpam-3545	362	69	:	:	PUNCT
ejpam-3545	362	70	a1	a1	NOUN
ejpam-3545	362	71	→	→	SYM
ejpam-3545	362	72	a2	a2	PROPN
ejpam-3545	362	73	,	,	PUNCT
ejpam-3545	362	74	h1	h1	NOUN
ejpam-3545	362	75	:	:	PUNCT
ejpam-3545	362	76	a2	a2	PROPN
ejpam-3545	362	77	→	→	SYM
ejpam-3545	362	78	a1	a1	NOUN
ejpam-3545	362	79	and	and	CCONJ
ejpam-3545	362	80	h2	h2	NOUN
ejpam-3545	362	81	:	:	PUNCT
ejpam-3545	362	82	a2	a2	PROPN
ejpam-3545	362	83	→	→	SYM
ejpam-3545	362	84	a1	a1	PROPN
ejpam-3545	362	85	.	.	PUNCT
ejpam-3545	363	1	definition	definition	NOUN
ejpam-3545	363	2	9	9	NUM
ejpam-3545	363	3	.	.	PUNCT
ejpam-3545	364	1	an	an	DET
ejpam-3545	364	2	abstract	abstract	ADJ
ejpam-3545	364	3	prearithmetic	prearithmetic	ADJ
ejpam-3545	364	4	a1	a1	NOUN
ejpam-3545	364	5	=	=	SYM
ejpam-3545	364	6	(	(	PUNCT
ejpam-3545	364	7	a1	a1	PROPN
ejpam-3545	364	8	;	;	PUNCT
ejpam-3545	364	9	+1	+1	PROPN
ejpam-3545	364	10	,	,	PUNCT
ejpam-3545	364	11	◦	◦	NOUN
ejpam-3545	364	12	1,≤1	1,≤1	ADJ
ejpam-3545	364	13	)	)	PUNCT
ejpam-3545	364	14	is	be	AUX
ejpam-3545	364	15	called	call	VERB
ejpam-3545	364	16	weakly	weakly	ADJ
ejpam-3545	364	17	biprojective	biprojective	NOUN
ejpam-3545	364	18	with	with	ADP
ejpam-3545	364	19	respect	respect	NOUN
ejpam-3545	364	20	to	to	ADP
ejpam-3545	364	21	an	an	DET
ejpam-3545	364	22	abstract	abstract	ADJ
ejpam-3545	364	23	prearithmetic	prearithmetic	ADJ
ejpam-3545	364	24	a2	a2	PROPN
ejpam-3545	364	25	=	=	SYM
ejpam-3545	364	26	(	(	PUNCT
ejpam-3545	364	27	a2	a2	PROPN
ejpam-3545	364	28	;	;	PUNCT
ejpam-3545	364	29	+2	+2	PROPN
ejpam-3545	364	30	,	,	PUNCT
ejpam-3545	364	31	◦	◦	NOUN
ejpam-3545	364	32	2,≤2	2,≤2	NOUN
ejpam-3545	364	33	)	)	PUNCT
ejpam-3545	364	34	if	if	SCONJ
ejpam-3545	364	35	addition	addition	NOUN
ejpam-3545	364	36	+1	+1	PROPN
ejpam-3545	364	37	in	in	ADP
ejpam-3545	364	38	a1	a1	NOUN
ejpam-3545	364	39	is	be	AUX
ejpam-3545	364	40	weakly	weakly	ADV
ejpam-3545	364	41	projective	projective	ADJ
ejpam-3545	364	42	with	with	ADP
ejpam-3545	364	43	respect	respect	NOUN
ejpam-3545	364	44	to	to	ADP
ejpam-3545	364	45	addition	addition	NOUN
ejpam-3545	364	46	+2	+2	PRON
ejpam-3545	364	47	in	in	ADP
ejpam-3545	364	48	a2	a2	PROPN
ejpam-3545	364	49	with	with	ADP
ejpam-3545	364	50	the	the	DET
ejpam-3545	364	51	projectors	projector	NOUN
ejpam-3545	364	52	g1	g1	NOUN
ejpam-3545	364	53	and	and	CCONJ
ejpam-3545	364	54	g2	g2	PROPN
ejpam-3545	364	55	and	and	CCONJ
ejpam-3545	364	56	the	the	DET
ejpam-3545	364	57	coprojector	coprojector	NOUN
ejpam-3545	364	58	h1	h1	PROPN
ejpam-3545	364	59	while	while	SCONJ
ejpam-3545	364	60	multiplication	multiplication	NOUN
ejpam-3545	364	61	◦	◦	NOUN
ejpam-3545	364	62	1	1	NUM
ejpam-3545	364	63	in	in	ADP
ejpam-3545	364	64	a1	a1	NOUN
ejpam-3545	364	65	is	be	AUX
ejpam-3545	364	66	weakly	weakly	ADV
ejpam-3545	364	67	projective	projective	ADJ
ejpam-3545	364	68	with	with	ADP
ejpam-3545	364	69	respect	respect	NOUN
ejpam-3545	364	70	to	to	ADP
ejpam-3545	364	71	multiplication	multiplication	NOUN
ejpam-3545	364	72	◦	◦	NOUN
ejpam-3545	364	73	2	2	NUM
ejpam-3545	364	74	in	in	ADP
ejpam-3545	364	75	a2	a2	PROPN
ejpam-3545	364	76	with	with	ADP
ejpam-3545	364	77	the	the	DET
ejpam-3545	364	78	projectors	projector	NOUN
ejpam-3545	364	79	g3	g3	NOUN
ejpam-3545	364	80	and	and	CCONJ
ejpam-3545	364	81	g4	g4	NOUN
ejpam-3545	364	82	and	and	CCONJ
ejpam-3545	364	83	the	the	DET
ejpam-3545	364	84	coprojector	coprojector	NOUN
ejpam-3545	364	85	h2	h2	NOUN
ejpam-3545	364	86	.	.	PUNCT
ejpam-3545	365	1	we	we	PRON
ejpam-3545	365	2	also	also	ADV
ejpam-3545	365	3	say	say	VERB
ejpam-3545	365	4	that	that	SCONJ
ejpam-3545	365	5	there	there	PRON
ejpam-3545	365	6	is	be	VERB
ejpam-3545	365	7	a	a	DET
ejpam-3545	365	8	weak	weak	ADJ
ejpam-3545	365	9	biprojectivity	biprojectivity	NOUN
ejpam-3545	365	10	between	between	ADP
ejpam-3545	365	11	the	the	DET
ejpam-3545	365	12	prearithmetic	prearithmetic	ADJ
ejpam-3545	365	13	a1	a1	NOUN
ejpam-3545	365	14	and	and	CCONJ
ejpam-3545	365	15	the	the	DET
ejpam-3545	365	16	prearithmetic	prearithmetic	PROPN
ejpam-3545	365	17	a2	a2	PROPN
ejpam-3545	365	18	.	.	PUNCT
ejpam-3545	366	1	example	example	NOUN
ejpam-3545	366	2	19	19	NUM
ejpam-3545	366	3	.	.	PUNCT
ejpam-3545	366	4	weak	weak	ADJ
ejpam-3545	366	5	projectivity	projectivity	NOUN
ejpam-3545	366	6	of	of	ADP
ejpam-3545	366	7	abstract	abstract	ADJ
ejpam-3545	366	8	prearithmetics	prearithmetic	NOUN
ejpam-3545	366	9	studied	study	VERB
ejpam-3545	366	10	in	in	ADP
ejpam-3545	366	11	[	[	X
ejpam-3545	366	12	5	5	NUM
ejpam-3545	366	13	,	,	PUNCT
ejpam-3545	366	14	7	7	NUM
ejpam-3545	366	15	,	,	PUNCT
ejpam-3545	366	16	11	11	NUM
ejpam-3545	366	17	]	]	PUNCT
ejpam-3545	366	18	is	be	AUX
ejpam-3545	366	19	a	a	DET
ejpam-3545	366	20	special	special	ADJ
ejpam-3545	366	21	case	case	NOUN
ejpam-3545	366	22	of	of	ADP
ejpam-3545	366	23	weak	weak	ADJ
ejpam-3545	366	24	biprojectivity	biprojectivity	NOUN
ejpam-3545	366	25	when	when	SCONJ
ejpam-3545	366	26	all	all	DET
ejpam-3545	366	27	projectors	projector	NOUN
ejpam-3545	366	28	coincide	coincide	VERB
ejpam-3545	366	29	,	,	PUNCT
ejpam-3545	366	30	i.e.	i.e.	X
ejpam-3545	366	31	,	,	PUNCT
ejpam-3545	366	32	g1	g1	NOUN
ejpam-3545	366	33	=	=	SYM
ejpam-3545	366	34	g2	g2	PROPN
ejpam-3545	366	35	=	=	SYM
ejpam-3545	366	36	g3	g3	PROPN
ejpam-3545	366	37	=	=	NOUN
ejpam-3545	366	38	g4	g4	NOUN
ejpam-3545	366	39	,	,	PUNCT
ejpam-3545	366	40	and	and	CCONJ
ejpam-3545	366	41	both	both	DET
ejpam-3545	366	42	coprojectors	coprojector	NOUN
ejpam-3545	366	43	coincide	coincide	VERB
ejpam-3545	366	44	,	,	PUNCT
ejpam-3545	366	45	i.e.	i.e.	X
ejpam-3545	366	46	,	,	PUNCT
ejpam-3545	366	47	h1	h1	PROPN
ejpam-3545	366	48	=	=	PUNCT
ejpam-3545	366	49	h2	h2	PROPN
ejpam-3545	366	50	.	.	PUNCT
ejpam-3545	366	51	example	example	NOUN
ejpam-3545	367	1	20	20	NUM
ejpam-3545	367	2	.	.	PUNCT
ejpam-3545	368	1	let	let	VERB
ejpam-3545	368	2	us	we	PRON
ejpam-3545	368	3	consider	consider	VERB
ejpam-3545	368	4	the	the	DET
ejpam-3545	368	5	conventional	conventional	ADJ
ejpam-3545	368	6	diophantine	diophantine	NOUN
ejpam-3545	368	7	arithmetic	arithmetic	ADJ
ejpam-3545	368	8	n	n	PROPN
ejpam-3545	368	9	of	of	ADP
ejpam-3545	368	10	all	all	DET
ejpam-3545	368	11	natural	natural	ADJ
ejpam-3545	368	12	numbers	number	NOUN
ejpam-3545	368	13	and	and	CCONJ
ejpam-3545	368	14	the	the	DET
ejpam-3545	368	15	abstract	abstract	ADJ
ejpam-3545	368	16	prearithmetic	prearithmetic	NOUN
ejpam-3545	368	17	a	a	PRON
ejpam-3545	368	18	=	=	X
ejpam-3545	368	19	(	(	PUNCT
ejpam-3545	368	20	n	n	NOUN
ejpam-3545	368	21	;	;	PUNCT
ejpam-3545	368	22	⊕,⊗,≤	⊕,⊗,≤	X
ejpam-3545	368	23	)	)	PUNCT
ejpam-3545	368	24	where	where	SCONJ
ejpam-3545	368	25	n	n	PRON
ejpam-3545	368	26	is	be	AUX
ejpam-3545	368	27	the	the	DET
ejpam-3545	368	28	set	set	NOUN
ejpam-3545	368	29	of	of	ADP
ejpam-3545	368	30	all	all	DET
ejpam-3545	368	31	natural	natural	ADJ
ejpam-3545	368	32	numbers	number	NOUN
ejpam-3545	368	33	and	and	CCONJ
ejpam-3545	368	34	≤	≤	NUM
ejpam-3545	368	35	is	be	AUX
ejpam-3545	368	36	the	the	DET
ejpam-3545	368	37	natural	natural	ADJ
ejpam-3545	368	38	order	order	NOUN
ejpam-3545	368	39	on	on	ADP
ejpam-3545	368	40	the	the	DET
ejpam-3545	368	41	set	set	NOUN
ejpam-3545	368	42	of	of	ADP
ejpam-3545	368	43	all	all	DET
ejpam-3545	368	44	natural	natural	ADJ
ejpam-3545	368	45	numbers	number	NOUN
ejpam-3545	368	46	.	.	PUNCT
ejpam-3545	369	1	to	to	PART
ejpam-3545	369	2	define	define	VERB
ejpam-3545	369	3	multiplication	multiplication	NOUN
ejpam-3545	369	4	⊗	⊗	NOUN
ejpam-3545	369	5	and	and	CCONJ
ejpam-3545	369	6	addition	addition	NOUN
ejpam-3545	369	7	⊕	⊕	PROPN
ejpam-3545	369	8	,	,	PUNCT
ejpam-3545	369	9	we	we	PRON
ejpam-3545	369	10	take	take	VERB
ejpam-3545	369	11	the	the	DET
ejpam-3545	369	12	following	follow	VERB
ejpam-3545	369	13	functions	function	NOUN
ejpam-3545	369	14	g1(n	g1(n	PRON
ejpam-3545	369	15	)	)	PUNCT
ejpam-3545	369	16	=	=	SYM
ejpam-3545	370	1	g2(n	g2(n	PROPN
ejpam-3545	370	2	)	)	PUNCT
ejpam-3545	370	3	=	=	SYM
ejpam-3545	370	4	n	n	PROPN
ejpam-3545	370	5	+	+	CCONJ
ejpam-3545	370	6	5	5	NUM
ejpam-3545	370	7	g3(n	g3(n	NOUN
ejpam-3545	370	8	)	)	PUNCT
ejpam-3545	370	9	=	=	SYM
ejpam-3545	370	10	g4(n	g4(n	PROPN
ejpam-3545	370	11	)	)	PUNCT
ejpam-3545	370	12	=	=	NOUN
ejpam-3545	370	13	3n	3n	NUM
ejpam-3545	370	14	h1(n	h1(n	PROPN
ejpam-3545	370	15	)	)	PUNCT
ejpam-3545	370	16	=	=	SYM
ejpam-3545	370	17	h2(n	h2(n	PROPN
ejpam-3545	370	18	)	)	PUNCT
ejpam-3545	370	19	=	=	SYM
ejpam-3545	370	20	1n	1n	NUM
ejpam-3545	370	21	then	then	ADV
ejpam-3545	370	22	for	for	ADP
ejpam-3545	370	23	arbitrary	arbitrary	ADJ
ejpam-3545	370	24	natural	natural	ADJ
ejpam-3545	370	25	numbers	number	NOUN
ejpam-3545	370	26	m	m	VERB
ejpam-3545	370	27	and	and	CCONJ
ejpam-3545	370	28	n	n	CCONJ
ejpam-3545	370	29	,	,	PUNCT
ejpam-3545	370	30	we	we	PRON
ejpam-3545	370	31	have	have	VERB
ejpam-3545	370	32	m⊕	m⊕	VERB
ejpam-3545	370	33	n	n	NOUN
ejpam-3545	370	34	=	=	PUNCT
ejpam-3545	370	35	(	(	PUNCT
ejpam-3545	370	36	m	m	VERB
ejpam-3545	370	37	+	+	ADJ
ejpam-3545	370	38	5	5	NUM
ejpam-3545	370	39	)	)	PUNCT
ejpam-3545	370	40	+	+	CCONJ
ejpam-3545	370	41	(	(	PUNCT
ejpam-3545	370	42	n	n	X
ejpam-3545	370	43	+	+	NUM
ejpam-3545	370	44	5	5	NUM
ejpam-3545	370	45	)	)	PUNCT
ejpam-3545	370	46	=	=	SYM
ejpam-3545	371	1	(	(	PUNCT
ejpam-3545	371	2	m	m	VERB
ejpam-3545	371	3	+	+	NOUN
ejpam-3545	371	4	n	n	CCONJ
ejpam-3545	371	5	)	)	PUNCT
ejpam-3545	371	6	+	+	CCONJ
ejpam-3545	371	7	10	10	NUM
ejpam-3545	371	8	m⊗	m⊗	NOUN
ejpam-3545	371	9	n	n	NOUN
ejpam-3545	371	10	=	=	SYM
ejpam-3545	371	11	(	(	PUNCT
ejpam-3545	371	12	3m)⊗	3m)⊗	PROPN
ejpam-3545	371	13	(	(	PUNCT
ejpam-3545	371	14	3n	3n	NUM
ejpam-3545	371	15	)	)	PUNCT
ejpam-3545	371	16	=	=	NOUN
ejpam-3545	372	1	9mn	9mn	NOUN
ejpam-3545	372	2	we	we	PRON
ejpam-3545	372	3	see	see	VERB
ejpam-3545	372	4	that	that	SCONJ
ejpam-3545	372	5	the	the	DET
ejpam-3545	372	6	abstract	abstract	ADJ
ejpam-3545	372	7	prearithmetic	prearithmetic	NOUN
ejpam-3545	372	8	a	a	PRON
ejpam-3545	372	9	is	be	AUX
ejpam-3545	372	10	weakly	weakly	ADJ
ejpam-3545	372	11	biprojective	biprojective	NOUN
ejpam-3545	372	12	with	with	ADP
ejpam-3545	372	13	respect	respect	NOUN
ejpam-3545	372	14	to	to	ADP
ejpam-3545	372	15	the	the	DET
ejpam-3545	372	16	arithmetic	arithmetic	ADJ
ejpam-3545	372	17	n	n	NOUN
ejpam-3545	372	18	although	although	SCONJ
ejpam-3545	372	19	projectors	projector	NOUN
ejpam-3545	372	20	for	for	ADP
ejpam-3545	372	21	addition	addition	NOUN
ejpam-3545	372	22	and	and	CCONJ
ejpam-3545	372	23	multiplication	multiplication	NOUN
ejpam-3545	372	24	are	be	AUX
ejpam-3545	372	25	different	different	ADJ
ejpam-3545	372	26	.	.	PUNCT
ejpam-3545	373	1	this	this	PRON
ejpam-3545	373	2	shows	show	VERB
ejpam-3545	373	3	that	that	SCONJ
ejpam-3545	373	4	in	in	ADP
ejpam-3545	373	5	a	a	DET
ejpam-3545	373	6	general	general	ADJ
ejpam-3545	373	7	case	case	NOUN
ejpam-3545	373	8	,	,	PUNCT
ejpam-3545	373	9	weak	weak	ADJ
ejpam-3545	373	10	biprojectivity	biprojectivity	NOUN
ejpam-3545	373	11	of	of	ADP
ejpam-3545	373	12	abstract	abstract	ADJ
ejpam-3545	373	13	prearithmetics	prearithmetic	NOUN
ejpam-3545	373	14	does	do	AUX
ejpam-3545	373	15	not	not	PART
ejpam-3545	373	16	coincide	coincide	VERB
ejpam-3545	373	17	with	with	ADP
ejpam-3545	373	18	weak	weak	ADJ
ejpam-3545	373	19	projectivity	projectivity	NOUN
ejpam-3545	373	20	of	of	ADP
ejpam-3545	373	21	abstract	abstract	ADJ
ejpam-3545	373	22	prearithmetics	prearithmetic	NOUN
ejpam-3545	373	23	studied	study	VERB
ejpam-3545	373	24	in	in	ADP
ejpam-3545	373	25	[	[	X
ejpam-3545	373	26	5	5	NUM
ejpam-3545	373	27	,	,	PUNCT
ejpam-3545	373	28	7	7	NUM
ejpam-3545	373	29	,	,	PUNCT
ejpam-3545	373	30	11	11	NUM
ejpam-3545	373	31	]	]	PUNCT
ejpam-3545	373	32	.	.	PUNCT
ejpam-3545	374	1	let	let	VERB
ejpam-3545	374	2	us	we	PRON
ejpam-3545	374	3	consider	consider	VERB
ejpam-3545	374	4	some	some	DET
ejpam-3545	374	5	properties	property	NOUN
ejpam-3545	374	6	of	of	ADP
ejpam-3545	374	7	weak	weak	ADJ
ejpam-3545	374	8	biprojectivity	biprojectivity	NOUN
ejpam-3545	374	9	taking	take	VERB
ejpam-3545	374	10	three	three	NUM
ejpam-3545	374	11	abstract	abstract	ADJ
ejpam-3545	374	12	prearithmetics	prearithmetic	NOUN
ejpam-3545	374	13	a1	a1	NOUN
ejpam-3545	374	14	=	=	SYM
ejpam-3545	374	15	(	(	PUNCT
ejpam-3545	374	16	a1	a1	PROPN
ejpam-3545	374	17	;	;	PUNCT
ejpam-3545	374	18	+1	+1	PROPN
ejpam-3545	374	19	,	,	PUNCT
ejpam-3545	374	20	◦	◦	NOUN
ejpam-3545	374	21	1,≤1	1,≤1	ADJ
ejpam-3545	374	22	)	)	PUNCT
ejpam-3545	374	23	,	,	PUNCT
ejpam-3545	374	24	a2	a2	PROPN
ejpam-3545	374	25	=	=	SYM
ejpam-3545	374	26	(	(	PUNCT
ejpam-3545	374	27	a2	a2	PROPN
ejpam-3545	374	28	;	;	PUNCT
ejpam-3545	374	29	+2	+2	PROPN
ejpam-3545	374	30	,	,	PUNCT
ejpam-3545	374	31	◦	◦	NOUN
ejpam-3545	374	32	2,≤2	2,≤2	NOUN
ejpam-3545	374	33	)	)	PUNCT
ejpam-3545	374	34	and	and	CCONJ
ejpam-3545	374	35	a3	a3	NOUN
ejpam-3545	374	36	=	=	SYM
ejpam-3545	374	37	(	(	PUNCT
ejpam-3545	374	38	a3	a3	NOUN
ejpam-3545	374	39	;	;	PUNCT
ejpam-3545	374	40	+3	+3	PROPN
ejpam-3545	374	41	,	,	PUNCT
ejpam-3545	374	42	◦	◦	NOUN
ejpam-3545	374	43	3,≤3	3,≤3	NOUN
ejpam-3545	374	44	)	)	PUNCT
ejpam-3545	374	45	.	.	PUNCT
ejpam-3545	375	1	proposition	proposition	NOUN
ejpam-3545	375	2	3.10	3.10	NUM
ejpam-3545	375	3	.	.	PUNCT
ejpam-3545	376	1	if	if	SCONJ
ejpam-3545	376	2	the	the	DET
ejpam-3545	376	3	abstract	abstract	ADJ
ejpam-3545	376	4	prearithmetic	prearithmetic	ADJ
ejpam-3545	376	5	a1	a1	NOUN
ejpam-3545	376	6	is	be	AUX
ejpam-3545	376	7	weakly	weakly	ADJ
ejpam-3545	376	8	biprojective	biprojective	NOUN
ejpam-3545	376	9	with	with	ADP
ejpam-3545	376	10	respect	respect	NOUN
ejpam-3545	376	11	to	to	ADP
ejpam-3545	376	12	the	the	DET
ejpam-3545	376	13	abstract	abstract	ADJ
ejpam-3545	376	14	prearithmetics	prearithmetic	NOUN
ejpam-3545	376	15	a2	a2	PROPN
ejpam-3545	376	16	and	and	CCONJ
ejpam-3545	376	17	the	the	DET
ejpam-3545	376	18	abstract	abstract	ADJ
ejpam-3545	376	19	prearithmetic	prearithmetic	PROPN
ejpam-3545	376	20	a2	a2	PROPN
ejpam-3545	376	21	is	be	AUX
ejpam-3545	376	22	weakly	weakly	ADJ
ejpam-3545	376	23	biprojective	biprojective	NOUN
ejpam-3545	376	24	with	with	ADP
ejpam-3545	376	25	respect	respect	NOUN
ejpam-3545	376	26	to	to	ADP
ejpam-3545	376	27	the	the	DET
ejpam-3545	376	28	abstract	abstract	ADJ
ejpam-3545	376	29	prearithmetic	prearithmetic	ADJ
ejpam-3545	376	30	a3	a3	NOUN
ejpam-3545	376	31	,	,	PUNCT
ejpam-3545	376	32	then	then	ADV
ejpam-3545	376	33	the	the	DET
ejpam-3545	376	34	abstract	abstract	ADJ
ejpam-3545	376	35	prearithmetic	prearithmetic	ADJ
ejpam-3545	376	36	a1	a1	NOUN
ejpam-3545	376	37	is	be	AUX
ejpam-3545	376	38	weakly	weakly	ADJ
ejpam-3545	376	39	biprojective	biprojective	NOUN
ejpam-3545	376	40	with	with	ADP
ejpam-3545	376	41	respect	respect	NOUN
ejpam-3545	376	42	to	to	ADP
ejpam-3545	376	43	the	the	DET
ejpam-3545	376	44	abstract	abstract	ADJ
ejpam-3545	376	45	prearithmetic	prearithmetic	ADJ
ejpam-3545	376	46	a3	a3	NOUN
ejpam-3545	376	47	.	.	PUNCT
ejpam-3545	377	1	m.	m.	NOUN
ejpam-3545	377	2	burgin	burgin	PROPN
ejpam-3545	377	3	/	/	SYM
ejpam-3545	377	4	eur	eur	PROPN
ejpam-3545	377	5	.	.	PUNCT
ejpam-3545	378	1	j.	j.	PROPN
ejpam-3545	378	2	pure	pure	PROPN
ejpam-3545	378	3	appl	appl	PROPN
ejpam-3545	378	4	.	.	PROPN
ejpam-3545	378	5	math	math	PROPN
ejpam-3545	378	6	,	,	PUNCT
ejpam-3545	378	7	12	12	NUM
ejpam-3545	378	8	(	(	PUNCT
ejpam-3545	378	9	4	4	NUM
ejpam-3545	378	10	)	)	PUNCT
ejpam-3545	378	11	(	(	PUNCT
ejpam-3545	378	12	2019	2019	NUM
ejpam-3545	378	13	)	)	PUNCT
ejpam-3545	378	14	,	,	PUNCT
ejpam-3545	378	15	1787	1787	NUM
ejpam-3545	378	16	-	-	SYM
ejpam-3545	378	17	1810	1810	NUM
ejpam-3545	378	18	1803	1803	NUM
ejpam-3545	378	19	proof	proof	NOUN
ejpam-3545	378	20	is	be	AUX
ejpam-3545	378	21	similar	similar	ADJ
ejpam-3545	378	22	to	to	ADP
ejpam-3545	378	23	the	the	DET
ejpam-3545	378	24	proof	proof	NOUN
ejpam-3545	378	25	of	of	ADP
ejpam-3545	378	26	proposition	proposition	NOUN
ejpam-3545	378	27	3.2	3.2	NUM
ejpam-3545	378	28	.	.	PUNCT
ejpam-3545	379	1	as	as	SCONJ
ejpam-3545	379	2	weak	weak	ADJ
ejpam-3545	379	3	projectivity	projectivity	NOUN
ejpam-3545	379	4	studied	study	VERB
ejpam-3545	379	5	in	in	ADP
ejpam-3545	379	6	[	[	X
ejpam-3545	379	7	5	5	NUM
ejpam-3545	379	8	,	,	PUNCT
ejpam-3545	379	9	7	7	NUM
ejpam-3545	379	10	,	,	PUNCT
ejpam-3545	379	11	11	11	NUM
ejpam-3545	379	12	]	]	PUNCT
ejpam-3545	379	13	is	be	AUX
ejpam-3545	379	14	a	a	DET
ejpam-3545	379	15	particular	particular	ADJ
ejpam-3545	379	16	case	case	NOUN
ejpam-3545	379	17	of	of	ADP
ejpam-3545	379	18	weak	weak	ADJ
ejpam-3545	379	19	biprojectivity	biprojectivity	NOUN
ejpam-3545	379	20	,	,	PUNCT
ejpam-3545	379	21	we	we	PRON
ejpam-3545	379	22	have	have	VERB
ejpam-3545	379	23	the	the	DET
ejpam-3545	379	24	following	follow	VERB
ejpam-3545	379	25	result	result	NOUN
ejpam-3545	379	26	.	.	PUNCT
ejpam-3545	380	1	corollary	corollary	ADJ
ejpam-3545	380	2	1	1	NUM
ejpam-3545	380	3	.	.	PUNCT
ejpam-3545	381	1	if	if	SCONJ
ejpam-3545	381	2	the	the	DET
ejpam-3545	381	3	abstract	abstract	ADJ
ejpam-3545	381	4	prearithmetic	prearithmetic	ADJ
ejpam-3545	381	5	a1	a1	NOUN
ejpam-3545	381	6	is	be	AUX
ejpam-3545	381	7	weakly	weakly	ADV
ejpam-3545	381	8	projective	projective	ADJ
ejpam-3545	381	9	with	with	ADP
ejpam-3545	381	10	respect	respect	NOUN
ejpam-3545	381	11	to	to	ADP
ejpam-3545	381	12	the	the	DET
ejpam-3545	381	13	abstract	abstract	ADJ
ejpam-3545	381	14	prearithmetic	prearithmetic	PROPN
ejpam-3545	381	15	a2	a2	PROPN
ejpam-3545	381	16	and	and	CCONJ
ejpam-3545	381	17	the	the	DET
ejpam-3545	381	18	abstract	abstract	ADJ
ejpam-3545	381	19	prearithmetic	prearithmetic	PROPN
ejpam-3545	381	20	a2	a2	PROPN
ejpam-3545	381	21	is	be	AUX
ejpam-3545	381	22	weakly	weakly	ADV
ejpam-3545	381	23	projective	projective	ADJ
ejpam-3545	381	24	with	with	ADP
ejpam-3545	381	25	respect	respect	NOUN
ejpam-3545	381	26	to	to	ADP
ejpam-3545	381	27	the	the	DET
ejpam-3545	381	28	abstract	abstract	ADJ
ejpam-3545	381	29	prearithmetic	prearithmetic	ADJ
ejpam-3545	381	30	a3	a3	NOUN
ejpam-3545	381	31	,	,	PUNCT
ejpam-3545	381	32	then	then	ADV
ejpam-3545	381	33	the	the	DET
ejpam-3545	381	34	abstract	abstract	ADJ
ejpam-3545	381	35	prearithmetic	prearithmetic	ADJ
ejpam-3545	381	36	a1	a1	NOUN
ejpam-3545	381	37	is	be	AUX
ejpam-3545	381	38	weakly	weakly	ADV
ejpam-3545	381	39	projective	projective	ADJ
ejpam-3545	381	40	with	with	ADP
ejpam-3545	381	41	respect	respect	NOUN
ejpam-3545	381	42	to	to	ADP
ejpam-3545	381	43	the	the	DET
ejpam-3545	381	44	abstract	abstract	ADJ
ejpam-3545	381	45	prearithmetic	prearithmetic	ADJ
ejpam-3545	381	46	a3	a3	NOUN
ejpam-3545	381	47	.	.	PUNCT
ejpam-3545	382	1	proposition	proposition	NOUN
ejpam-3545	382	2	3.10	3.10	NUM
ejpam-3545	382	3	allows	allow	VERB
ejpam-3545	382	4	proving	prove	VERB
ejpam-3545	382	5	the	the	DET
ejpam-3545	382	6	following	follow	VERB
ejpam-3545	382	7	result	result	NOUN
ejpam-3545	382	8	.	.	PUNCT
ejpam-3545	383	1	theorem	theorem	ADJ
ejpam-3545	383	2	4	4	NUM
ejpam-3545	383	3	.	.	PUNCT
ejpam-3545	383	4	abstract	abstract	ADJ
ejpam-3545	383	5	prearithmetics	prearithmetic	NOUN
ejpam-3545	383	6	with	with	ADP
ejpam-3545	383	7	weak	weak	ADJ
ejpam-3545	383	8	biprojectivity	biprojectivity	NOUN
ejpam-3545	383	9	relations	relation	NOUN
ejpam-3545	383	10	form	form	VERB
ejpam-3545	383	11	the	the	DET
ejpam-3545	383	12	category	category	NOUN
ejpam-3545	383	13	awbp	awbp	NOUN
ejpam-3545	383	14	where	where	SCONJ
ejpam-3545	383	15	objects	object	NOUN
ejpam-3545	383	16	are	be	AUX
ejpam-3545	383	17	abstract	abstract	ADJ
ejpam-3545	383	18	prearithmetics	prearithmetic	NOUN
ejpam-3545	383	19	and	and	CCONJ
ejpam-3545	383	20	morphisms	morphism	NOUN
ejpam-3545	383	21	are	be	AUX
ejpam-3545	383	22	weak	weak	ADJ
ejpam-3545	383	23	biprojectivity	biprojectivity	NOUN
ejpam-3545	383	24	relations	relation	NOUN
ejpam-3545	383	25	between	between	ADP
ejpam-3545	383	26	abstract	abstract	ADJ
ejpam-3545	383	27	prearithmetics	prearithmetic	NOUN
ejpam-3545	383	28	.	.	PUNCT
ejpam-3545	384	1	proof	proof	NOUN
ejpam-3545	384	2	is	be	AUX
ejpam-3545	384	3	similar	similar	ADJ
ejpam-3545	384	4	to	to	ADP
ejpam-3545	384	5	the	the	DET
ejpam-3545	384	6	proof	proof	NOUN
ejpam-3545	384	7	of	of	ADP
ejpam-3545	384	8	theorem	theorem	ADJ
ejpam-3545	384	9	1	1	NUM
ejpam-3545	384	10	.	.	PUNCT
ejpam-3545	384	11	corollary	corollary	ADJ
ejpam-3545	384	12	2	2	NUM
ejpam-3545	384	13	.	.	PUNCT
ejpam-3545	384	14	abstract	abstract	ADJ
ejpam-3545	384	15	prearithmetics	prearithmetic	NOUN
ejpam-3545	384	16	with	with	ADP
ejpam-3545	384	17	weak	weak	ADJ
ejpam-3545	384	18	projectivity	projectivity	NOUN
ejpam-3545	384	19	relations	relation	NOUN
ejpam-3545	384	20	form	form	VERB
ejpam-3545	384	21	the	the	DET
ejpam-3545	384	22	category	category	NOUN
ejpam-3545	384	23	awp	awp	NOUN
ejpam-3545	384	24	where	where	SCONJ
ejpam-3545	384	25	objects	object	NOUN
ejpam-3545	384	26	are	be	AUX
ejpam-3545	384	27	abstract	abstract	ADJ
ejpam-3545	384	28	prearithmetics	prearithmetic	NOUN
ejpam-3545	384	29	and	and	CCONJ
ejpam-3545	384	30	morphisms	morphism	NOUN
ejpam-3545	384	31	are	be	AUX
ejpam-3545	384	32	weak	weak	ADJ
ejpam-3545	384	33	biprojectivity	biprojectivity	NOUN
ejpam-3545	384	34	relations	relation	NOUN
ejpam-3545	384	35	between	between	ADP
ejpam-3545	384	36	abstract	abstract	ADJ
ejpam-3545	384	37	prearithmetics	prearithmetic	NOUN
ejpam-3545	384	38	.	.	PUNCT
ejpam-3545	385	1	corollary	corollary	ADJ
ejpam-3545	385	2	3	3	NUM
ejpam-3545	385	3	.	.	PUNCT
ejpam-3545	386	1	the	the	DET
ejpam-3545	386	2	category	category	NOUN
ejpam-3545	386	3	awp	awp	NOUN
ejpam-3545	386	4	is	be	AUX
ejpam-3545	386	5	a	a	DET
ejpam-3545	386	6	wide	wide	ADJ
ejpam-3545	386	7	subcategory	subcategory	NOUN
ejpam-3545	386	8	of	of	ADP
ejpam-3545	386	9	the	the	DET
ejpam-3545	386	10	category	category	NOUN
ejpam-3545	386	11	awbp	awbp	NOUN
ejpam-3545	386	12	.	.	PUNCT
ejpam-3545	387	1	corollary	corollary	ADJ
ejpam-3545	387	2	4	4	NUM
ejpam-3545	387	3	.	.	PUNCT
ejpam-3545	388	1	the	the	DET
ejpam-3545	388	2	categories	category	NOUN
ejpam-3545	388	3	aawp	aawp	ADV
ejpam-3545	388	4	and	and	CCONJ
ejpam-3545	388	5	amwp	amwp	VERB
ejpam-3545	388	6	are	be	AUX
ejpam-3545	388	7	wide	wide	ADJ
ejpam-3545	388	8	subcategories	subcategorie	NOUN
ejpam-3545	388	9	of	of	ADP
ejpam-3545	388	10	the	the	DET
ejpam-3545	388	11	category	category	NOUN
ejpam-3545	388	12	awbp	awbp	NOUN
ejpam-3545	388	13	.	.	PUNCT
ejpam-3545	389	1	biprojectivity	biprojectivity	NOUN
ejpam-3545	389	2	allows	allow	VERB
ejpam-3545	389	3	turning	turn	VERB
ejpam-3545	389	4	an	an	DET
ejpam-3545	389	5	arbitrary	arbitrary	ADJ
ejpam-3545	389	6	set	set	NOUN
ejpam-3545	389	7	into	into	ADP
ejpam-3545	389	8	an	an	DET
ejpam-3545	389	9	abstract	abstract	ADJ
ejpam-3545	389	10	prearithmetic	prearithmetic	NOUN
ejpam-3545	389	11	.	.	PUNCT
ejpam-3545	390	1	let	let	VERB
ejpam-3545	390	2	us	we	PRON
ejpam-3545	390	3	consider	consider	VERB
ejpam-3545	390	4	a	a	DET
ejpam-3545	390	5	set	set	NOUN
ejpam-3545	390	6	a	a	PRON
ejpam-3545	390	7	and	and	CCONJ
ejpam-3545	390	8	an	an	DET
ejpam-3545	390	9	abstract	abstract	ADJ
ejpam-3545	390	10	prearithmetic	prearithmetic	ADJ
ejpam-3545	390	11	a2	a2	PROPN
ejpam-3545	390	12	=	=	SYM
ejpam-3545	390	13	(	(	PUNCT
ejpam-3545	390	14	a2	a2	PROPN
ejpam-3545	390	15	;	;	PUNCT
ejpam-3545	390	16	+2	+2	PROPN
ejpam-3545	390	17	,	,	PUNCT
ejpam-3545	390	18	◦	◦	NOUN
ejpam-3545	390	19	2,≤2	2,≤2	NUM
ejpam-3545	390	20	)	)	PUNCT
ejpam-3545	390	21	.	.	PUNCT
ejpam-3545	391	1	proposition	proposition	NOUN
ejpam-3545	391	2	3.11	3.11	NUM
ejpam-3545	391	3	.	.	PUNCT
ejpam-3545	392	1	for	for	ADP
ejpam-3545	392	2	any	any	DET
ejpam-3545	392	3	six	six	NUM
ejpam-3545	392	4	mappings	mapping	NOUN
ejpam-3545	392	5	g1	g1	NOUN
ejpam-3545	392	6	:	:	PUNCT
ejpam-3545	392	7	a→	a→	PROPN
ejpam-3545	392	8	a2	a2	PROPN
ejpam-3545	392	9	,	,	PUNCT
ejpam-3545	392	10	g2	g2	PROPN
ejpam-3545	392	11	:	:	PUNCT
ejpam-3545	392	12	a→	a→	PROPN
ejpam-3545	392	13	a2	a2	PROPN
ejpam-3545	392	14	,	,	PUNCT
ejpam-3545	392	15	g3	g3	PROPN
ejpam-3545	392	16	:	:	PUNCT
ejpam-3545	392	17	a→	a→	PROPN
ejpam-3545	392	18	a2	a2	PROPN
ejpam-3545	392	19	,	,	PUNCT
ejpam-3545	392	20	g4	g4	NOUN
ejpam-3545	392	21	:	:	PUNCT
ejpam-3545	392	22	a→	a→	NOUN
ejpam-3545	392	23	a2	a2	PROPN
ejpam-3545	392	24	,	,	PUNCT
ejpam-3545	392	25	h1	h1	NOUN
ejpam-3545	392	26	:	:	PUNCT
ejpam-3545	392	27	a2	a2	PROPN
ejpam-3545	392	28	→	→	SYM
ejpam-3545	392	29	a	a	PRON
ejpam-3545	392	30	,	,	PUNCT
ejpam-3545	392	31	and	and	CCONJ
ejpam-3545	392	32	h2	h2	NOUN
ejpam-3545	392	33	:	:	PUNCT
ejpam-3545	392	34	a2	a2	PROPN
ejpam-3545	392	35	→	→	SYM
ejpam-3545	392	36	a	a	X
ejpam-3545	392	37	,	,	PUNCT
ejpam-3545	392	38	it	it	PRON
ejpam-3545	392	39	is	be	AUX
ejpam-3545	392	40	possible	possible	ADJ
ejpam-3545	392	41	to	to	PART
ejpam-3545	392	42	define	define	VERB
ejpam-3545	392	43	an	an	DET
ejpam-3545	392	44	abstract	abstract	ADJ
ejpam-3545	392	45	prearithmetic	prearithmetic	NOUN
ejpam-3545	392	46	a	a	DET
ejpam-3545	392	47	=	=	X
ejpam-3545	392	48	(	(	PUNCT
ejpam-3545	392	49	a	a	X
ejpam-3545	392	50	;	;	PUNCT
ejpam-3545	392	51	+	+	ADJ
ejpam-3545	392	52	,	,	PUNCT
ejpam-3545	392	53	◦	◦	NOUN
ejpam-3545	392	54	,	,	PUNCT
ejpam-3545	392	55	≤	≤	NUM
ejpam-3545	392	56	)	)	PUNCT
ejpam-3545	392	57	,	,	PUNCT
ejpam-3545	392	58	in	in	ADP
ejpam-3545	392	59	which	which	PRON
ejpam-3545	392	60	is	be	AUX
ejpam-3545	392	61	weakly	weakly	ADJ
ejpam-3545	392	62	biprojective	biprojective	NOUN
ejpam-3545	392	63	with	with	ADP
ejpam-3545	392	64	respect	respect	NOUN
ejpam-3545	392	65	to	to	ADP
ejpam-3545	392	66	the	the	DET
ejpam-3545	392	67	abstract	abstract	ADJ
ejpam-3545	392	68	prearithmetic	prearithmetic	PROPN
ejpam-3545	392	69	a2	a2	PROPN
ejpam-3545	392	70	with	with	ADP
ejpam-3545	392	71	the	the	DET
ejpam-3545	392	72	projectors	projector	NOUN
ejpam-3545	392	73	g1	g1	NOUN
ejpam-3545	392	74	and	and	CCONJ
ejpam-3545	392	75	g2	g2	PROPN
ejpam-3545	392	76	and	and	CCONJ
ejpam-3545	392	77	the	the	DET
ejpam-3545	392	78	coprojector	coprojector	NOUN
ejpam-3545	392	79	h1	h1	NOUN
ejpam-3545	392	80	for	for	ADP
ejpam-3545	392	81	addition	addition	NOUN
ejpam-3545	392	82	and	and	CCONJ
ejpam-3545	392	83	the	the	DET
ejpam-3545	392	84	projectors	projector	NOUN
ejpam-3545	392	85	g3	g3	NOUN
ejpam-3545	392	86	and	and	CCONJ
ejpam-3545	392	87	g4	g4	NOUN
ejpam-3545	392	88	and	and	CCONJ
ejpam-3545	392	89	the	the	DET
ejpam-3545	392	90	coprojector	coprojector	NOUN
ejpam-3545	392	91	h2	h2	NOUN
ejpam-3545	392	92	for	for	ADP
ejpam-3545	392	93	multiplication	multiplication	NOUN
ejpam-3545	392	94	.	.	PUNCT
ejpam-3545	393	1	indeed	indeed	ADV
ejpam-3545	393	2	,	,	PUNCT
ejpam-3545	393	3	it	it	PRON
ejpam-3545	393	4	is	be	AUX
ejpam-3545	393	5	possible	possible	ADJ
ejpam-3545	393	6	to	to	PART
ejpam-3545	393	7	take	take	VERB
ejpam-3545	393	8	the	the	DET
ejpam-3545	393	9	trivial	trivial	ADJ
ejpam-3545	393	10	partial	partial	ADJ
ejpam-3545	393	11	order	order	NOUN
ejpam-3545	393	12	on	on	ADP
ejpam-3545	393	13	a	a	PRON
ejpam-3545	393	14	and	and	CCONJ
ejpam-3545	393	15	define	define	VERB
ejpam-3545	393	16	addition	addition	NOUN
ejpam-3545	393	17	+	+	CCONJ
ejpam-3545	393	18	in	in	ADP
ejpam-3545	393	19	a	a	PRON
ejpam-3545	393	20	by	by	ADP
ejpam-3545	393	21	the	the	DET
ejpam-3545	393	22	formula	formula	NOUN
ejpam-3545	393	23	a	a	DET
ejpam-3545	393	24	+	+	NOUN
ejpam-3545	393	25	b	b	NOUN
ejpam-3545	393	26	=	=	SYM
ejpam-3545	393	27	h1(g1(a	h1(g1(a	NOUN
ejpam-3545	393	28	)	)	PUNCT
ejpam-3545	393	29	+2	+2	PROPN
ejpam-3545	393	30	g2(b	g2(b	PROPN
ejpam-3545	393	31	)	)	PUNCT
ejpam-3545	393	32	)	)	PUNCT
ejpam-3545	393	33	multiplication	multiplication	NOUN
ejpam-3545	393	34	◦	◦	NOUN
ejpam-3545	393	35	in	in	ADP
ejpam-3545	393	36	a	a	PRON
ejpam-3545	393	37	by	by	ADP
ejpam-3545	393	38	the	the	DET
ejpam-3545	393	39	formula	formula	NOUN
ejpam-3545	393	40	a	a	DET
ejpam-3545	393	41	◦	◦	NOUN
ejpam-3545	393	42	b	b	NOUN
ejpam-3545	393	43	=	=	NOUN
ejpam-3545	393	44	h2(g3(a	h2(g3(a	NOUN
ejpam-3545	393	45	)	)	PUNCT
ejpam-3545	393	46	◦	◦	NOUN
ejpam-3545	393	47	2	2	NUM
ejpam-3545	393	48	g4(b	g4(b	NOUN
ejpam-3545	393	49	)	)	PUNCT
ejpam-3545	393	50	)	)	PUNCT
ejpam-3545	394	1	the	the	PRON
ejpam-3545	394	2	obtained	obtain	VERB
ejpam-3545	394	3	abstract	abstract	ADJ
ejpam-3545	394	4	prearithmetic	prearithmetic	NOUN
ejpam-3545	394	5	a	a	PRON
ejpam-3545	394	6	=	=	X
ejpam-3545	394	7	(	(	PUNCT
ejpam-3545	394	8	a	a	X
ejpam-3545	394	9	;	;	PUNCT
ejpam-3545	394	10	+	+	ADJ
ejpam-3545	394	11	,	,	PUNCT
ejpam-3545	394	12	◦	◦	NOUN
ejpam-3545	394	13	,	,	PUNCT
ejpam-3545	394	14	≤	≤	NUM
ejpam-3545	394	15	)	)	PUNCT
ejpam-3545	394	16	is	be	AUX
ejpam-3545	394	17	called	call	VERB
ejpam-3545	394	18	the	the	DET
ejpam-3545	394	19	biprojective	biprojective	ADJ
ejpam-3545	394	20	extension	extension	NOUN
ejpam-3545	394	21	of	of	ADP
ejpam-3545	394	22	a	a	PRON
ejpam-3545	394	23	by	by	ADP
ejpam-3545	394	24	the	the	DET
ejpam-3545	394	25	function	function	NOUN
ejpam-3545	394	26	vector	vector	NOUN
ejpam-3545	394	27	(	(	PUNCT
ejpam-3545	394	28	g1	g1	PROPN
ejpam-3545	394	29	,	,	PUNCT
ejpam-3545	394	30	g2	g2	PROPN
ejpam-3545	394	31	,	,	PUNCT
ejpam-3545	394	32	g3	g3	NOUN
ejpam-3545	394	33	,	,	PUNCT
ejpam-3545	394	34	g4	g4	NOUN
ejpam-3545	394	35	,	,	PUNCT
ejpam-3545	394	36	h1	h1	NOUN
ejpam-3545	394	37	,	,	PUNCT
ejpam-3545	394	38	h2	h2	PROPN
ejpam-3545	394	39	)	)	PUNCT
ejpam-3545	394	40	.	.	PUNCT
ejpam-3545	395	1	m.	m.	NOUN
ejpam-3545	395	2	burgin	burgin	PROPN
ejpam-3545	395	3	/	/	SYM
ejpam-3545	395	4	eur	eur	PROPN
ejpam-3545	395	5	.	.	PUNCT
ejpam-3545	396	1	j.	j.	PROPN
ejpam-3545	396	2	pure	pure	PROPN
ejpam-3545	396	3	appl	appl	PROPN
ejpam-3545	396	4	.	.	PROPN
ejpam-3545	396	5	math	math	PROPN
ejpam-3545	396	6	,	,	PUNCT
ejpam-3545	396	7	12	12	NUM
ejpam-3545	396	8	(	(	PUNCT
ejpam-3545	396	9	4	4	NUM
ejpam-3545	396	10	)	)	PUNCT
ejpam-3545	396	11	(	(	PUNCT
ejpam-3545	396	12	2019	2019	NUM
ejpam-3545	396	13	)	)	PUNCT
ejpam-3545	396	14	,	,	PUNCT
ejpam-3545	396	15	1787	1787	NUM
ejpam-3545	396	16	-	-	SYM
ejpam-3545	396	17	1810	1810	NUM
ejpam-3545	396	18	1804	1804	NUM
ejpam-3545	396	19	the	the	DET
ejpam-3545	396	20	utilized	utilize	VERB
ejpam-3545	396	21	construction	construction	NOUN
ejpam-3545	396	22	implies	imply	VERB
ejpam-3545	396	23	the	the	DET
ejpam-3545	396	24	following	follow	VERB
ejpam-3545	396	25	result	result	NOUN
ejpam-3545	396	26	.	.	PUNCT
ejpam-3545	397	1	let	let	VERB
ejpam-3545	397	2	us	we	PRON
ejpam-3545	397	3	consider	consider	VERB
ejpam-3545	397	4	eight	eight	NUM
ejpam-3545	397	5	mappings	mapping	NOUN
ejpam-3545	397	6	g1	g1	NOUN
ejpam-3545	397	7	:	:	PUNCT
ejpam-3545	397	8	a	a	DET
ejpam-3545	397	9	→	→	SYM
ejpam-3545	397	10	a2	a2	PROPN
ejpam-3545	397	11	,	,	PUNCT
ejpam-3545	397	12	g2	g2	PROPN
ejpam-3545	397	13	:	:	PUNCT
ejpam-3545	397	14	→	→	SYM
ejpam-3545	397	15	a2	a2	PROPN
ejpam-3545	397	16	,	,	PUNCT
ejpam-3545	397	17	g3	g3	NOUN
ejpam-3545	397	18	:	:	PUNCT
ejpam-3545	397	19	→	→	SYM
ejpam-3545	397	20	a2	a2	PROPN
ejpam-3545	397	21	,	,	PUNCT
ejpam-3545	397	22	g4	g4	NOUN
ejpam-3545	397	23	:	:	PUNCT
ejpam-3545	397	24	→	→	SYM
ejpam-3545	397	25	a2	a2	PROPN
ejpam-3545	397	26	,	,	PUNCT
ejpam-3545	397	27	h1	h1	NOUN
ejpam-3545	397	28	:	:	PUNCT
ejpam-3545	397	29	a2	a2	PROPN
ejpam-3545	397	30	→	→	SYM
ejpam-3545	397	31	a	a	NOUN
ejpam-3545	397	32	,	,	PUNCT
ejpam-3545	397	33	and	and	CCONJ
ejpam-3545	397	34	h2	h2	NOUN
ejpam-3545	397	35	:	:	PUNCT
ejpam-3545	397	36	a2	a2	PROPN
ejpam-3545	397	37	→	→	SYM
ejpam-3545	397	38	a	a	PRON
ejpam-3545	397	39	,	,	PUNCT
ejpam-3545	397	40	f1	f1	NOUN
ejpam-3545	397	41	:	:	PUNCT
ejpam-3545	397	42	a2	a2	PROPN
ejpam-3545	397	43	→	→	SYM
ejpam-3545	397	44	a	a	PRON
ejpam-3545	397	45	,	,	PUNCT
ejpam-3545	397	46	and	and	CCONJ
ejpam-3545	397	47	f2	f2	PROPN
ejpam-3545	397	48	:	:	PUNCT
ejpam-3545	397	49	a2	a2	PROPN
ejpam-3545	397	50	→	→	SYM
ejpam-3545	397	51	a.	a.	NOUN
ejpam-3545	397	52	proposition	proposition	NOUN
ejpam-3545	397	53	3.12	3.12	NUM
ejpam-3545	397	54	.	.	PUNCT
ejpam-3545	398	1	if	if	SCONJ
ejpam-3545	398	2	g1	g1	PROPN
ejpam-3545	398	3	=	=	SYM
ejpam-3545	398	4	g2	g2	PROPN
ejpam-3545	398	5	,	,	PUNCT
ejpam-3545	398	6	g3	g3	NOUN
ejpam-3545	398	7	=	=	NOUN
ejpam-3545	398	8	g4	g4	NOUN
ejpam-3545	398	9	,	,	PUNCT
ejpam-3545	398	10	mappings	mapping	NOUN
ejpam-3545	398	11	f1	f1	NOUN
ejpam-3545	398	12	and	and	CCONJ
ejpam-3545	398	13	h1	h1	VERB
ejpam-3545	398	14	coincide	coincide	NOUN
ejpam-3545	398	15	on	on	ADP
ejpam-3545	398	16	the	the	DET
ejpam-3545	398	17	abstract	abstract	ADJ
ejpam-3545	398	18	prearithmetic	prearithmetic	ADJ
ejpam-3545	398	19	pa(g1(a	pa(g1(a	NOUN
ejpam-3545	398	20	)	)	PUNCT
ejpam-3545	398	21	)	)	PUNCT
ejpam-3545	398	22	generated	generate	VERB
ejpam-3545	398	23	by	by	ADP
ejpam-3545	398	24	image	image	NOUN
ejpam-3545	398	25	g1(a	g1(a	PROPN
ejpam-3545	398	26	)	)	PUNCT
ejpam-3545	398	27	of	of	ADP
ejpam-3545	398	28	a	a	DET
ejpam-3545	398	29	in	in	ADP
ejpam-3545	398	30	a2	a2	NOUN
ejpam-3545	398	31	and	and	CCONJ
ejpam-3545	398	32	mappings	mapping	NOUN
ejpam-3545	398	33	f2	f2	PROPN
ejpam-3545	398	34	and	and	CCONJ
ejpam-3545	398	35	h2	h2	NOUN
ejpam-3545	398	36	coincide	coincide	NOUN
ejpam-3545	398	37	on	on	ADP
ejpam-3545	398	38	the	the	DET
ejpam-3545	398	39	abstract	abstract	ADJ
ejpam-3545	398	40	prearithmetic	prearithmetic	ADJ
ejpam-3545	398	41	pa(g3(a	pa(g3(a	NOUN
ejpam-3545	398	42	)	)	PUNCT
ejpam-3545	398	43	)	)	PUNCT
ejpam-3545	398	44	generated	generate	VERB
ejpam-3545	398	45	by	by	ADP
ejpam-3545	398	46	image	image	NOUN
ejpam-3545	398	47	g3(a	g3(a	NOUN
ejpam-3545	398	48	)	)	PUNCT
ejpam-3545	398	49	of	of	ADP
ejpam-3545	398	50	a	a	PRON
ejpam-3545	398	51	in	in	ADP
ejpam-3545	398	52	a2	a2	PROPN
ejpam-3545	398	53	,	,	PUNCT
ejpam-3545	398	54	then	then	ADV
ejpam-3545	398	55	the	the	DET
ejpam-3545	398	56	biprojective	biprojective	ADJ
ejpam-3545	398	57	extensions	extension	NOUN
ejpam-3545	398	58	of	of	ADP
ejpam-3545	398	59	a	a	PRON
ejpam-3545	398	60	by	by	ADP
ejpam-3545	398	61	the	the	DET
ejpam-3545	398	62	function	function	NOUN
ejpam-3545	398	63	vectors	vector	NOUN
ejpam-3545	398	64	(	(	PUNCT
ejpam-3545	398	65	g1	g1	PROPN
ejpam-3545	398	66	,	,	PUNCT
ejpam-3545	398	67	g2	g2	PROPN
ejpam-3545	398	68	,	,	PUNCT
ejpam-3545	398	69	g3	g3	NOUN
ejpam-3545	398	70	,	,	PUNCT
ejpam-3545	398	71	g4	g4	NOUN
ejpam-3545	398	72	,	,	PUNCT
ejpam-3545	398	73	h1	h1	NOUN
ejpam-3545	398	74	,	,	PUNCT
ejpam-3545	398	75	h2	h2	PROPN
ejpam-3545	398	76	)	)	PUNCT
ejpam-3545	398	77	and	and	CCONJ
ejpam-3545	398	78	(	(	PUNCT
ejpam-3545	398	79	g1	g1	PROPN
ejpam-3545	398	80	,	,	PUNCT
ejpam-3545	398	81	g2	g2	PROPN
ejpam-3545	398	82	,	,	PUNCT
ejpam-3545	398	83	g3	g3	NOUN
ejpam-3545	398	84	,	,	PUNCT
ejpam-3545	398	85	g4	g4	NOUN
ejpam-3545	398	86	,	,	PUNCT
ejpam-3545	398	87	f1	f1	NOUN
ejpam-3545	398	88	,	,	PUNCT
ejpam-3545	398	89	f2	f2	PROPN
ejpam-3545	398	90	)	)	PUNCT
ejpam-3545	398	91	coincide	coincide	NOUN
ejpam-3545	398	92	.	.	PUNCT
ejpam-3545	399	1	proof	proof	NOUN
ejpam-3545	399	2	follows	follow	VERB
ejpam-3545	399	3	directly	directly	ADV
ejpam-3545	399	4	from	from	ADP
ejpam-3545	399	5	definitions	definition	NOUN
ejpam-3545	399	6	.	.	PUNCT
ejpam-3545	400	1	4	4	X
ejpam-3545	400	2	.	.	X
ejpam-3545	400	3	conclusion	conclusion	NOUN
ejpam-3545	400	4	we	we	PRON
ejpam-3545	400	5	have	have	AUX
ejpam-3545	400	6	explained	explain	VERB
ejpam-3545	400	7	that	that	SCONJ
ejpam-3545	400	8	abstract	abstract	ADJ
ejpam-3545	400	9	prearithmetics	prearithmetic	NOUN
ejpam-3545	400	10	encompass	encompass	VERB
ejpam-3545	400	11	a	a	DET
ejpam-3545	400	12	wide	wide	ADJ
ejpam-3545	400	13	range	range	NOUN
ejpam-3545	400	14	of	of	ADP
ejpam-3545	400	15	various	various	ADJ
ejpam-3545	400	16	mathematical	mathematical	ADJ
ejpam-3545	400	17	systems	system	NOUN
ejpam-3545	400	18	,	,	PUNCT
ejpam-3545	400	19	which	which	PRON
ejpam-3545	400	20	are	be	AUX
ejpam-3545	400	21	used	use	VERB
ejpam-3545	400	22	in	in	ADP
ejpam-3545	400	23	traditional	traditional	ADJ
ejpam-3545	400	24	and	and	CCONJ
ejpam-3545	400	25	novel	novel	ADJ
ejpam-3545	400	26	mathematical	mathematical	ADJ
ejpam-3545	400	27	domains	domain	NOUN
ejpam-3545	400	28	and	and	CCONJ
ejpam-3545	400	29	applications	application	NOUN
ejpam-3545	400	30	.	.	PUNCT
ejpam-3545	401	1	we	we	PRON
ejpam-3545	401	2	also	also	ADV
ejpam-3545	401	3	demonstrated	demonstrate	VERB
ejpam-3545	401	4	how	how	SCONJ
ejpam-3545	401	5	projectivity	projectivity	NOUN
ejpam-3545	401	6	relations	relation	NOUN
ejpam-3545	401	7	between	between	ADP
ejpam-3545	401	8	abstract	abstract	ADJ
ejpam-3545	401	9	prearithmetics	prearithmetic	NOUN
ejpam-3545	401	10	allow	allow	VERB
ejpam-3545	401	11	one	one	PRON
ejpam-3545	401	12	to	to	PART
ejpam-3545	401	13	deduce	deduce	VERB
ejpam-3545	401	14	properties	property	NOUN
ejpam-3545	401	15	of	of	ADP
ejpam-3545	401	16	one	one	NUM
ejpam-3545	401	17	abstract	abstract	ADJ
ejpam-3545	401	18	prearithmetic	prearithmetic	ADJ
ejpam-3545	401	19	from	from	ADP
ejpam-3545	401	20	properties	property	NOUN
ejpam-3545	401	21	of	of	ADP
ejpam-3545	401	22	another	another	DET
ejpam-3545	401	23	one	one	NUM
ejpam-3545	401	24	.	.	PUNCT
ejpam-3545	402	1	techniques	technique	NOUN
ejpam-3545	402	2	for	for	ADP
ejpam-3545	402	3	building	build	VERB
ejpam-3545	402	4	new	new	ADJ
ejpam-3545	402	5	abstract	abstract	ADJ
ejpam-3545	402	6	prearithmetics	prearithmetic	NOUN
ejpam-3545	402	7	from	from	ADP
ejpam-3545	402	8	given	give	VERB
ejpam-3545	402	9	ones	one	NOUN
ejpam-3545	402	10	were	be	AUX
ejpam-3545	402	11	elaborated	elaborate	VERB
ejpam-3545	402	12	and	and	CCONJ
ejpam-3545	402	13	studied	study	VERB
ejpam-3545	402	14	.	.	PUNCT
ejpam-3545	403	1	it	it	PRON
ejpam-3545	403	2	is	be	AUX
ejpam-3545	403	3	necessary	necessary	ADJ
ejpam-3545	403	4	to	to	PART
ejpam-3545	403	5	remark	remark	VERB
ejpam-3545	403	6	that	that	SCONJ
ejpam-3545	403	7	traditionally	traditionally	ADV
ejpam-3545	403	8	the	the	DET
ejpam-3545	403	9	main	main	ADJ
ejpam-3545	403	10	relation	relation	NOUN
ejpam-3545	403	11	between	between	ADP
ejpam-3545	403	12	algebraic	algebraic	ADJ
ejpam-3545	403	13	systems	system	NOUN
ejpam-3545	403	14	is	be	AUX
ejpam-3545	403	15	homomorphism	homomorphism	NOUN
ejpam-3545	403	16	with	with	ADP
ejpam-3545	403	17	its	its	PRON
ejpam-3545	403	18	special	special	ADJ
ejpam-3545	403	19	types	type	NOUN
ejpam-3545	403	20	such	such	ADJ
ejpam-3545	403	21	as	as	ADP
ejpam-3545	403	22	monomorphism	monomorphism	NOUN
ejpam-3545	403	23	,	,	PUNCT
ejpam-3545	403	24	epimorphism	epimorphism	NOUN
ejpam-3545	403	25	and	and	CCONJ
ejpam-3545	403	26	isomorphism	isomorphism	NOUN
ejpam-3545	403	27	.	.	PUNCT
ejpam-3545	404	1	the	the	DET
ejpam-3545	404	2	basic	basic	ADJ
ejpam-3545	404	3	property	property	NOUN
ejpam-3545	404	4	of	of	ADP
ejpam-3545	404	5	homomorphisms	homomorphisms	PROPN
ejpam-3545	404	6	is	be	AUX
ejpam-3545	404	7	that	that	SCONJ
ejpam-3545	404	8	they	they	PRON
ejpam-3545	404	9	preserve	preserve	VERB
ejpam-3545	404	10	operations	operation	NOUN
ejpam-3545	404	11	.	.	PUNCT
ejpam-3545	405	1	systems	system	NOUN
ejpam-3545	405	2	of	of	ADP
ejpam-3545	405	3	algebraic	algebraic	ADJ
ejpam-3545	405	4	systems	system	NOUN
ejpam-3545	405	5	such	such	ADJ
ejpam-3545	405	6	as	as	ADP
ejpam-3545	405	7	groups	group	NOUN
ejpam-3545	405	8	,	,	PUNCT
ejpam-3545	405	9	vector	vector	NOUN
ejpam-3545	405	10	spaces	space	NOUN
ejpam-3545	405	11	or	or	CCONJ
ejpam-3545	405	12	rings	ring	NOUN
ejpam-3545	405	13	with	with	ADP
ejpam-3545	405	14	their	their	PRON
ejpam-3545	405	15	homomorphisms	homomorphism	NOUN
ejpam-3545	405	16	form	form	NOUN
ejpam-3545	405	17	categories	category	NOUN
ejpam-3545	405	18	.	.	PUNCT
ejpam-3545	406	1	in	in	ADP
ejpam-3545	406	2	the	the	DET
ejpam-3545	406	3	theory	theory	NOUN
ejpam-3545	406	4	of	of	ADP
ejpam-3545	406	5	non	non	ADJ
ejpam-3545	406	6	-	-	ADJ
ejpam-3545	406	7	diophantine	diophantine	ADJ
ejpam-3545	406	8	arithmetics	arithmetic	NOUN
ejpam-3545	406	9	,	,	PUNCT
ejpam-3545	406	10	another	another	DET
ejpam-3545	406	11	basic	basic	ADJ
ejpam-3545	406	12	relation	relation	NOUN
ejpam-3545	406	13	between	between	ADP
ejpam-3545	406	14	algebraic	algebraic	ADJ
ejpam-3545	406	15	systems	system	NOUN
ejpam-3545	406	16	is	be	AUX
ejpam-3545	406	17	introduced	introduce	VERB
ejpam-3545	406	18	.	.	PUNCT
ejpam-3545	407	1	it	it	PRON
ejpam-3545	407	2	is	be	AUX
ejpam-3545	407	3	called	call	VERB
ejpam-3545	407	4	projectivity	projectivity	NOUN
ejpam-3545	407	5	and	and	CCONJ
ejpam-3545	407	6	has	have	VERB
ejpam-3545	407	7	three	three	NUM
ejpam-3545	407	8	basic	basic	ADJ
ejpam-3545	407	9	types	type	NOUN
ejpam-3545	407	10	:	:	PUNCT
ejpam-3545	407	11	weak	weak	ADJ
ejpam-3545	407	12	projectivity	projectivity	NOUN
ejpam-3545	407	13	,	,	PUNCT
ejpam-3545	407	14	projectivity	projectivity	NOUN
ejpam-3545	407	15	per	per	ADP
ejpam-3545	407	16	se	se	X
ejpam-3545	407	17	and	and	CCONJ
ejpam-3545	407	18	exact	exact	ADJ
ejpam-3545	407	19	projectivity	projectivity	NOUN
ejpam-3545	407	20	.	.	PUNCT
ejpam-3545	408	1	in	in	ADP
ejpam-3545	408	2	this	this	DET
ejpam-3545	408	3	work	work	NOUN
ejpam-3545	408	4	,	,	PUNCT
ejpam-3545	408	5	we	we	PRON
ejpam-3545	408	6	show	show	VERB
ejpam-3545	408	7	that	that	SCONJ
ejpam-3545	408	8	there	there	PRON
ejpam-3545	408	9	also	also	ADV
ejpam-3545	408	10	partial	partial	ADJ
ejpam-3545	408	11	and	and	CCONJ
ejpam-3545	408	12	total	total	ADJ
ejpam-3545	408	13	weak	weak	ADJ
ejpam-3545	408	14	projectivity	projectivity	NOUN
ejpam-3545	408	15	while	while	SCONJ
ejpam-3545	408	16	partial	partial	ADJ
ejpam-3545	408	17	weak	weak	ADJ
ejpam-3545	408	18	projectivity	projectivity	NOUN
ejpam-3545	408	19	has	have	VERB
ejpam-3545	408	20	three	three	NUM
ejpam-3545	408	21	types	type	NOUN
ejpam-3545	408	22	:	:	PUNCT
ejpam-3545	408	23	additive	additive	VERB
ejpam-3545	408	24	weak	weak	ADJ
ejpam-3545	408	25	projectivity	projectivity	NOUN
ejpam-3545	408	26	,	,	PUNCT
ejpam-3545	408	27	multiplicative	multiplicative	ADJ
ejpam-3545	408	28	weak	weak	ADJ
ejpam-3545	408	29	projectivity	projectivity	NOUN
ejpam-3545	408	30	and	and	CCONJ
ejpam-3545	408	31	weak	weak	ADJ
ejpam-3545	408	32	biprojectivity	biprojectivity	NOUN
ejpam-3545	408	33	.	.	PUNCT
ejpam-3545	409	1	the	the	DET
ejpam-3545	409	2	key	key	ADJ
ejpam-3545	409	3	property	property	NOUN
ejpam-3545	409	4	of	of	ADP
ejpam-3545	409	5	projectivity	projectivity	NOUN
ejpam-3545	409	6	relations	relation	NOUN
ejpam-3545	409	7	is	be	AUX
ejpam-3545	409	8	that	that	SCONJ
ejpam-3545	409	9	they	they	PRON
ejpam-3545	409	10	transfer	transfer	VERB
ejpam-3545	409	11	operations	operation	NOUN
ejpam-3545	409	12	from	from	ADP
ejpam-3545	409	13	one	one	NUM
ejpam-3545	409	14	prearithmetic	prearithmetic	ADJ
ejpam-3545	409	15	to	to	ADP
ejpam-3545	409	16	another	another	PRON
ejpam-3545	409	17	.	.	PUNCT
ejpam-3545	410	1	similar	similar	ADJ
ejpam-3545	410	2	to	to	ADP
ejpam-3545	410	3	homomorphisms	homomorphism	NOUN
ejpam-3545	410	4	,	,	PUNCT
ejpam-3545	410	5	systems	system	NOUN
ejpam-3545	410	6	of	of	ADP
ejpam-3545	410	7	prearithmetics	prearithmetic	NOUN
ejpam-3545	410	8	with	with	ADP
ejpam-3545	410	9	their	their	PRON
ejpam-3545	410	10	projectivity	projectivity	NOUN
ejpam-3545	410	11	relations	relation	NOUN
ejpam-3545	410	12	of	of	ADP
ejpam-3545	410	13	a	a	DET
ejpam-3545	410	14	fixed	fix	VERB
ejpam-3545	410	15	type	type	NOUN
ejpam-3545	410	16	form	form	NOUN
ejpam-3545	410	17	categories	category	NOUN
ejpam-3545	410	18	as	as	SCONJ
ejpam-3545	410	19	it	it	PRON
ejpam-3545	410	20	is	be	AUX
ejpam-3545	410	21	demonstrated	demonstrate	VERB
ejpam-3545	410	22	in	in	ADP
ejpam-3545	410	23	this	this	DET
ejpam-3545	410	24	paper	paper	NOUN
ejpam-3545	410	25	.	.	PUNCT
ejpam-3545	411	1	the	the	DET
ejpam-3545	411	2	obtained	obtain	VERB
ejpam-3545	411	3	results	result	NOUN
ejpam-3545	411	4	open	open	VERB
ejpam-3545	411	5	potential	potential	ADJ
ejpam-3545	411	6	directions	direction	NOUN
ejpam-3545	411	7	for	for	ADP
ejpam-3545	411	8	future	future	ADJ
ejpam-3545	411	9	research	research	NOUN
ejpam-3545	411	10	.	.	PUNCT
ejpam-3545	412	1	for	for	ADP
ejpam-3545	412	2	instance	instance	NOUN
ejpam-3545	412	3	,	,	PUNCT
ejpam-3545	412	4	it	it	PRON
ejpam-3545	412	5	would	would	AUX
ejpam-3545	412	6	be	be	AUX
ejpam-3545	412	7	interesting	interesting	ADJ
ejpam-3545	412	8	to	to	PART
ejpam-3545	412	9	study	study	VERB
ejpam-3545	412	10	properties	property	NOUN
ejpam-3545	412	11	of	of	ADP
ejpam-3545	412	12	categories	category	NOUN
ejpam-3545	412	13	of	of	ADP
ejpam-3545	412	14	abstract	abstract	ADJ
ejpam-3545	412	15	prearithmetics	prearithmetic	NOUN
ejpam-3545	412	16	with	with	ADP
ejpam-3545	412	17	different	different	ADJ
ejpam-3545	412	18	types	type	NOUN
ejpam-3545	412	19	of	of	ADP
ejpam-3545	412	20	partial	partial	ADJ
ejpam-3545	412	21	weak	weak	ADJ
ejpam-3545	412	22	projectivity	projectivity	NOUN
ejpam-3545	412	23	or	or	CCONJ
ejpam-3545	412	24	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	412	25	relations	relation	NOUN
ejpam-3545	412	26	as	as	ADP
ejpam-3545	412	27	morphisms	morphism	NOUN
ejpam-3545	412	28	.	.	PUNCT
ejpam-3545	413	1	in	in	ADP
ejpam-3545	413	2	particular	particular	ADJ
ejpam-3545	413	3	,	,	PUNCT
ejpam-3545	413	4	we	we	PRON
ejpam-3545	413	5	can	can	AUX
ejpam-3545	413	6	explore	explore	VERB
ejpam-3545	413	7	relations	relation	NOUN
ejpam-3545	413	8	between	between	ADP
ejpam-3545	413	9	these	these	DET
ejpam-3545	413	10	categories	category	NOUN
ejpam-3545	413	11	and	and	CCONJ
ejpam-3545	413	12	traditionally	traditionally	ADV
ejpam-3545	413	13	studied	study	VERB
ejpam-3545	413	14	categories	category	NOUN
ejpam-3545	413	15	,	,	PUNCT
ejpam-3545	413	16	references	reference	NOUN
ejpam-3545	413	17	1805	1805	NUM
ejpam-3545	413	18	such	such	ADJ
ejpam-3545	413	19	as	as	ADP
ejpam-3545	413	20	categories	category	NOUN
ejpam-3545	413	21	of	of	ADP
ejpam-3545	413	22	sets	set	NOUN
ejpam-3545	413	23	or	or	CCONJ
ejpam-3545	413	24	categories	category	NOUN
ejpam-3545	413	25	of	of	ADP
ejpam-3545	413	26	groups	group	NOUN
ejpam-3545	413	27	.	.	PUNCT
ejpam-3545	414	1	in	in	ADP
ejpam-3545	414	2	this	this	DET
ejpam-3545	414	3	paper	paper	NOUN
ejpam-3545	414	4	,	,	PUNCT
ejpam-3545	414	5	we	we	PRON
ejpam-3545	414	6	study	study	VERB
ejpam-3545	414	7	abstract	abstract	ADJ
ejpam-3545	414	8	prearithmetics	prearithmetic	NOUN
ejpam-3545	414	9	and	and	CCONJ
ejpam-3545	414	10	partial	partial	ADJ
ejpam-3545	414	11	weak	weak	ADJ
ejpam-3545	414	12	projectivity	projectivity	NOUN
ejpam-3545	414	13	between	between	ADP
ejpam-3545	414	14	them	they	PRON
ejpam-3545	414	15	.	.	PUNCT
ejpam-3545	415	1	that	that	PRON
ejpam-3545	415	2	is	be	AUX
ejpam-3545	415	3	why	why	SCONJ
ejpam-3545	415	4	another	another	DET
ejpam-3545	415	5	appealing	appealing	ADJ
ejpam-3545	415	6	direction	direction	NOUN
ejpam-3545	415	7	for	for	ADP
ejpam-3545	415	8	future	future	ADJ
ejpam-3545	415	9	research	research	NOUN
ejpam-3545	415	10	is	be	AUX
ejpam-3545	415	11	exploration	exploration	NOUN
ejpam-3545	415	12	of	of	ADP
ejpam-3545	415	13	partial	partial	ADJ
ejpam-3545	415	14	weak	weak	ADJ
ejpam-3545	415	15	projectivity	projectivity	NOUN
ejpam-3545	415	16	and	and	CCONJ
ejpam-3545	415	17	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	415	18	relations	relation	NOUN
ejpam-3545	415	19	between	between	ADP
ejpam-3545	415	20	operations	operation	NOUN
ejpam-3545	415	21	in	in	ADP
ejpam-3545	415	22	numerical	numerical	ADJ
ejpam-3545	415	23	prearithmetics	prearithmetic	NOUN
ejpam-3545	415	24	and	and	CCONJ
ejpam-3545	415	25	arithmetics	arithmetic	NOUN
ejpam-3545	415	26	,	,	PUNCT
ejpam-3545	415	27	which	which	PRON
ejpam-3545	415	28	form	form	VERB
ejpam-3545	415	29	an	an	DET
ejpam-3545	415	30	important	important	ADJ
ejpam-3545	415	31	class	class	NOUN
ejpam-3545	415	32	of	of	ADP
ejpam-3545	415	33	prearithmetics	prearithmetic	NOUN
ejpam-3545	415	34	containing	contain	VERB
ejpam-3545	415	35	non	non	ADJ
ejpam-3545	415	36	-	-	ADJ
ejpam-3545	415	37	diophantine	diophantine	ADJ
ejpam-3545	415	38	arithmetics	arithmetic	NOUN
ejpam-3545	415	39	.	.	PUNCT
ejpam-3545	416	1	one	one	NUM
ejpam-3545	416	2	more	more	ADV
ejpam-3545	416	3	attractive	attractive	ADJ
ejpam-3545	416	4	direction	direction	NOUN
ejpam-3545	416	5	of	of	ADP
ejpam-3545	416	6	research	research	NOUN
ejpam-3545	416	7	in	in	ADP
ejpam-3545	416	8	this	this	DET
ejpam-3545	416	9	area	area	NOUN
ejpam-3545	416	10	is	be	AUX
ejpam-3545	416	11	introduction	introduction	NOUN
ejpam-3545	416	12	and	and	CCONJ
ejpam-3545	416	13	study	study	NOUN
ejpam-3545	416	14	of	of	ADP
ejpam-3545	416	15	stronger	strong	ADJ
ejpam-3545	416	16	relations	relation	NOUN
ejpam-3545	416	17	of	of	ADP
ejpam-3545	416	18	partial	partial	ADJ
ejpam-3545	416	19	projectivity	projectivity	NOUN
ejpam-3545	416	20	,	,	PUNCT
ejpam-3545	416	21	biprojectivity	biprojectivity	NOUN
ejpam-3545	416	22	and	and	CCONJ
ejpam-3545	416	23	monoprojectivity	monoprojectivity	NOUN
ejpam-3545	416	24	between	between	ADP
ejpam-3545	416	25	operations	operation	NOUN
ejpam-3545	416	26	in	in	ADP
ejpam-3545	416	27	prearithmetics	prearithmetic	NOUN
ejpam-3545	416	28	.	.	PUNCT
ejpam-3545	417	1	these	these	DET
ejpam-3545	417	2	relations	relation	NOUN
ejpam-3545	417	3	can	can	AUX
ejpam-3545	417	4	disclose	disclose	VERB
ejpam-3545	417	5	closer	close	ADJ
ejpam-3545	417	6	ties	tie	NOUN
ejpam-3545	417	7	between	between	ADP
ejpam-3545	417	8	operations	operation	NOUN
ejpam-3545	417	9	in	in	ADP
ejpam-3545	417	10	related	related	ADJ
ejpam-3545	417	11	prearithmetics	prearithmetic	NOUN
ejpam-3545	417	12	.	.	PUNCT
ejpam-3545	418	1	references	reference	NOUN
ejpam-3545	418	2	[	[	X
ejpam-3545	418	3	1	1	NUM
ejpam-3545	418	4	]	]	PUNCT
ejpam-3545	418	5	tm	tm	PRON
ejpam-3545	418	6	baranovich	baranovich	NOUN
ejpam-3545	418	7	and	and	CCONJ
ejpam-3545	418	8	mark	mark	PROPN
ejpam-3545	418	9	s	s	PART
ejpam-3545	418	10	burgin	burgin	NOUN
ejpam-3545	418	11	.	.	PUNCT
ejpam-3545	419	1	linear	linear	PROPN
ejpam-3545	419	2	ω	ω	PROPN
ejpam-3545	419	3	-	-	PUNCT
ejpam-3545	419	4	algebras	algebras	PROPN
ejpam-3545	419	5	.	.	PUNCT
ejpam-3545	420	1	russian	russian	ADJ
ejpam-3545	420	2	mathematical	mathematical	ADJ
ejpam-3545	420	3	surveys	survey	NOUN
ejpam-3545	420	4	,	,	PUNCT
ejpam-3545	420	5	30(4):61–106	30(4):61–106	NUM
ejpam-3545	420	6	,	,	PUNCT
ejpam-3545	420	7	1975	1975	NUM
ejpam-3545	420	8	.	.	PUNCT
ejpam-3545	421	1	[	[	X
ejpam-3545	421	2	2	2	NUM
ejpam-3545	421	3	]	]	X
ejpam-3545	421	4	d	d	NOUN
ejpam-3545	421	5	beechler	beechler	NOUN
ejpam-3545	421	6	.	.	PUNCT
ejpam-3545	422	1	how	how	SCONJ
ejpam-3545	422	2	to	to	PART
ejpam-3545	422	3	create	create	VERB
ejpam-3545	422	4	“	"	PUNCT
ejpam-3545	422	5	1	1	NUM
ejpam-3545	422	6	+	+	NUM
ejpam-3545	422	7	1=	1=	NUM
ejpam-3545	422	8	3	3	NUM
ejpam-3545	422	9	”	"	PUNCT
ejpam-3545	422	10	marketing	marketing	NOUN
ejpam-3545	422	11	campaigns	campaign	NOUN
ejpam-3545	422	12	,	,	PUNCT
ejpam-3545	422	13	2013	2013	NUM
ejpam-3545	422	14	.	.	PUNCT
ejpam-3545	423	1	[	[	X
ejpam-3545	423	2	3	3	X
ejpam-3545	423	3	]	]	X
ejpam-3545	423	4	nicolas	nicolas	PROPN
ejpam-3545	423	5	bourbaki	bourbaki	PROPN
ejpam-3545	423	6	.	.	PUNCT
ejpam-3545	424	1	théorie	théorie	PROPN
ejpam-3545	424	2	des	des	PROPN
ejpam-3545	424	3	ensembles	ensemble	NOUN
ejpam-3545	424	4	,	,	PUNCT
ejpam-3545	424	5	volume	volume	NOUN
ejpam-3545	424	6	1	1	NUM
ejpam-3545	424	7	.	.	PUNCT
ejpam-3545	425	1	hermann	hermann	PROPN
ejpam-3545	425	2	paris	paris	PROPN
ejpam-3545	425	3	,	,	PUNCT
ejpam-3545	425	4	1960	1960	NUM
ejpam-3545	425	5	.	.	PUNCT
ejpam-3545	426	1	[	[	X
ejpam-3545	426	2	4	4	X
ejpam-3545	426	3	]	]	X
ejpam-3545	426	4	anne	anne	PROPN
ejpam-3545	426	5	e	e	PROPN
ejpam-3545	426	6	brodsky	brodsky	PROPN
ejpam-3545	426	7	,	,	PUNCT
ejpam-3545	426	8	kathleen	kathleen	PROPN
ejpam-3545	426	9	rogers	rogers	PROPN
ejpam-3545	426	10	senuta	senuta	PROPN
ejpam-3545	426	11	,	,	PUNCT
ejpam-3545	426	12	catharine	catharine	PROPN
ejpam-3545	426	13	la	la	PROPN
ejpam-3545	426	14	weiss	weiss	PROPN
ejpam-3545	426	15	,	,	PUNCT
ejpam-3545	426	16	christine	christine	PROPN
ejpam-3545	426	17	m	m	PROPN
ejpam-3545	426	18	marx	marx	PROPN
ejpam-3545	426	19	,	,	PUNCT
ejpam-3545	426	20	colleen	colleen	PROPN
ejpam-3545	426	21	loomis	loomis	PROPN
ejpam-3545	426	22	,	,	PUNCT
ejpam-3545	426	23	s	s	PART
ejpam-3545	426	24	sonia	sonia	PROPN
ejpam-3545	426	25	arteaga	arteaga	NOUN
ejpam-3545	426	26	,	,	PUNCT
ejpam-3545	426	27	heidi	heidi	PROPN
ejpam-3545	426	28	moore	moore	PROPN
ejpam-3545	426	29	,	,	PUNCT
ejpam-3545	426	30	rona	rona	PROPN
ejpam-3545	426	31	benhorin	benhorin	PROPN
ejpam-3545	426	32	,	,	PUNCT
ejpam-3545	426	33	and	and	CCONJ
ejpam-3545	426	34	alisha	alisha	PROPN
ejpam-3545	426	35	castagnera	castagnera	PROPN
ejpam-3545	426	36	-	-	PUNCT
ejpam-3545	426	37	fletcher	fletcher	PROPN
ejpam-3545	426	38	.	.	PUNCT
ejpam-3545	427	1	when	when	SCONJ
ejpam-3545	427	2	one	one	NUM
ejpam-3545	427	3	plus	plus	CCONJ
ejpam-3545	427	4	one	one	NUM
ejpam-3545	427	5	equals	equal	VERB
ejpam-3545	427	6	three	three	NUM
ejpam-3545	427	7	:	:	PUNCT
ejpam-3545	427	8	the	the	DET
ejpam-3545	427	9	role	role	NOUN
ejpam-3545	427	10	of	of	ADP
ejpam-3545	427	11	relationships	relationship	NOUN
ejpam-3545	427	12	and	and	CCONJ
ejpam-3545	427	13	context	context	NOUN
ejpam-3545	427	14	in	in	ADP
ejpam-3545	427	15	community	community	NOUN
ejpam-3545	427	16	research	research	NOUN
ejpam-3545	427	17	.	.	PUNCT
ejpam-3545	428	1	american	american	ADJ
ejpam-3545	428	2	journal	journal	PROPN
ejpam-3545	428	3	of	of	ADP
ejpam-3545	428	4	community	community	NOUN
ejpam-3545	428	5	psychology	psychology	NOUN
ejpam-3545	428	6	,	,	PUNCT
ejpam-3545	428	7	33(34):229–241	33(34):229–241	NUM
ejpam-3545	428	8	,	,	PUNCT
ejpam-3545	428	9	2004	2004	NUM
ejpam-3545	428	10	.	.	PUNCT
ejpam-3545	429	1	[	[	X
ejpam-3545	429	2	5	5	NUM
ejpam-3545	429	3	]	]	PUNCT
ejpam-3545	429	4	m	m	AUX
ejpam-3545	429	5	burgin	burgin	NOUN
ejpam-3545	429	6	.	.	PUNCT
ejpam-3545	430	1	elements	element	NOUN
ejpam-3545	430	2	of	of	ADP
ejpam-3545	430	3	non	non	ADJ
ejpam-3545	430	4	-	-	ADJ
ejpam-3545	430	5	diophantine	diophantine	ADJ
ejpam-3545	430	6	arithmetics	arithmetic	NOUN
ejpam-3545	430	7	.	.	PUNCT
ejpam-3545	431	1	in	in	ADP
ejpam-3545	431	2	6th	6th	ADJ
ejpam-3545	431	3	annual	annual	ADJ
ejpam-3545	431	4	international	international	ADJ
ejpam-3545	431	5	conference	conference	NOUN
ejpam-3545	431	6	on	on	ADP
ejpam-3545	431	7	statistics	statistic	NOUN
ejpam-3545	431	8	,	,	PUNCT
ejpam-3545	431	9	mathematics	mathematic	NOUN
ejpam-3545	431	10	and	and	CCONJ
ejpam-3545	431	11	related	related	ADJ
ejpam-3545	431	12	fields	field	NOUN
ejpam-3545	431	13	,	,	PUNCT
ejpam-3545	431	14	2007	2007	NUM
ejpam-3545	431	15	conference	conference	NOUN
ejpam-3545	431	16	proceedings	proceeding	NOUN
ejpam-3545	431	17	,	,	PUNCT
ejpam-3545	431	18	honolulu	honolulu	PROPN
ejpam-3545	431	19	,	,	PUNCT
ejpam-3545	431	20	hawaii	hawaii	PROPN
ejpam-3545	431	21	,	,	PUNCT
ejpam-3545	431	22	pages	page	NOUN
ejpam-3545	431	23	190–203	190–203	NUM
ejpam-3545	431	24	,	,	PUNCT
ejpam-3545	431	25	2007	2007	NUM
ejpam-3545	431	26	.	.	PUNCT
ejpam-3545	432	1	[	[	X
ejpam-3545	432	2	6	6	NUM
ejpam-3545	432	3	]	]	PUNCT
ejpam-3545	432	4	mark	mark	NOUN
ejpam-3545	432	5	burgin	burgin	NOUN
ejpam-3545	432	6	.	.	PUNCT
ejpam-3545	433	1	diophantine	diophantine	VERB
ejpam-3545	433	2	and	and	CCONJ
ejpam-3545	433	3	non	non	ADJ
ejpam-3545	433	4	-	-	ADJ
ejpam-3545	433	5	diophantine	diophantine	ADJ
ejpam-3545	433	6	arithmetics	arithmetic	NOUN
ejpam-3545	433	7	:	:	PUNCT
ejpam-3545	433	8	operations	operation	NOUN
ejpam-3545	433	9	with	with	ADP
ejpam-3545	433	10	numbers	number	NOUN
ejpam-3545	433	11	in	in	ADP
ejpam-3545	433	12	science	science	NOUN
ejpam-3545	433	13	and	and	CCONJ
ejpam-3545	433	14	everyday	everyday	ADJ
ejpam-3545	433	15	life	life	NOUN
ejpam-3545	433	16	.	.	PUNCT
ejpam-3545	434	1	preprint	preprint	NOUN
ejpam-3545	434	2	in	in	ADP
ejpam-3545	434	3	mathematics	mathematic	NOUN
ejpam-3545	434	4	,	,	PUNCT
ejpam-3545	434	5	(	(	PUNCT
ejpam-3545	434	6	math/0108149	math/0108149	PROPN
ejpam-3545	434	7	)	)	PUNCT
ejpam-3545	434	8	,	,	PUNCT
ejpam-3545	434	9	2001	2001	NUM
ejpam-3545	434	10	.	.	PUNCT
ejpam-3545	435	1	[	[	X
ejpam-3545	435	2	7	7	NUM
ejpam-3545	435	3	]	]	PUNCT
ejpam-3545	435	4	mark	mark	NOUN
ejpam-3545	435	5	burgin	burgin	NOUN
ejpam-3545	435	6	.	.	PUNCT
ejpam-3545	436	1	introduction	introduction	NOUN
ejpam-3545	436	2	to	to	ADP
ejpam-3545	436	3	projective	projective	ADJ
ejpam-3545	436	4	arithmetics	arithmetic	NOUN
ejpam-3545	436	5	.	.	PUNCT
ejpam-3545	437	1	arxiv	arxiv	PROPN
ejpam-3545	437	2	preprint	preprint	PROPN
ejpam-3545	437	3	(	(	PUNCT
ejpam-3545	437	4	arxiv:1010.3287	arxiv:1010.3287	NOUN
ejpam-3545	437	5	)	)	PUNCT
ejpam-3545	437	6	,	,	PUNCT
ejpam-3545	437	7	2010	2010	NUM
ejpam-3545	437	8	.	.	PUNCT
ejpam-3545	438	1	[	[	X
ejpam-3545	438	2	8	8	NUM
ejpam-3545	438	3	]	]	PUNCT
ejpam-3545	438	4	mark	mark	NOUN
ejpam-3545	438	5	burgin	burgin	NOUN
ejpam-3545	438	6	.	.	PUNCT
ejpam-3545	439	1	bidirectional	bidirectional	NOUN
ejpam-3545	439	2	named	name	VERB
ejpam-3545	439	3	sets	set	NOUN
ejpam-3545	439	4	as	as	ADP
ejpam-3545	439	5	structural	structural	ADJ
ejpam-3545	439	6	models	model	NOUN
ejpam-3545	439	7	of	of	ADP
ejpam-3545	439	8	interpersonal	interpersonal	ADJ
ejpam-3545	439	9	communication	communication	NOUN
ejpam-3545	439	10	.	.	PUNCT
ejpam-3545	440	1	in	in	ADP
ejpam-3545	440	2	multidisciplinary	multidisciplinary	ADJ
ejpam-3545	440	3	digital	digital	PROPN
ejpam-3545	440	4	publishing	publishing	PROPN
ejpam-3545	440	5	institute	institute	NOUN
ejpam-3545	440	6	proceedings	proceeding	NOUN
ejpam-3545	440	7	,	,	PUNCT
ejpam-3545	440	8	volume	volume	NOUN
ejpam-3545	440	9	1	1	NUM
ejpam-3545	440	10	,	,	PUNCT
ejpam-3545	440	11	page	page	NOUN
ejpam-3545	440	12	58	58	NUM
ejpam-3545	440	13	,	,	PUNCT
ejpam-3545	440	14	2017	2017	NUM
ejpam-3545	440	15	.	.	PUNCT
ejpam-3545	441	1	[	[	X
ejpam-3545	441	2	9	9	NUM
ejpam-3545	441	3	]	]	PUNCT
ejpam-3545	441	4	mark	mark	NOUN
ejpam-3545	441	5	burgin	burgin	PROPN
ejpam-3545	441	6	and	and	CCONJ
ejpam-3545	441	7	gunter	gunter	PROPN
ejpam-3545	441	8	meissner	meissner	PROPN
ejpam-3545	441	9	.	.	PUNCT
ejpam-3545	442	1	1	1	NUM
ejpam-3545	442	2	+	+	NUM
ejpam-3545	442	3	1=	1=	NUM
ejpam-3545	442	4	3	3	NUM
ejpam-3545	442	5	:	:	PUNCT
ejpam-3545	442	6	synergy	synergy	NOUN
ejpam-3545	442	7	arithmetic	arithmetic	ADJ
ejpam-3545	442	8	in	in	ADP
ejpam-3545	442	9	economics	economic	NOUN
ejpam-3545	442	10	.	.	PUNCT
ejpam-3545	443	1	applied	apply	VERB
ejpam-3545	443	2	mathematics	mathematic	NOUN
ejpam-3545	443	3	,	,	PUNCT
ejpam-3545	443	4	8(2):133–144	8(2):133–144	NUM
ejpam-3545	443	5	,	,	PUNCT
ejpam-3545	443	6	2017	2017	NUM
ejpam-3545	443	7	.	.	PUNCT
ejpam-3545	444	1	references	reference	NOUN
ejpam-3545	444	2	1806	1806	NUM
ejpam-3545	444	3	[	[	X
ejpam-3545	444	4	10	10	NUM
ejpam-3545	444	5	]	]	X
ejpam-3545	444	6	m.s	m.s	PROPN
ejpam-3545	444	7	.	.	PROPN
ejpam-3545	444	8	burgin	burgin	PROPN
ejpam-3545	444	9	.	.	PUNCT
ejpam-3545	445	1	nonclassical	nonclassical	ADJ
ejpam-3545	445	2	models	model	NOUN
ejpam-3545	445	3	of	of	ADP
ejpam-3545	445	4	the	the	DET
ejpam-3545	445	5	natural	natural	ADJ
ejpam-3545	445	6	numbers	number	NOUN
ejpam-3545	445	7	.	.	PUNCT
ejpam-3545	446	1	uspekhi	uspekhi	PROPN
ejpam-3545	446	2	mat	mat	PROPN
ejpam-3545	446	3	.	.	PUNCT
ejpam-3545	446	4	nauk	nauk	PROPN
ejpam-3545	446	5	,	,	PUNCT
ejpam-3545	446	6	32:209	32:209	NUM
ejpam-3545	446	7	–	–	PUNCT
ejpam-3545	446	8	210	210	NUM
ejpam-3545	446	9	,	,	PUNCT
ejpam-3545	446	10	1977	1977	NUM
ejpam-3545	446	11	.	.	PUNCT
ejpam-3545	447	1	[	[	X
ejpam-3545	447	2	11	11	NUM
ejpam-3545	447	3	]	]	X
ejpam-3545	447	4	ms	ms	PROPN
ejpam-3545	447	5	burgin	burgin	NOUN
ejpam-3545	447	6	.	.	PUNCT
ejpam-3545	448	1	non	non	ADJ
ejpam-3545	448	2	-	-	ADJ
ejpam-3545	448	3	diophantine	diophantine	ADJ
ejpam-3545	448	4	arithmetics	arithmetic	NOUN
ejpam-3545	448	5	or	or	CCONJ
ejpam-3545	448	6	what	what	DET
ejpam-3545	448	7	number	number	NOUN
ejpam-3545	448	8	is	be	AUX
ejpam-3545	448	9	2	2	NUM
ejpam-3545	448	10	+	+	NOUN
ejpam-3545	448	11	2	2	NUM
ejpam-3545	448	12	?	?	SYM
ejpam-3545	448	13	ukrainian	ukrainian	PROPN
ejpam-3545	448	14	academy	academy	PROPN
ejpam-3545	448	15	of	of	ADP
ejpam-3545	448	16	information	information	NOUN
ejpam-3545	448	17	sciences	sciences	PROPN
ejpam-3545	448	18	,	,	PUNCT
ejpam-3545	448	19	kiev	kiev	PROPN
ejpam-3545	448	20	,	,	PUNCT
ejpam-3545	448	21	1997	1997	NUM
ejpam-3545	448	22	.	.	PUNCT
ejpam-3545	449	1	[	[	X
ejpam-3545	449	2	12	12	NUM
ejpam-3545	449	3	]	]	X
ejpam-3545	449	4	johannes	johanne	NOUN
ejpam-3545	449	5	bj	bj	VERB
ejpam-3545	449	6	bussmann	bussmann	NOUN
ejpam-3545	449	7	.	.	PUNCT
ejpam-3545	450	1	one	one	NUM
ejpam-3545	450	2	plus	plus	CCONJ
ejpam-3545	450	3	one	one	NUM
ejpam-3545	450	4	equals	equal	VERB
ejpam-3545	450	5	three	three	NUM
ejpam-3545	450	6	(	(	PUNCT
ejpam-3545	450	7	or	or	CCONJ
ejpam-3545	450	8	more	more	ADJ
ejpam-3545	450	9	?	?	PUNCT
ejpam-3545	450	10	):	):	PUNCT
ejpam-3545	450	11	combining	combine	VERB
ejpam-3545	450	12	the	the	DET
ejpam-3545	450	13	assessment	assessment	NOUN
ejpam-3545	450	14	of	of	ADP
ejpam-3545	450	15	movement	movement	NOUN
ejpam-3545	450	16	behavior	behavior	NOUN
ejpam-3545	450	17	and	and	CCONJ
ejpam-3545	450	18	subjective	subjective	ADJ
ejpam-3545	450	19	states	state	NOUN
ejpam-3545	450	20	in	in	ADP
ejpam-3545	450	21	everyday	everyday	ADJ
ejpam-3545	450	22	life	life	NOUN
ejpam-3545	450	23	.	.	PUNCT
ejpam-3545	451	1	frontiers	frontier	NOUN
ejpam-3545	451	2	in	in	ADP
ejpam-3545	451	3	psychology	psychology	NOUN
ejpam-3545	451	4	,	,	PUNCT
ejpam-3545	451	5	4:216	4:216	NUM
ejpam-3545	451	6	,	,	PUNCT
ejpam-3545	451	7	2013	2013	NUM
ejpam-3545	451	8	.	.	PUNCT
ejpam-3545	452	1	[	[	X
ejpam-3545	452	2	13	13	NUM
ejpam-3545	452	3	]	]	PUNCT
ejpam-3545	452	4	a	a	DET
ejpam-3545	452	5	cleveland	cleveland	PROPN
ejpam-3545	452	6	.	.	PUNCT
ejpam-3545	453	1	circadian	circadian	PROPN
ejpam-3545	453	2	math	math	NOUN
ejpam-3545	453	3	:	:	PUNCT
ejpam-3545	453	4	one	one	NUM
ejpam-3545	453	5	plus	plus	CCONJ
ejpam-3545	453	6	one	one	NUM
ejpam-3545	453	7	does	do	AUX
ejpam-3545	453	8	n’t	not	PART
ejpam-3545	453	9	always	always	ADV
ejpam-3545	453	10	equal	equal	VERB
ejpam-3545	453	11	two	two	NUM
ejpam-3545	453	12	.	.	PUNCT
ejpam-3545	454	1	rpi	rpi	PROPN
ejpam-3545	454	2	news	news	PROPN
ejpam-3545	454	3	,	,	PUNCT
ejpam-3545	454	4	june	june	PROPN
ejpam-3545	454	5	6	6	NUM
ejpam-3545	454	6	,	,	PUNCT
ejpam-3545	454	7	2008	2008	NUM
ejpam-3545	454	8	.	.	PUNCT
ejpam-3545	455	1	[	[	X
ejpam-3545	455	2	14	14	NUM
ejpam-3545	455	3	]	]	X
ejpam-3545	455	4	guy	guy	NOUN
ejpam-3545	455	5	cohen	cohen	PROPN
ejpam-3545	455	6	,	,	PUNCT
ejpam-3545	455	7	stéphane	stéphane	PROPN
ejpam-3545	455	8	gaubert	gaubert	NOUN
ejpam-3545	455	9	,	,	PUNCT
ejpam-3545	455	10	and	and	CCONJ
ejpam-3545	455	11	jean	jean	PROPN
ejpam-3545	455	12	-	-	PUNCT
ejpam-3545	455	13	pierre	pierre	PROPN
ejpam-3545	455	14	quadrat	quadrat	NOUN
ejpam-3545	455	15	.	.	PUNCT
ejpam-3545	456	1	max	max	PROPN
ejpam-3545	456	2	-	-	PUNCT
ejpam-3545	456	3	plus	plus	CCONJ
ejpam-3545	456	4	algebra	algebra	NOUN
ejpam-3545	456	5	and	and	CCONJ
ejpam-3545	456	6	system	system	NOUN
ejpam-3545	456	7	theory	theory	NOUN
ejpam-3545	456	8	:	:	PUNCT
ejpam-3545	456	9	where	where	SCONJ
ejpam-3545	456	10	we	we	PRON
ejpam-3545	456	11	are	be	AUX
ejpam-3545	456	12	and	and	CCONJ
ejpam-3545	456	13	where	where	SCONJ
ejpam-3545	456	14	to	to	PART
ejpam-3545	456	15	go	go	VERB
ejpam-3545	456	16	now	now	ADV
ejpam-3545	456	17	.	.	PUNCT
ejpam-3545	457	1	annual	annual	ADJ
ejpam-3545	457	2	reviews	review	NOUN
ejpam-3545	457	3	in	in	ADP
ejpam-3545	457	4	control	control	NOUN
ejpam-3545	457	5	,	,	PUNCT
ejpam-3545	457	6	23:207	23:207	NUM
ejpam-3545	457	7	–	–	PUNCT
ejpam-3545	457	8	219	219	NUM
ejpam-3545	457	9	,	,	PUNCT
ejpam-3545	457	10	1999	1999	NUM
ejpam-3545	457	11	.	.	PUNCT
ejpam-3545	458	1	[	[	X
ejpam-3545	458	2	15	15	NUM
ejpam-3545	458	3	]	]	X
ejpam-3545	458	4	lawrence	lawrence	PROPN
ejpam-3545	458	5	b	b	PROPN
ejpam-3545	458	6	cohen	cohen	PROPN
ejpam-3545	458	7	.	.	PUNCT
ejpam-3545	459	1	making	make	VERB
ejpam-3545	459	2	1	1	NUM
ejpam-3545	459	3	+	+	NUM
ejpam-3545	459	4	1=	1=	NUM
ejpam-3545	459	5	3	3	NUM
ejpam-3545	459	6	:	:	PUNCT
ejpam-3545	459	7	improving	improve	VERB
ejpam-3545	459	8	sedation	sedation	NOUN
ejpam-3545	459	9	through	through	ADP
ejpam-3545	459	10	drug	drug	NOUN
ejpam-3545	459	11	synergy	synergy	NOUN
ejpam-3545	459	12	.	.	PUNCT
ejpam-3545	460	1	gastrointestinal	gastrointestinal	ADJ
ejpam-3545	460	2	endoscopy	endoscopy	NOUN
ejpam-3545	460	3	,	,	PUNCT
ejpam-3545	460	4	73(2):215–217	73(2):215–217	NUM
ejpam-3545	460	5	,	,	PUNCT
ejpam-3545	460	6	2011	2011	NUM
ejpam-3545	460	7	.	.	PUNCT
ejpam-3545	461	1	[	[	X
ejpam-3545	461	2	16	16	NUM
ejpam-3545	461	3	]	]	PUNCT
ejpam-3545	461	4	ray	ray	NOUN
ejpam-3545	461	5	a	a	DET
ejpam-3545	461	6	cuninghame	cuninghame	NOUN
ejpam-3545	461	7	-	-	PUNCT
ejpam-3545	461	8	green	green	NOUN
ejpam-3545	461	9	.	.	PUNCT
ejpam-3545	462	1	minimax	minimax	NOUN
ejpam-3545	462	2	algebra	algebra	NOUN
ejpam-3545	462	3	and	and	CCONJ
ejpam-3545	462	4	applications	application	NOUN
ejpam-3545	462	5	.	.	PUNCT
ejpam-3545	463	1	in	in	ADP
ejpam-3545	463	2	advances	advance	NOUN
ejpam-3545	463	3	in	in	ADP
ejpam-3545	463	4	imaging	imaging	NOUN
ejpam-3545	463	5	and	and	CCONJ
ejpam-3545	463	6	electron	electron	NOUN
ejpam-3545	463	7	physics	physics	PROPN
ejpam-3545	463	8	,	,	PUNCT
ejpam-3545	463	9	volume	volume	NOUN
ejpam-3545	463	10	90	90	NUM
ejpam-3545	463	11	,	,	PUNCT
ejpam-3545	463	12	pages	page	NOUN
ejpam-3545	463	13	1–121	1–121	NUM
ejpam-3545	463	14	.	.	PUNCT
ejpam-3545	463	15	elsevier	elsevier	PROPN
ejpam-3545	463	16	,	,	PUNCT
ejpam-3545	463	17	1994	1994	NUM
ejpam-3545	463	18	.	.	PUNCT
ejpam-3545	464	1	[	[	X
ejpam-3545	464	2	17	17	NUM
ejpam-3545	464	3	]	]	X
ejpam-3545	464	4	marek	marek	PROPN
ejpam-3545	464	5	czachor	czachor	PROPN
ejpam-3545	464	6	.	.	PUNCT
ejpam-3545	465	1	relativity	relativity	NOUN
ejpam-3545	465	2	of	of	ADP
ejpam-3545	465	3	arithmetic	arithmetic	ADJ
ejpam-3545	465	4	as	as	ADP
ejpam-3545	465	5	a	a	DET
ejpam-3545	465	6	fundamental	fundamental	ADJ
ejpam-3545	465	7	symmetry	symmetry	NOUN
ejpam-3545	465	8	of	of	ADP
ejpam-3545	465	9	physics	physics	PROPN
ejpam-3545	465	10	.	.	PUNCT
ejpam-3545	466	1	quantum	quantum	PROPN
ejpam-3545	466	2	studies	study	NOUN
ejpam-3545	466	3	:	:	PUNCT
ejpam-3545	466	4	mathematics	mathematic	NOUN
ejpam-3545	466	5	and	and	CCONJ
ejpam-3545	466	6	foundations	foundation	NOUN
ejpam-3545	466	7	,	,	PUNCT
ejpam-3545	466	8	3(2):123–133	3(2):123–133	NUM
ejpam-3545	466	9	,	,	PUNCT
ejpam-3545	466	10	2016	2016	NUM
ejpam-3545	466	11	.	.	PUNCT
ejpam-3545	467	1	[	[	X
ejpam-3545	467	2	18	18	NUM
ejpam-3545	467	3	]	]	X
ejpam-3545	467	4	marek	marek	PROPN
ejpam-3545	467	5	czachor	czachor	PROPN
ejpam-3545	467	6	.	.	PUNCT
ejpam-3545	468	1	if	if	SCONJ
ejpam-3545	468	2	gravity	gravity	NOUN
ejpam-3545	468	3	is	be	AUX
ejpam-3545	468	4	geometry	geometry	NOUN
ejpam-3545	468	5	,	,	PUNCT
ejpam-3545	468	6	is	be	AUX
ejpam-3545	468	7	dark	dark	ADJ
ejpam-3545	468	8	energy	energy	NOUN
ejpam-3545	468	9	just	just	ADV
ejpam-3545	468	10	arithmetic	arithmetic	ADJ
ejpam-3545	468	11	?	?	PUNCT
ejpam-3545	469	1	international	international	ADJ
ejpam-3545	469	2	journal	journal	NOUN
ejpam-3545	469	3	of	of	ADP
ejpam-3545	469	4	theoretical	theoretical	ADJ
ejpam-3545	469	5	physics	physics	NOUN
ejpam-3545	469	6	,	,	PUNCT
ejpam-3545	469	7	56(4):1364–1381	56(4):1364–1381	PROPN
ejpam-3545	469	8	,	,	PUNCT
ejpam-3545	469	9	2017	2017	NUM
ejpam-3545	469	10	.	.	PUNCT
ejpam-3545	470	1	[	[	X
ejpam-3545	470	2	19	19	NUM
ejpam-3545	470	3	]	]	X
ejpam-3545	470	4	marek	marek	PROPN
ejpam-3545	470	5	czachor	czachor	PROPN
ejpam-3545	470	6	.	.	PUNCT
ejpam-3545	470	7	information	information	NOUN
ejpam-3545	470	8	processing	processing	NOUN
ejpam-3545	470	9	and	and	CCONJ
ejpam-3545	470	10	fechner	fechner	NOUN
ejpam-3545	470	11	’s	’s	PART
ejpam-3545	470	12	problem	problem	NOUN
ejpam-3545	470	13	as	as	ADP
ejpam-3545	470	14	a	a	DET
ejpam-3545	470	15	choice	choice	NOUN
ejpam-3545	470	16	of	of	ADP
ejpam-3545	470	17	arithmetic	arithmetic	NOUN
ejpam-3545	470	18	.	.	PUNCT
ejpam-3545	471	1	in	in	ADP
ejpam-3545	471	2	information	information	NOUN
ejpam-3545	471	3	studies	study	NOUN
ejpam-3545	471	4	and	and	CCONJ
ejpam-3545	471	5	the	the	DET
ejpam-3545	471	6	quest	quest	NOUN
ejpam-3545	471	7	for	for	ADP
ejpam-3545	471	8	transdisciplinarity	transdisciplinarity	NOUN
ejpam-3545	471	9	:	:	PUNCT
ejpam-3545	471	10	unity	unity	NOUN
ejpam-3545	471	11	through	through	ADP
ejpam-3545	471	12	diversity	diversity	NOUN
ejpam-3545	471	13	,	,	PUNCT
ejpam-3545	471	14	pages	page	NOUN
ejpam-3545	471	15	363–372	363–372	NUM
ejpam-3545	471	16	.	.	PUNCT
ejpam-3545	471	17	world	world	PROPN
ejpam-3545	471	18	scientific	scientific	ADJ
ejpam-3545	471	19	,	,	PUNCT
ejpam-3545	471	20	2017	2017	NUM
ejpam-3545	471	21	.	.	PUNCT
ejpam-3545	472	1	[	[	X
ejpam-3545	472	2	20	20	NUM
ejpam-3545	472	3	]	]	X
ejpam-3545	472	4	marek	marek	PROPN
ejpam-3545	472	5	czachor	czachor	PROPN
ejpam-3545	472	6	and	and	CCONJ
ejpam-3545	472	7	andrzej	andrzej	PROPN
ejpam-3545	472	8	posiewnik	posiewnik	PROPN
ejpam-3545	472	9	.	.	PUNCT
ejpam-3545	473	1	wavepacket	wavepacket	NOUN
ejpam-3545	473	2	of	of	ADP
ejpam-3545	473	3	the	the	DET
ejpam-3545	473	4	universe	universe	NOUN
ejpam-3545	473	5	and	and	CCONJ
ejpam-3545	473	6	its	its	PRON
ejpam-3545	473	7	spreading	spreading	NOUN
ejpam-3545	473	8	.	.	PUNCT
ejpam-3545	474	1	international	international	ADJ
ejpam-3545	474	2	journal	journal	NOUN
ejpam-3545	474	3	of	of	ADP
ejpam-3545	474	4	theoretical	theoretical	ADJ
ejpam-3545	474	5	physics	physics	NOUN
ejpam-3545	474	6	,	,	PUNCT
ejpam-3545	474	7	55(4):2001–2019	55(4):2001–2019	PROPN
ejpam-3545	474	8	,	,	PUNCT
ejpam-3545	474	9	2016	2016	NUM
ejpam-3545	474	10	.	.	PUNCT
ejpam-3545	475	1	[	[	X
ejpam-3545	475	2	21	21	NUM
ejpam-3545	475	3	]	]	X
ejpam-3545	475	4	philip	philip	PROPN
ejpam-3545	475	5	davis	davis	PROPN
ejpam-3545	475	6	and	and	CCONJ
ejpam-3545	475	7	reuben	reuben	PROPN
ejpam-3545	475	8	hersh	hersh	PROPN
ejpam-3545	475	9	.	.	PUNCT
ejpam-3545	476	1	the	the	DET
ejpam-3545	476	2	mathematical	mathematical	ADJ
ejpam-3545	476	3	experience	experience	NOUN
ejpam-3545	476	4	.	.	PUNCT
ejpam-3545	477	1	birkhauser	birkhauser	PROPN
ejpam-3545	477	2	,	,	PUNCT
ejpam-3545	477	3	boston	boston	PROPN
ejpam-3545	477	4	,	,	PUNCT
ejpam-3545	477	5	mass	mass	PROPN
ejpam-3545	477	6	.	.	PROPN
ejpam-3545	477	7	,	,	PUNCT
ejpam-3545	477	8	1981	1981	NUM
ejpam-3545	477	9	.	.	PUNCT
ejpam-3545	478	1	[	[	X
ejpam-3545	478	2	22	22	NUM
ejpam-3545	478	3	]	]	X
ejpam-3545	478	4	philip	philip	PROPN
ejpam-3545	478	5	j	j	PROPN
ejpam-3545	478	6	davis	davis	PROPN
ejpam-3545	478	7	.	.	PUNCT
ejpam-3545	479	1	fidelity	fidelity	PROPN
ejpam-3545	479	2	in	in	ADP
ejpam-3545	479	3	mathematical	mathematical	ADJ
ejpam-3545	479	4	discourse	discourse	NOUN
ejpam-3545	479	5	:	:	PUNCT
ejpam-3545	479	6	is	be	AUX
ejpam-3545	479	7	one	one	NUM
ejpam-3545	479	8	and	and	CCONJ
ejpam-3545	479	9	one	one	NUM
ejpam-3545	479	10	really	really	ADV
ejpam-3545	479	11	two	two	NUM
ejpam-3545	479	12	?	?	PUNCT
ejpam-3545	480	1	the	the	DET
ejpam-3545	480	2	american	american	PROPN
ejpam-3545	480	3	mathematical	mathematical	PROPN
ejpam-3545	480	4	monthly	monthly	ADV
ejpam-3545	480	5	,	,	PUNCT
ejpam-3545	480	6	79(3):252–263	79(3):252–263	PROPN
ejpam-3545	480	7	,	,	PUNCT
ejpam-3545	480	8	1972	1972	NUM
ejpam-3545	480	9	.	.	PUNCT
ejpam-3545	481	1	[	[	X
ejpam-3545	481	2	23	23	NUM
ejpam-3545	481	3	]	]	X
ejpam-3545	481	4	bruno	bruno	PROPN
ejpam-3545	481	5	de	de	PROPN
ejpam-3545	481	6	finetti	finetti	PROPN
ejpam-3545	481	7	.	.	PUNCT
ejpam-3545	482	1	sul	sul	PROPN
ejpam-3545	482	2	concetto	concetto	PROPN
ejpam-3545	482	3	di	di	NOUN
ejpam-3545	482	4	media	medium	NOUN
ejpam-3545	482	5	.	.	PUNCT
ejpam-3545	483	1	istituto	istituto	ADJ
ejpam-3545	483	2	italiano	italiano	PROPN
ejpam-3545	483	3	degli	degli	NOUN
ejpam-3545	483	4	attuari	attuari	NOUN
ejpam-3545	483	5	,	,	PUNCT
ejpam-3545	483	6	1931	1931	NUM
ejpam-3545	483	7	.	.	PUNCT
ejpam-3545	484	1	[	[	X
ejpam-3545	484	2	24	24	NUM
ejpam-3545	484	3	]	]	PUNCT
ejpam-3545	484	4	jan	jan	PROPN
ejpam-3545	484	5	derboven	derboven	PROPN
ejpam-3545	484	6	.	.	PUNCT
ejpam-3545	485	1	one	one	NUM
ejpam-3545	485	2	plus	plus	CCONJ
ejpam-3545	485	3	one	one	NUM
ejpam-3545	485	4	equals	equal	VERB
ejpam-3545	485	5	three	three	NUM
ejpam-3545	485	6	:	:	PUNCT
ejpam-3545	485	7	eye	eye	NOUN
ejpam-3545	485	8	-	-	PUNCT
ejpam-3545	485	9	tracking	tracking	NOUN
ejpam-3545	485	10	and	and	CCONJ
ejpam-3545	485	11	semiotics	semiotic	NOUN
ejpam-3545	485	12	as	as	ADP
ejpam-3545	485	13	complementary	complementary	ADJ
ejpam-3545	485	14	methods	method	NOUN
ejpam-3545	485	15	in	in	ADP
ejpam-3545	485	16	hci	hci	NOUN
ejpam-3545	485	17	.	.	PUNCT
ejpam-3545	486	1	in	in	ADP
ejpam-3545	486	2	ccid2	ccid2	PROPN
ejpam-3545	486	3	:	:	PUNCT
ejpam-3545	486	4	the	the	DET
ejpam-3545	486	5	second	second	ADJ
ejpam-3545	486	6	international	international	ADJ
ejpam-3545	486	7	symposium	symposium	NOUN
ejpam-3545	486	8	on	on	ADP
ejpam-3545	486	9	culture	culture	NOUN
ejpam-3545	486	10	,	,	PUNCT
ejpam-3545	486	11	creativity	creativity	NOUN
ejpam-3545	486	12	,	,	PUNCT
ejpam-3545	486	13	and	and	CCONJ
ejpam-3545	486	14	interaction	interaction	NOUN
ejpam-3545	486	15	design	design	NOUN
ejpam-3545	486	16	,	,	PUNCT
ejpam-3545	486	17	location	location	NOUN
ejpam-3545	486	18	:	:	PUNCT
ejpam-3545	486	19	newcastle	newcastle	PROPN
ejpam-3545	486	20	,	,	PUNCT
ejpam-3545	486	21	uk	uk	PROPN
ejpam-3545	486	22	,	,	PUNCT
ejpam-3545	486	23	2011	2011	NUM
ejpam-3545	486	24	.	.	PUNCT
ejpam-3545	487	1	references	reference	NOUN
ejpam-3545	487	2	1807	1807	NUM
ejpam-3545	487	3	[	[	X
ejpam-3545	487	4	25	25	NUM
ejpam-3545	487	5	]	]	X
ejpam-3545	487	6	e	e	X
ejpam-3545	487	7	enge	enge	PROPN
ejpam-3545	487	8	.	.	PUNCT
ejpam-3545	488	1	seo	seo	NOUN
ejpam-3545	488	2	and	and	CCONJ
ejpam-3545	488	3	social	social	ADJ
ejpam-3545	488	4	:	:	PUNCT
ejpam-3545	488	5	1	1	NUM
ejpam-3545	488	6	+	+	SYM
ejpam-3545	488	7	1	1	NUM
ejpam-3545	488	8	=	=	SYM
ejpam-3545	488	9	3	3	NUM
ejpam-3545	488	10	,	,	PUNCT
ejpam-3545	488	11	searchengineland	searchengineland	NOUN
ejpam-3545	488	12	,	,	PUNCT
ejpam-3545	488	13	2017	2017	NUM
ejpam-3545	488	14	.	.	PUNCT
ejpam-3545	489	1	[	[	X
ejpam-3545	489	2	26	26	NUM
ejpam-3545	489	3	]	]	X
ejpam-3545	489	4	alex	alex	PROPN
ejpam-3545	489	5	frame	frame	PROPN
ejpam-3545	489	6	and	and	CCONJ
ejpam-3545	489	7	paul	paul	PROPN
ejpam-3545	489	8	meredith	meredith	PROPN
ejpam-3545	489	9	.	.	PUNCT
ejpam-3545	490	1	chapter	chapter	PROPN
ejpam-3545	490	2	sixteen	sixteen	PROPN
ejpam-3545	490	3	.	.	PUNCT
ejpam-3545	491	1	one	one	NUM
ejpam-3545	491	2	plus	plus	CCONJ
ejpam-3545	491	3	one	one	NUM
ejpam-3545	491	4	equals	equal	VERB
ejpam-3545	491	5	three	three	NUM
ejpam-3545	491	6	:	:	PUNCT
ejpam-3545	491	7	legal	legal	ADJ
ejpam-3545	491	8	hybridity	hybridity	NOUN
ejpam-3545	491	9	in	in	ADP
ejpam-3545	491	10	aotearoa	aotearoa	PROPN
ejpam-3545	491	11	/	/	SYM
ejpam-3545	491	12	new	new	PROPN
ejpam-3545	491	13	zealand	zealand	PROPN
ejpam-3545	491	14	.	.	PUNCT
ejpam-3545	492	1	in	in	ADP
ejpam-3545	492	2	hybrid	hybrid	ADJ
ejpam-3545	492	3	identities	identity	NOUN
ejpam-3545	492	4	,	,	PUNCT
ejpam-3545	492	5	pages	page	NOUN
ejpam-3545	492	6	313–332	313–332	NUM
ejpam-3545	492	7	.	.	PUNCT
ejpam-3545	493	1	brill	brill	PROPN
ejpam-3545	493	2	,	,	PUNCT
ejpam-3545	493	3	2008	2008	NUM
ejpam-3545	493	4	.	.	PUNCT
ejpam-3545	494	1	[	[	X
ejpam-3545	494	2	27	27	NUM
ejpam-3545	494	3	]	]	X
ejpam-3545	494	4	laszlo	laszlo	ADJ
ejpam-3545	494	5	fuchs	fuch	NOUN
ejpam-3545	494	6	.	.	PUNCT
ejpam-3545	495	1	partially	partially	ADV
ejpam-3545	495	2	ordered	order	VERB
ejpam-3545	495	3	algebraic	algebraic	ADJ
ejpam-3545	495	4	systems	system	NOUN
ejpam-3545	495	5	.	.	PUNCT
ejpam-3545	496	1	pergamon	pergamon	PROPN
ejpam-3545	496	2	press	press	PROPN
ejpam-3545	496	3	,	,	PUNCT
ejpam-3545	496	4	oxford	oxford	PROPN
ejpam-3545	496	5	/	/	SYM
ejpam-3545	496	6	london	london	PROPN
ejpam-3545	496	7	/	/	SYM
ejpam-3545	496	8	new	new	PROPN
ejpam-3545	496	9	york	york	PROPN
ejpam-3545	496	10	/	/	SYM
ejpam-3545	496	11	paris	paris	PROPN
ejpam-3545	496	12	,	,	PUNCT
ejpam-3545	496	13	1963	1963	NUM
ejpam-3545	496	14	.	.	PUNCT
ejpam-3545	497	1	[	[	X
ejpam-3545	497	2	28	28	NUM
ejpam-3545	497	3	]	]	X
ejpam-3545	497	4	martin	martin	PROPN
ejpam-3545	497	5	gardner	gardner	PROPN
ejpam-3545	497	6	.	.	PUNCT
ejpam-3545	498	1	review	review	NOUN
ejpam-3545	498	2	of	of	ADP
ejpam-3545	498	3	science	science	NOUN
ejpam-3545	498	4	in	in	ADP
ejpam-3545	498	5	the	the	DET
ejpam-3545	498	6	looking	look	VERB
ejpam-3545	498	7	glass	glass	NOUN
ejpam-3545	498	8	:	:	PUNCT
ejpam-3545	498	9	what	what	PRON
ejpam-3545	498	10	do	do	AUX
ejpam-3545	498	11	scientists	scientist	NOUN
ejpam-3545	498	12	really	really	ADV
ejpam-3545	498	13	know	know	VERB
ejpam-3545	498	14	?	?	PUNCT
ejpam-3545	499	1	by	by	ADP
ejpam-3545	499	2	e.	e.	PROPN
ejpam-3545	499	3	brian	brian	PROPN
ejpam-3545	499	4	davies	davies	PROPN
ejpam-3545	499	5	(	(	PUNCT
ejpam-3545	499	6	oxford	oxford	PROPN
ejpam-3545	499	7	university	university	PROPN
ejpam-3545	499	8	press	press	NOUN
ejpam-3545	499	9	,	,	PUNCT
ejpam-3545	499	10	2003	2003	NUM
ejpam-3545	499	11	)	)	PUNCT
ejpam-3545	499	12	.	.	PUNCT
ejpam-3545	500	1	notices	notice	NOUN
ejpam-3545	500	2	of	of	ADP
ejpam-3545	500	3	the	the	DET
ejpam-3545	500	4	american	american	PROPN
ejpam-3545	500	5	mathematical	mathematical	PROPN
ejpam-3545	500	6	society	society	NOUN
ejpam-3545	500	7	,	,	PUNCT
ejpam-3545	500	8	v.52	v.52	PROPN
ejpam-3545	500	9	,	,	PUNCT
ejpam-3545	500	10	no	no	INTJ
ejpam-3545	500	11	.	.	PUNCT
ejpam-3545	501	1	11,2005	11,2005	NUM
ejpam-3545	501	2	.	.	PUNCT
ejpam-3545	502	1	[	[	X
ejpam-3545	502	2	29	29	NUM
ejpam-3545	502	3	]	]	SYM
ejpam-3545	502	4	dat	dat	ADJ
ejpam-3545	502	5	gasking	gasking	NOUN
ejpam-3545	502	6	.	.	PUNCT
ejpam-3545	503	1	mathematics	mathematic	NOUN
ejpam-3545	503	2	and	and	CCONJ
ejpam-3545	503	3	the	the	DET
ejpam-3545	503	4	world	world	NOUN
ejpam-3545	503	5	.	.	PUNCT
ejpam-3545	504	1	the	the	DET
ejpam-3545	504	2	australasian	australasian	ADJ
ejpam-3545	504	3	journal	journal	NOUN
ejpam-3545	504	4	of	of	ADP
ejpam-3545	504	5	psychology	psychology	NOUN
ejpam-3545	504	6	and	and	CCONJ
ejpam-3545	504	7	philosophy	philosophy	NOUN
ejpam-3545	504	8	,	,	PUNCT
ejpam-3545	504	9	18(2):97–116	18(2):97–116	NUM
ejpam-3545	504	10	,	,	PUNCT
ejpam-3545	504	11	1940	1940	NUM
ejpam-3545	504	12	.	.	PUNCT
ejpam-3545	505	1	[	[	X
ejpam-3545	505	2	30	30	NUM
ejpam-3545	505	3	]	]	X
ejpam-3545	505	4	a	a	DET
ejpam-3545	505	5	glyn	glyn	NOUN
ejpam-3545	505	6	.	.	PUNCT
ejpam-3545	506	1	one	one	NUM
ejpam-3545	506	2	plus	plus	CCONJ
ejpam-3545	506	3	one	one	NUM
ejpam-3545	506	4	equals	equal	VERB
ejpam-3545	506	5	three	three	NUM
ejpam-3545	506	6	—	—	PUNCT
ejpam-3545	506	7	the	the	DET
ejpam-3545	506	8	power	power	NOUN
ejpam-3545	506	9	of	of	ADP
ejpam-3545	506	10	data	datum	NOUN
ejpam-3545	506	11	combinations	combination	NOUN
ejpam-3545	506	12	.	.	PUNCT
ejpam-3545	507	1	luciad	luciad	PROPN
ejpam-3545	507	2	,	,	PUNCT
ejpam-3545	507	3	30	30	NUM
ejpam-3545	507	4	nov	nov	PROPN
ejpam-3545	507	5	2017	2017	NUM
ejpam-3545	507	6	.	.	PUNCT
ejpam-3545	508	1	[	[	X
ejpam-3545	508	2	31	31	NUM
ejpam-3545	508	3	]	]	X
ejpam-3545	508	4	jonathan	jonathan	PROPN
ejpam-3545	508	5	s	s	PROPN
ejpam-3545	508	6	golan	golan	PROPN
ejpam-3545	508	7	.	.	PUNCT
ejpam-3545	509	1	semirings	semiring	NOUN
ejpam-3545	509	2	and	and	CCONJ
ejpam-3545	509	3	affine	affine	PROPN
ejpam-3545	509	4	equations	equation	NOUN
ejpam-3545	509	5	over	over	ADP
ejpam-3545	509	6	them	they	PRON
ejpam-3545	509	7	.	.	PUNCT
ejpam-3545	510	1	springer	springer	NOUN
ejpam-3545	510	2	science	science	PROPN
ejpam-3545	510	3	&	&	CCONJ
ejpam-3545	510	4	business	business	NOUN
ejpam-3545	510	5	media	medium	NOUN
ejpam-3545	510	6	,	,	PUNCT
ejpam-3545	510	7	new	new	PROPN
ejpam-3545	510	8	york	york	PROPN
ejpam-3545	510	9	,	,	PUNCT
ejpam-3545	510	10	2003	2003	NUM
ejpam-3545	510	11	.	.	PUNCT
ejpam-3545	511	1	[	[	X
ejpam-3545	511	2	32	32	NUM
ejpam-3545	511	3	]	]	PUNCT
ejpam-3545	511	4	m	m	VERB
ejpam-3545	511	5	gondran	gondran	NOUN
ejpam-3545	511	6	and	and	CCONJ
ejpam-3545	511	7	m	m	PROPN
ejpam-3545	511	8	minoux	minoux	NOUN
ejpam-3545	511	9	.	.	PUNCT
ejpam-3545	512	1	graphes	graphe	NOUN
ejpam-3545	512	2	et	et	PROPN
ejpam-3545	512	3	algorithmes	algorithme	NOUN
ejpam-3545	512	4	.	.	PUNCT
ejpam-3545	513	1	editions	edition	NOUN
ejpam-3545	513	2	eyrolles	eyrolle	NOUN
ejpam-3545	513	3	,	,	PUNCT
ejpam-3545	513	4	paris	paris	PROPN
ejpam-3545	513	5	,	,	PUNCT
ejpam-3545	513	6	1979	1979	NUM
ejpam-3545	513	7	.	.	PUNCT
ejpam-3545	514	1	[	[	X
ejpam-3545	514	2	33	33	NUM
ejpam-3545	514	3	]	]	PUNCT
ejpam-3545	514	4	a	a	DET
ejpam-3545	514	5	gottlieb	gottlieb	PROPN
ejpam-3545	514	6	.	.	PUNCT
ejpam-3545	514	7	’	'	PUNCT
ejpam-3545	515	1	1	1	NUM
ejpam-3545	515	2	+	+	SYM
ejpam-3545	515	3	1	1	NUM
ejpam-3545	515	4	=	=	SYM
ejpam-3545	515	5	3	3	NUM
ejpam-3545	515	6	’	'	PUNCT
ejpam-3545	515	7	:	:	PUNCT
ejpam-3545	515	8	the	the	DET
ejpam-3545	515	9	synergy	synergy	NOUN
ejpam-3545	515	10	between	between	ADP
ejpam-3545	515	11	the	the	DET
ejpam-3545	515	12	new	new	ADJ
ejpam-3545	515	13	key	key	ADJ
ejpam-3545	515	14	technologies	technology	NOUN
ejpam-3545	515	15	,	,	PUNCT
ejpam-3545	515	16	nextgeneration	nextgeneration	NOUN
ejpam-3545	515	17	enterprise	enterprise	NOUN
ejpam-3545	515	18	wans	wan	NOUN
ejpam-3545	515	19	.	.	PUNCT
ejpam-3545	516	1	network	network	NOUN
ejpam-3545	516	2	world	world	NOUN
ejpam-3545	516	3	,	,	PUNCT
ejpam-3545	516	4	july	july	PROPN
ejpam-3545	516	5	15	15	NUM
ejpam-3545	516	6	,	,	PUNCT
ejpam-3545	516	7	2013	2013	NUM
ejpam-3545	516	8	.	.	PUNCT
ejpam-3545	517	1	[	[	X
ejpam-3545	517	2	34	34	NUM
ejpam-3545	517	3	]	]	X
ejpam-3545	517	4	m	m	VERB
ejpam-3545	517	5	grant	grant	NOUN
ejpam-3545	517	6	and	and	CCONJ
ejpam-3545	517	7	c	c	PROPN
ejpam-3545	517	8	johnston	johnston	PROPN
ejpam-3545	517	9	.	.	PUNCT
ejpam-3545	518	1	1	1	NUM
ejpam-3545	519	1	+	+	SYM
ejpam-3545	519	2	1	1	NUM
ejpam-3545	519	3	=	=	SYM
ejpam-3545	519	4	3	3	NUM
ejpam-3545	519	5	:	:	PUNCT
ejpam-3545	519	6	cmo	cmo	PROPN
ejpam-3545	519	7	&	&	CCONJ
ejpam-3545	519	8	cio	cio	PROPN
ejpam-3545	519	9	cio	cio	PROPN
ejpam-3545	519	10	collaboration	collaboration	PROPN
ejpam-3545	519	11	best	good	ADJ
ejpam-3545	519	12	practices	practice	NOUN
ejpam-3545	519	13	that	that	PRON
ejpam-3545	519	14	drive	drive	VERB
ejpam-3545	519	15	growth	growth	NOUN
ejpam-3545	519	16	.	.	PUNCT
ejpam-3545	520	1	canadian	canadian	ADJ
ejpam-3545	520	2	marketing	marketing	PROPN
ejpam-3545	520	3	association	association	PROPN
ejpam-3545	520	4	,	,	PUNCT
ejpam-3545	520	5	don	don	PROPN
ejpam-3545	520	6	mills	mill	NOUN
ejpam-3545	520	7	,	,	PUNCT
ejpam-3545	520	8	canada	canada	PROPN
ejpam-3545	520	9	,	,	PUNCT
ejpam-3545	520	10	2013	2013	NUM
ejpam-3545	520	11	.	.	PUNCT
ejpam-3545	521	1	[	[	X
ejpam-3545	521	2	35	35	NUM
ejpam-3545	521	3	]	]	X
ejpam-3545	521	4	gh	gh	PROPN
ejpam-3545	521	5	hardy	hardy	PROPN
ejpam-3545	521	6	,	,	PUNCT
ejpam-3545	521	7	je	je	PROPN
ejpam-3545	521	8	littlewood	littlewood	PROPN
ejpam-3545	521	9	,	,	PUNCT
ejpam-3545	521	10	and	and	CCONJ
ejpam-3545	521	11	g	g	PROPN
ejpam-3545	521	12	pólya	pólya	PROPN
ejpam-3545	521	13	.	.	PUNCT
ejpam-3545	522	1	inequalities	inequality	NOUN
ejpam-3545	522	2	.	.	PUNCT
ejpam-3545	523	1	cambridge	cambridge	PROPN
ejpam-3545	523	2	university	university	PROPN
ejpam-3545	523	3	press	press	PROPN
ejpam-3545	523	4	,	,	PUNCT
ejpam-3545	523	5	cambridge	cambridge	PROPN
ejpam-3545	523	6	,	,	PUNCT
ejpam-3545	523	7	1934	1934	NUM
ejpam-3545	523	8	.	.	PUNCT
ejpam-3545	524	1	[	[	X
ejpam-3545	524	2	36	36	NUM
ejpam-3545	524	3	]	]	X
ejpam-3545	524	4	h	h	NOUN
ejpam-3545	524	5	herrlich	herrlich	PROPN
ejpam-3545	524	6	and	and	CCONJ
ejpam-3545	524	7	g.e	g.e	PROPN
ejpam-3545	524	8	.	.	PROPN
ejpam-3545	524	9	strecker	strecker	PROPN
ejpam-3545	524	10	.	.	PUNCT
ejpam-3545	525	1	category	category	PROPN
ejpam-3545	525	2	theory	theory	NOUN
ejpam-3545	525	3	.	.	PUNCT
ejpam-3545	526	1	allyn	allyn	PROPN
ejpam-3545	526	2	and	and	CCONJ
ejpam-3545	526	3	bacon	bacon	PROPN
ejpam-3545	526	4	inc	inc	PROPN
ejpam-3545	526	5	.	.	PROPN
ejpam-3545	526	6	,	,	PUNCT
ejpam-3545	526	7	boston	boston	PROPN
ejpam-3545	526	8	,	,	PUNCT
ejpam-3545	526	9	1973	1973	NUM
ejpam-3545	526	10	.	.	PUNCT
ejpam-3545	527	1	[	[	X
ejpam-3545	527	2	37	37	NUM
ejpam-3545	527	3	]	]	PUNCT
ejpam-3545	527	4	dale	dale	NOUN
ejpam-3545	527	5	husemoller	husemoller	NOUN
ejpam-3545	527	6	.	.	PUNCT
ejpam-3545	527	7	fibre	fibre	NOUN
ejpam-3545	527	8	bundles	bundle	NOUN
ejpam-3545	527	9	.	.	PUNCT
ejpam-3545	528	1	springer	springer	NOUN
ejpam-3545	528	2	verlag	verlag	PROPN
ejpam-3545	528	3	,	,	PUNCT
ejpam-3545	528	4	berlin	berlin	PROPN
ejpam-3545	528	5	/	/	SYM
ejpam-3545	528	6	new	new	PROPN
ejpam-3545	528	7	york	york	PROPN
ejpam-3545	528	8	,	,	PUNCT
ejpam-3545	528	9	1994	1994	NUM
ejpam-3545	528	10	.	.	PUNCT
ejpam-3545	529	1	[	[	X
ejpam-3545	529	2	38	38	NUM
ejpam-3545	529	3	]	]	SYM
ejpam-3545	529	4	b	b	PROPN
ejpam-3545	529	5	jude	jude	PROPN
ejpam-3545	529	6	.	.	PUNCT
ejpam-3545	529	7	synergy	synergy	NOUN
ejpam-3545	529	8	1	1	NUM
ejpam-3545	530	1	+	+	CCONJ
ejpam-3545	530	2	1	1	NUM
ejpam-3545	530	3	=	=	SYM
ejpam-3545	530	4	3	3	NUM
ejpam-3545	530	5	.	.	PUNCT
ejpam-3545	531	1	https://www.linkedin.com/pulse/	https://www.linkedin.com/pulse/	NOUN
ejpam-3545	531	2	20140820054514	20140820054514	NUM
ejpam-3545	531	3	-	-	SYM
ejpam-3545	531	4	115081853	115081853	NUM
ejpam-3545	531	5	-	-	PUNCT
ejpam-3545	531	6	synergy-1	synergy-1	NUM
ejpam-3545	531	7	-	-	PUNCT
ejpam-3545	531	8	1	1	NUM
ejpam-3545	531	9	-	-	SYM
ejpam-3545	531	10	3	3	NUM
ejpam-3545	531	11	,	,	PUNCT
ejpam-3545	531	12	aug	aug	PROPN
ejpam-3545	531	13	20	20	NUM
ejpam-3545	531	14	,	,	PUNCT
ejpam-3545	531	15	2014	2014	NUM
ejpam-3545	531	16	,	,	PUNCT
ejpam-3545	531	17	.	.	PUNCT
ejpam-3545	532	1	[	[	X
ejpam-3545	532	2	39	39	NUM
ejpam-3545	532	3	]	]	PUNCT
ejpam-3545	532	4	stephen	stephen	PROPN
ejpam-3545	532	5	cole	cole	PROPN
ejpam-3545	532	6	kleene	kleene	PROPN
ejpam-3545	532	7	.	.	PUNCT
ejpam-3545	533	1	representation	representation	NOUN
ejpam-3545	533	2	of	of	ADP
ejpam-3545	533	3	events	event	NOUN
ejpam-3545	533	4	in	in	ADP
ejpam-3545	533	5	nerve	nerve	NOUN
ejpam-3545	533	6	sets	set	NOUN
ejpam-3545	533	7	and	and	CCONJ
ejpam-3545	533	8	finite	finite	ADJ
ejpam-3545	533	9	automata	automata	NOUN
ejpam-3545	533	10	.	.	PUNCT
ejpam-3545	534	1	automata	automata	PROPN
ejpam-3545	534	2	studies	study	NOUN
ejpam-3545	534	3	,	,	PUNCT
ejpam-3545	534	4	pages	page	NOUN
ejpam-3545	534	5	3–40	3–40	PROPN
ejpam-3545	534	6	,	,	PUNCT
ejpam-3545	534	7	1956	1956	NUM
ejpam-3545	534	8	.	.	PUNCT
ejpam-3545	535	1	[	[	X
ejpam-3545	535	2	40	40	NUM
ejpam-3545	535	3	]	]	PUNCT
ejpam-3545	535	4	emerson	emerson	PROPN
ejpam-3545	535	5	klees	klees	PROPN
ejpam-3545	535	6	.	.	PUNCT
ejpam-3545	536	1	one	one	NUM
ejpam-3545	536	2	plus	plus	CCONJ
ejpam-3545	536	3	one	one	NUM
ejpam-3545	536	4	equals	equal	VERB
ejpam-3545	536	5	three	three	NUM
ejpam-3545	536	6	pairing	pair	VERB
ejpam-3545	536	7	man	man	NOUN
ejpam-3545	536	8	/	/	SYM
ejpam-3545	536	9	woman	woman	NOUN
ejpam-3545	536	10	strengths	strength	NOUN
ejpam-3545	536	11	:	:	PUNCT
ejpam-3545	536	12	role	role	NOUN
ejpam-3545	536	13	models	model	NOUN
ejpam-3545	536	14	of	of	ADP
ejpam-3545	536	15	teamwork	teamwork	NOUN
ejpam-3545	536	16	(	(	PUNCT
ejpam-3545	536	17	the	the	DET
ejpam-3545	536	18	role	role	NOUN
ejpam-3545	536	19	models	model	NOUN
ejpam-3545	536	20	of	of	ADP
ejpam-3545	536	21	human	human	ADJ
ejpam-3545	536	22	values	value	NOUN
ejpam-3545	536	23	series	series	NOUN
ejpam-3545	536	24	,	,	PUNCT
ejpam-3545	536	25	vol	vol	NOUN
ejpam-3545	536	26	.	.	PROPN
ejpam-3545	536	27	1	1	NUM
ejpam-3545	536	28	)	)	PUNCT
ejpam-3545	536	29	.	.	PUNCT
ejpam-3545	537	1	cameo	cameo	NOUN
ejpam-3545	537	2	press	press	PROPN
ejpam-3545	537	3	,	,	PUNCT
ejpam-3545	537	4	new	new	PROPN
ejpam-3545	537	5	york	york	PROPN
ejpam-3545	537	6	,	,	PUNCT
ejpam-3545	537	7	2006	2006	NUM
ejpam-3545	537	8	.	.	PUNCT
ejpam-3545	538	1	[	[	X
ejpam-3545	538	2	41	41	NUM
ejpam-3545	538	3	]	]	PUNCT
ejpam-3545	538	4	morris	morris	PROPN
ejpam-3545	538	5	kline	kline	PROPN
ejpam-3545	538	6	.	.	PUNCT
ejpam-3545	539	1	mathematics	mathematics	PROPN
ejpam-3545	539	2	for	for	ADP
ejpam-3545	539	3	the	the	DET
ejpam-3545	539	4	nonmathematician	nonmathematician	PROPN
ejpam-3545	539	5	.	.	PUNCT
ejpam-3545	540	1	dover	dover	PROPN
ejpam-3545	540	2	publications	publication	NOUN
ejpam-3545	540	3	,	,	PUNCT
ejpam-3545	540	4	new	new	PROPN
ejpam-3545	540	5	york	york	PROPN
ejpam-3545	540	6	,	,	PUNCT
ejpam-3545	540	7	1967	1967	NUM
ejpam-3545	540	8	.	.	PUNCT
ejpam-3545	541	1	references	reference	NOUN
ejpam-3545	541	2	1808	1808	NUM
ejpam-3545	541	3	[	[	X
ejpam-3545	541	4	42	42	NUM
ejpam-3545	541	5	]	]	PUNCT
ejpam-3545	541	6	morris	morris	PROPN
ejpam-3545	541	7	kline	kline	PROPN
ejpam-3545	541	8	.	.	PUNCT
ejpam-3545	542	1	mathematics	mathematic	NOUN
ejpam-3545	542	2	:	:	PUNCT
ejpam-3545	542	3	the	the	DET
ejpam-3545	542	4	loss	loss	NOUN
ejpam-3545	542	5	of	of	ADP
ejpam-3545	542	6	certainty	certainty	NOUN
ejpam-3545	542	7	.	.	PUNCT
ejpam-3545	543	1	oxford	oxford	PROPN
ejpam-3545	543	2	university	university	PROPN
ejpam-3545	543	3	press	press	NOUN
ejpam-3545	543	4	,	,	PUNCT
ejpam-3545	543	5	new	new	PROPN
ejpam-3545	543	6	york	york	PROPN
ejpam-3545	543	7	,	,	PUNCT
ejpam-3545	543	8	1980	1980	NUM
ejpam-3545	543	9	.	.	PUNCT
ejpam-3545	544	1	[	[	X
ejpam-3545	544	2	43	43	NUM
ejpam-3545	544	3	]	]	PUNCT
ejpam-3545	544	4	andrey	andrey	PROPN
ejpam-3545	544	5	nikolaevich	nikolaevich	PROPN
ejpam-3545	544	6	kolmogorov	kolmogorov	PROPN
ejpam-3545	544	7	.	.	PUNCT
ejpam-3545	545	1	sur	sur	PROPN
ejpam-3545	545	2	la	la	PROPN
ejpam-3545	545	3	notion	notion	PROPN
ejpam-3545	545	4	de	de	X
ejpam-3545	545	5	la	la	PROPN
ejpam-3545	545	6	moyenne	moyenne	PROPN
ejpam-3545	545	7	.	.	PUNCT
ejpam-3545	546	1	atti	atti	PROPN
ejpam-3545	546	2	accad	accad	PROPN
ejpam-3545	546	3	.	.	PUNCT
ejpam-3545	547	1	naz.lincei	naz.lincei	NOUN
ejpam-3545	547	2	,	,	PUNCT
ejpam-3545	547	3	12:388–391	12:388–391	NUM
ejpam-3545	547	4	,	,	PUNCT
ejpam-3545	547	5	1930	1930	NUM
ejpam-3545	547	6	.	.	PUNCT
ejpam-3545	548	1	[	[	X
ejpam-3545	548	2	44	44	NUM
ejpam-3545	548	3	]	]	X
ejpam-3545	548	4	vasily	vasily	NOUN
ejpam-3545	548	5	kolokoltsov	kolokoltsov	NOUN
ejpam-3545	548	6	and	and	CCONJ
ejpam-3545	548	7	victor	victor	PROPN
ejpam-3545	548	8	p	p	PROPN
ejpam-3545	548	9	maslov	maslov	PROPN
ejpam-3545	548	10	.	.	PUNCT
ejpam-3545	549	1	idempotent	idempotent	ADJ
ejpam-3545	549	2	analysis	analysis	NOUN
ejpam-3545	549	3	and	and	CCONJ
ejpam-3545	549	4	its	its	PRON
ejpam-3545	549	5	applications	application	NOUN
ejpam-3545	549	6	,	,	PUNCT
ejpam-3545	549	7	volume	volume	NOUN
ejpam-3545	549	8	401	401	NUM
ejpam-3545	549	9	.	.	PUNCT
ejpam-3545	550	1	springer	springer	PROPN
ejpam-3545	550	2	science	science	PROPN
ejpam-3545	550	3	&	&	CCONJ
ejpam-3545	550	4	business	business	NOUN
ejpam-3545	550	5	media	medium	NOUN
ejpam-3545	550	6	,	,	PUNCT
ejpam-3545	550	7	1997	1997	NUM
ejpam-3545	550	8	.	.	PUNCT
ejpam-3545	551	1	[	[	X
ejpam-3545	551	2	45	45	NUM
ejpam-3545	551	3	]	]	PUNCT
ejpam-3545	551	4	s	s	PROPN
ejpam-3545	551	5	kress	kress	PROPN
ejpam-3545	551	6	.	.	PUNCT
ejpam-3545	552	1	synergy	synergy	NOUN
ejpam-3545	552	2	:	:	PUNCT
ejpam-3545	552	3	when	when	SCONJ
ejpam-3545	552	4	one	one	NUM
ejpam-3545	552	5	plus	plus	CCONJ
ejpam-3545	552	6	one	one	NUM
ejpam-3545	552	7	equals	equal	VERB
ejpam-3545	552	8	three	three	NUM
ejpam-3545	552	9	.	.	PUNCT
ejpam-3545	553	1	http://www	http://www	PROPN
ejpam-3545	553	2	.	.	PUNCT
ejpam-3545	553	3	summitteambuilding.com/synergy-when-one-plus-one-equals-three	summitteambuilding.com/synergy-when-one-plus-one-equals-three	PROPN
ejpam-3545	553	4	,	,	PUNCT
ejpam-3545	553	5	2015	2015	NUM
ejpam-3545	553	6	.	.	PUNCT
ejpam-3545	554	1	[	[	X
ejpam-3545	554	2	46	46	NUM
ejpam-3545	554	3	]	]	X
ejpam-3545	554	4	matthias	matthias	PROPN
ejpam-3545	554	5	kroiss	kroiss	PROPN
ejpam-3545	554	6	,	,	PUNCT
ejpam-3545	554	7	utz	utz	PROPN
ejpam-3545	554	8	fischer	fischer	PROPN
ejpam-3545	554	9	,	,	PUNCT
ejpam-3545	554	10	and	and	CCONJ
ejpam-3545	554	11	jörg	jörg	NUM
ejpam-3545	554	12	schultz	schultz	PROPN
ejpam-3545	554	13	.	.	PUNCT
ejpam-3545	555	1	when	when	SCONJ
ejpam-3545	555	2	one	one	NUM
ejpam-3545	555	3	plus	plus	CCONJ
ejpam-3545	555	4	one	one	NUM
ejpam-3545	555	5	equals	equal	VERB
ejpam-3545	555	6	three	three	NUM
ejpam-3545	555	7	:	:	PUNCT
ejpam-3545	555	8	biochemistry	biochemistry	NOUN
ejpam-3545	555	9	and	and	CCONJ
ejpam-3545	555	10	bioinformatics	bioinformatics	NOUN
ejpam-3545	555	11	combine	combine	VERB
ejpam-3545	555	12	to	to	PART
ejpam-3545	555	13	answer	answer	VERB
ejpam-3545	555	14	complex	complex	ADJ
ejpam-3545	555	15	questions	question	NOUN
ejpam-3545	555	16	.	.	PUNCT
ejpam-3545	556	1	fly	fly	VERB
ejpam-3545	556	2	,	,	PUNCT
ejpam-3545	556	3	3(3):212	3(3):212	NUM
ejpam-3545	556	4	–	–	PUNCT
ejpam-3545	556	5	214	214	NUM
ejpam-3545	556	6	,	,	PUNCT
ejpam-3545	556	7	2009	2009	NUM
ejpam-3545	556	8	.	.	PUNCT
ejpam-3545	557	1	[	[	X
ejpam-3545	557	2	47	47	NUM
ejpam-3545	557	3	]	]	PUNCT
ejpam-3545	557	4	werner	werner	PROPN
ejpam-3545	557	5	kuich	kuich	PROPN
ejpam-3545	557	6	and	and	CCONJ
ejpam-3545	557	7	arto	arto	PROPN
ejpam-3545	557	8	salomaa	salomaa	PROPN
ejpam-3545	557	9	.	.	PUNCT
ejpam-3545	558	1	semirings	semiring	NOUN
ejpam-3545	558	2	,	,	PUNCT
ejpam-3545	558	3	automata	automata	NOUN
ejpam-3545	558	4	,	,	PUNCT
ejpam-3545	558	5	languages	language	NOUN
ejpam-3545	558	6	.	.	PUNCT
ejpam-3545	559	1	eatcs	eatcs	NOUN
ejpam-3545	559	2	monographs	monograph	NOUN
ejpam-3545	559	3	on	on	ADP
ejpam-3545	559	4	theoretical	theoretical	ADJ
ejpam-3545	559	5	computer	computer	NOUN
ejpam-3545	559	6	science	science	NOUN
ejpam-3545	559	7	,	,	PUNCT
ejpam-3545	559	8	5	5	NUM
ejpam-3545	559	9	,	,	PUNCT
ejpam-3545	559	10	1986	1986	NUM
ejpam-3545	559	11	.	.	PUNCT
ejpam-3545	560	1	[	[	X
ejpam-3545	560	2	48	48	NUM
ejpam-3545	560	3	]	]	PUNCT
ejpam-3545	560	4	ag	ag	PROPN
ejpam-3545	560	5	kurosh	kurosh	ADV
ejpam-3545	560	6	.	.	PUNCT
ejpam-3545	561	1	lectures	lecture	NOUN
ejpam-3545	561	2	on	on	ADP
ejpam-3545	561	3	general	general	ADJ
ejpam-3545	561	4	algebra	algebra	NOUN
ejpam-3545	561	5	.	.	PUNCT
ejpam-3545	562	1	chelsea	chelsea	PROPN
ejpam-3545	562	2	p.	p.	PROPN
ejpam-3545	562	3	c.	c.	PROPN
ejpam-3545	562	4	,	,	PUNCT
ejpam-3545	562	5	new	new	PROPN
ejpam-3545	562	6	york	york	PROPN
ejpam-3545	562	7	,	,	PUNCT
ejpam-3545	562	8	1963	1963	NUM
ejpam-3545	562	9	.	.	PUNCT
ejpam-3545	563	1	[	[	X
ejpam-3545	563	2	49	49	NUM
ejpam-3545	563	3	]	]	X
ejpam-3545	563	4	marion	marion	PROPN
ejpam-3545	563	5	lang	lang	PROPN
ejpam-3545	563	6	.	.	PUNCT
ejpam-3545	564	1	one	one	NUM
ejpam-3545	564	2	plus	plus	CCONJ
ejpam-3545	564	3	one	one	NUM
ejpam-3545	564	4	equals	equal	VERB
ejpam-3545	564	5	three	three	NUM
ejpam-3545	564	6	:	:	PUNCT
ejpam-3545	564	7	multi	multi	ADJ
ejpam-3545	564	8	-	-	ADJ
ejpam-3545	564	9	line	line	ADJ
ejpam-3545	564	10	fiber	fiber	NOUN
ejpam-3545	564	11	lasers	laser	NOUN
ejpam-3545	564	12	for	for	ADP
ejpam-3545	564	13	nonlinear	nonlinear	ADJ
ejpam-3545	564	14	microscopy	microscopy	NOUN
ejpam-3545	564	15	.	.	PUNCT
ejpam-3545	565	1	optik	optik	PROPN
ejpam-3545	565	2	&	&	CCONJ
ejpam-3545	565	3	photonik	photonik	PROPN
ejpam-3545	565	4	,	,	PUNCT
ejpam-3545	565	5	9(4):53–56	9(4):53–56	NUM
ejpam-3545	565	6	,	,	PUNCT
ejpam-3545	565	7	2014	2014	NUM
ejpam-3545	565	8	.	.	PUNCT
ejpam-3545	566	1	[	[	X
ejpam-3545	566	2	50	50	NUM
ejpam-3545	566	3	]	]	X
ejpam-3545	566	4	r	r	NOUN
ejpam-3545	566	5	lea	lea	NOUN
ejpam-3545	566	6	.	.	PUNCT
ejpam-3545	567	1	why	why	SCONJ
ejpam-3545	567	2	one	one	NUM
ejpam-3545	567	3	plus	plus	CCONJ
ejpam-3545	567	4	one	one	NUM
ejpam-3545	567	5	equals	equal	VERB
ejpam-3545	567	6	three	three	NUM
ejpam-3545	567	7	in	in	ADP
ejpam-3545	567	8	big	big	ADJ
ejpam-3545	567	9	analytics	analytic	NOUN
ejpam-3545	567	10	.	.	PUNCT
ejpam-3545	568	1	forbes	forbes	PROPN
ejpam-3545	568	2	,	,	PUNCT
ejpam-3545	568	3	may	may	AUX
ejpam-3545	568	4	27	27	NUM
ejpam-3545	568	5	,	,	PUNCT
ejpam-3545	568	6	2016	2016	NUM
ejpam-3545	568	7	.	.	PUNCT
ejpam-3545	569	1	[	[	X
ejpam-3545	569	2	51	51	NUM
ejpam-3545	569	3	]	]	PUNCT
ejpam-3545	569	4	grigori	grigori	PROPN
ejpam-3545	569	5	l	l	PROPN
ejpam-3545	569	6	litvinov	litvinov	PROPN
ejpam-3545	569	7	.	.	PUNCT
ejpam-3545	570	1	maslov	maslov	PROPN
ejpam-3545	570	2	dequantization	dequantization	PROPN
ejpam-3545	570	3	,	,	PUNCT
ejpam-3545	570	4	idempotent	idempotent	NOUN
ejpam-3545	570	5	and	and	CCONJ
ejpam-3545	570	6	tropical	tropical	ADJ
ejpam-3545	570	7	mathematics	mathematic	NOUN
ejpam-3545	570	8	:	:	PUNCT
ejpam-3545	570	9	a	a	DET
ejpam-3545	570	10	brief	brief	ADJ
ejpam-3545	570	11	introduction	introduction	NOUN
ejpam-3545	570	12	.	.	PUNCT
ejpam-3545	571	1	journal	journal	PROPN
ejpam-3545	571	2	of	of	ADP
ejpam-3545	571	3	mathematical	mathematical	ADJ
ejpam-3545	571	4	sciences	science	NOUN
ejpam-3545	571	5	,	,	PUNCT
ejpam-3545	571	6	140(3):426–444	140(3):426–444	NUM
ejpam-3545	571	7	,	,	PUNCT
ejpam-3545	571	8	2007	2007	NUM
ejpam-3545	571	9	.	.	PUNCT
ejpam-3545	572	1	[	[	X
ejpam-3545	572	2	52	52	NUM
ejpam-3545	572	3	]	]	X
ejpam-3545	572	4	r	r	NOUN
ejpam-3545	572	5	duncan	duncan	PROPN
ejpam-3545	572	6	luce	luce	NOUN
ejpam-3545	572	7	.	.	PUNCT
ejpam-3545	573	1	the	the	DET
ejpam-3545	573	2	mathematics	mathematic	NOUN
ejpam-3545	573	3	used	use	VERB
ejpam-3545	573	4	in	in	ADP
ejpam-3545	573	5	mathematical	mathematical	ADJ
ejpam-3545	573	6	psychology	psychology	NOUN
ejpam-3545	573	7	.	.	PUNCT
ejpam-3545	574	1	the	the	DET
ejpam-3545	574	2	american	american	PROPN
ejpam-3545	574	3	mathematical	mathematical	PROPN
ejpam-3545	574	4	monthly	monthly	ADV
ejpam-3545	574	5	,	,	PUNCT
ejpam-3545	574	6	71(4):364–378	71(4):364–378	NOUN
ejpam-3545	574	7	,	,	PUNCT
ejpam-3545	574	8	1964	1964	NUM
ejpam-3545	574	9	.	.	PUNCT
ejpam-3545	575	1	[	[	X
ejpam-3545	575	2	53	53	NUM
ejpam-3545	575	3	]	]	X
ejpam-3545	575	4	r	r	NOUN
ejpam-3545	575	5	duncan	duncan	PROPN
ejpam-3545	575	6	luce	luce	NOUN
ejpam-3545	575	7	.	.	PUNCT
ejpam-3545	576	1	a	a	DET
ejpam-3545	576	2	psychophysical	psychophysical	ADJ
ejpam-3545	576	3	theory	theory	NOUN
ejpam-3545	576	4	of	of	ADP
ejpam-3545	576	5	intensity	intensity	NOUN
ejpam-3545	576	6	proportions	proportion	NOUN
ejpam-3545	576	7	,	,	PUNCT
ejpam-3545	576	8	joint	joint	ADJ
ejpam-3545	576	9	presentations	presentation	NOUN
ejpam-3545	576	10	,	,	PUNCT
ejpam-3545	576	11	and	and	CCONJ
ejpam-3545	576	12	matches	match	NOUN
ejpam-3545	576	13	.	.	PUNCT
ejpam-3545	577	1	psychological	psychological	ADJ
ejpam-3545	577	2	review	review	NOUN
ejpam-3545	577	3	,	,	PUNCT
ejpam-3545	577	4	109(3):520	109(3):520	NUM
ejpam-3545	577	5	,	,	PUNCT
ejpam-3545	577	6	2002	2002	NUM
ejpam-3545	577	7	.	.	PUNCT
ejpam-3545	578	1	[	[	X
ejpam-3545	578	2	54	54	NUM
ejpam-3545	578	3	]	]	PUNCT
ejpam-3545	578	4	rd	rd	NOUN
ejpam-3545	578	5	luce	luce	PROPN
ejpam-3545	578	6	,	,	PUNCT
ejpam-3545	578	7	robert	robert	PROPN
ejpam-3545	578	8	r	r	PROPN
ejpam-3545	578	9	bush	bush	PROPN
ejpam-3545	578	10	,	,	PUNCT
ejpam-3545	578	11	and	and	CCONJ
ejpam-3545	578	12	eugene	eugene	PROPN
ejpam-3545	578	13	ed	ed	PROPN
ejpam-3545	578	14	galanter	galanter	PROPN
ejpam-3545	578	15	.	.	PUNCT
ejpam-3545	579	1	handbook	handbook	NOUN
ejpam-3545	579	2	of	of	ADP
ejpam-3545	579	3	mathematical	mathematical	ADJ
ejpam-3545	579	4	psychology	psychology	NOUN
ejpam-3545	579	5	:	:	PUNCT
ejpam-3545	579	6	i.	i.	NOUN
ejpam-3545	579	7	1963	1963	NUM
ejpam-3545	579	8	.	.	PUNCT
ejpam-3545	580	1	[	[	X
ejpam-3545	580	2	55	55	NUM
ejpam-3545	580	3	]	]	X
ejpam-3545	580	4	r	r	NOUN
ejpam-3545	580	5	mane	mane	NOUN
ejpam-3545	580	6	.	.	PUNCT
ejpam-3545	581	1	evolution	evolution	NOUN
ejpam-3545	581	2	of	of	ADP
ejpam-3545	581	3	mutuality	mutuality	NOUN
ejpam-3545	581	4	:	:	PUNCT
ejpam-3545	581	5	one	one	NUM
ejpam-3545	581	6	plus	plus	CCONJ
ejpam-3545	581	7	one	one	NUM
ejpam-3545	581	8	equals	equal	VERB
ejpam-3545	581	9	three	three	NUM
ejpam-3545	581	10	;	;	PUNCT
ejpam-3545	581	11	formula	formula	NOUN
ejpam-3545	581	12	characterizing	characterize	VERB
ejpam-3545	581	13	mutuality	mutuality	NOUN
ejpam-3545	581	14	.	.	PUNCT
ejpam-3545	582	1	la	la	PROPN
ejpam-3545	582	2	revue	revue	PROPN
ejpam-3545	582	3	du	du	PROPN
ejpam-3545	582	4	praticien	praticien	PROPN
ejpam-3545	582	5	,	,	PUNCT
ejpam-3545	582	6	2(5):302	2(5):302	NUM
ejpam-3545	582	7	,	,	PUNCT
ejpam-3545	582	8	1952	1952	NUM
ejpam-3545	582	9	.	.	PUNCT
ejpam-3545	583	1	[	[	X
ejpam-3545	583	2	56	56	NUM
ejpam-3545	583	3	]	]	X
ejpam-3545	583	4	jean	jean	PROPN
ejpam-3545	583	5	-	-	PUNCT
ejpam-3545	583	6	luc	luc	PROPN
ejpam-3545	583	7	marichal	marichal	NOUN
ejpam-3545	583	8	.	.	PUNCT
ejpam-3545	584	1	aggregation	aggregation	NOUN
ejpam-3545	584	2	functions	function	NOUN
ejpam-3545	584	3	for	for	ADP
ejpam-3545	584	4	decision	decision	NOUN
ejpam-3545	584	5	making	making	NOUN
ejpam-3545	584	6	.	.	PUNCT
ejpam-3545	585	1	decision	decision	NOUN
ejpam-3545	585	2	-	-	PUNCT
ejpam-3545	585	3	making	make	VERB
ejpam-3545	585	4	process	process	NOUN
ejpam-3545	585	5	:	:	PUNCT
ejpam-3545	585	6	concepts	concept	NOUN
ejpam-3545	585	7	and	and	CCONJ
ejpam-3545	585	8	methods	method	NOUN
ejpam-3545	585	9	,	,	PUNCT
ejpam-3545	585	10	pages	page	NOUN
ejpam-3545	585	11	673–721	673–721	NUM
ejpam-3545	585	12	,	,	PUNCT
ejpam-3545	585	13	2009	2009	NUM
ejpam-3545	585	14	.	.	PUNCT
ejpam-3545	586	1	[	[	X
ejpam-3545	586	2	57	57	NUM
ejpam-3545	586	3	]	]	PUNCT
ejpam-3545	586	4	kirsten	kirsten	PROPN
ejpam-3545	586	5	l	l	PROPN
ejpam-3545	586	6	marie	marie	PROPN
ejpam-3545	586	7	.	.	PUNCT
ejpam-3545	587	1	one	one	NUM
ejpam-3545	587	2	plus	plus	CCONJ
ejpam-3545	587	3	one	one	NUM
ejpam-3545	587	4	equals	equal	VERB
ejpam-3545	587	5	three	three	NUM
ejpam-3545	587	6	:	:	PUNCT
ejpam-3545	587	7	joint	joint	ADJ
ejpam-3545	587	8	-	-	PUNCT
ejpam-3545	587	9	use	use	NOUN
ejpam-3545	587	10	libraries	library	NOUN
ejpam-3545	587	11	in	in	ADP
ejpam-3545	587	12	urban	urban	ADJ
ejpam-3545	587	13	areas	area	NOUN
ejpam-3545	587	14	—	—	PUNCT
ejpam-3545	587	15	the	the	DET
ejpam-3545	587	16	ultimate	ultimate	ADJ
ejpam-3545	587	17	form	form	NOUN
ejpam-3545	587	18	of	of	ADP
ejpam-3545	587	19	library	library	ADJ
ejpam-3545	587	20	cooperation	cooperation	NOUN
ejpam-3545	587	21	.	.	PUNCT
ejpam-3545	588	1	library	library	PROPN
ejpam-3545	588	2	leadership	leadership	PROPN
ejpam-3545	588	3	&	&	CCONJ
ejpam-3545	588	4	management	management	NOUN
ejpam-3545	588	5	,	,	PUNCT
ejpam-3545	588	6	21(1):23–28	21(1):23–28	NUM
ejpam-3545	588	7	,	,	PUNCT
ejpam-3545	588	8	2007	2007	NUM
ejpam-3545	588	9	.	.	PUNCT
ejpam-3545	589	1	references	reference	NOUN
ejpam-3545	589	2	1809	1809	NUM
ejpam-3545	590	1	[	[	X
ejpam-3545	590	2	58	58	NUM
ejpam-3545	590	3	]	]	X
ejpam-3545	590	4	mitchell	mitchell	PROPN
ejpam-3545	590	5	lee	lee	PROPN
ejpam-3545	590	6	marks	marks	PROPN
ejpam-3545	590	7	and	and	CCONJ
ejpam-3545	590	8	philip	philip	PROPN
ejpam-3545	590	9	h	h	PROPN
ejpam-3545	590	10	mirvis	mirvis	PROPN
ejpam-3545	590	11	.	.	PUNCT
ejpam-3545	591	1	joining	join	VERB
ejpam-3545	591	2	forces	force	NOUN
ejpam-3545	591	3	:	:	PUNCT
ejpam-3545	591	4	making	make	VERB
ejpam-3545	591	5	one	one	NUM
ejpam-3545	591	6	plus	plus	CCONJ
ejpam-3545	591	7	one	one	NUM
ejpam-3545	591	8	equal	equal	ADJ
ejpam-3545	591	9	three	three	NUM
ejpam-3545	591	10	in	in	ADP
ejpam-3545	591	11	mergers	merger	NOUN
ejpam-3545	591	12	,	,	PUNCT
ejpam-3545	591	13	acquisitions	acquisition	NOUN
ejpam-3545	591	14	,	,	PUNCT
ejpam-3545	591	15	and	and	CCONJ
ejpam-3545	591	16	alliances	alliance	NOUN
ejpam-3545	591	17	.	.	PUNCT
ejpam-3545	592	1	jossey	jossey	NOUN
ejpam-3545	592	2	-	-	PUNCT
ejpam-3545	592	3	bass	bass	NOUN
ejpam-3545	592	4	,	,	PUNCT
ejpam-3545	592	5	san	san	PROPN
ejpam-3545	592	6	francisco	francisco	PROPN
ejpam-3545	592	7	,	,	PUNCT
ejpam-3545	592	8	2010	2010	NUM
ejpam-3545	592	9	.	.	PUNCT
ejpam-3545	593	1	[	[	X
ejpam-3545	593	2	59	59	NUM
ejpam-3545	593	3	]	]	X
ejpam-3545	593	4	vp	vp	PROPN
ejpam-3545	593	5	maslov	maslov	PROPN
ejpam-3545	593	6	.	.	PUNCT
ejpam-3545	594	1	asymptotic	asymptotic	ADJ
ejpam-3545	594	2	methods	method	NOUN
ejpam-3545	594	3	for	for	ADP
ejpam-3545	594	4	solving	solve	VERB
ejpam-3545	594	5	pseudodifferential	pseudodifferential	ADJ
ejpam-3545	594	6	equations	equation	NOUN
ejpam-3545	594	7	.	.	PUNCT
ejpam-3545	595	1	nauka	nauka	PROPN
ejpam-3545	595	2	,	,	PUNCT
ejpam-3545	595	3	moscow	moscow	PROPN
ejpam-3545	595	4	,	,	PUNCT
ejpam-3545	595	5	1987	1987	NUM
ejpam-3545	595	6	,	,	PUNCT
ejpam-3545	595	7	(	(	PUNCT
ejpam-3545	595	8	in	in	ADP
ejpam-3545	595	9	russian	russian	NOUN
ejpam-3545	595	10	)	)	PUNCT
ejpam-3545	595	11	.	.	PUNCT
ejpam-3545	596	1	[	[	X
ejpam-3545	596	2	60	60	NUM
ejpam-3545	596	3	]	]	X
ejpam-3545	596	4	vp	vp	PROPN
ejpam-3545	596	5	maslov	maslov	PROPN
ejpam-3545	596	6	and	and	CCONJ
ejpam-3545	596	7	sn	sn	PROPN
ejpam-3545	596	8	samborskii	samborskii	PROPN
ejpam-3545	596	9	(	(	PUNCT
ejpam-3545	596	10	eds	ed	NOUN
ejpam-3545	596	11	.	.	PUNCT
ejpam-3545	596	12	)	)	PUNCT
ejpam-3545	596	13	.	.	PUNCT
ejpam-3545	597	1	idempotent	idempotent	ADJ
ejpam-3545	597	2	analysis	analysis	NOUN
ejpam-3545	597	3	.	.	PUNCT
ejpam-3545	598	1	amer	amer	PROPN
ejpam-3545	598	2	.	.	PUNCT
ejpam-3545	598	3	math	math	PROPN
ejpam-3545	598	4	.	.	PUNCT
ejpam-3545	599	1	soc	soc	PROPN
ejpam-3545	599	2	.	.	PROPN
ejpam-3545	599	3	,	,	PUNCT
ejpam-3545	599	4	new	new	PROPN
ejpam-3545	599	5	york	york	PROPN
ejpam-3545	599	6	,	,	PUNCT
ejpam-3545	599	7	1992	1992	NUM
ejpam-3545	599	8	.	.	PUNCT
ejpam-3545	600	1	[	[	X
ejpam-3545	600	2	61	61	NUM
ejpam-3545	600	3	]	]	PUNCT
ejpam-3545	600	4	mitio	mitio	NOUN
ejpam-3545	600	5	nagumo	nagumo	PROPN
ejpam-3545	600	6	.	.	PUNCT
ejpam-3545	601	1	über	über	PROPN
ejpam-3545	601	2	eine	eine	PROPN
ejpam-3545	601	3	klasse	klasse	PROPN
ejpam-3545	601	4	der	der	PROPN
ejpam-3545	601	5	mittelwerte	mittelwerte	NOUN
ejpam-3545	601	6	.	.	PUNCT
ejpam-3545	602	1	in	in	ADP
ejpam-3545	602	2	japanese	japanese	ADJ
ejpam-3545	602	3	journal	journal	PROPN
ejpam-3545	602	4	of	of	ADP
ejpam-3545	602	5	mathematics	mathematic	NOUN
ejpam-3545	602	6	:	:	PUNCT
ejpam-3545	602	7	transactions	transaction	NOUN
ejpam-3545	602	8	and	and	CCONJ
ejpam-3545	602	9	abstracts	abstract	NOUN
ejpam-3545	602	10	,	,	PUNCT
ejpam-3545	602	11	volume	volume	NOUN
ejpam-3545	602	12	7	7	NUM
ejpam-3545	602	13	,	,	PUNCT
ejpam-3545	602	14	pages	page	NOUN
ejpam-3545	602	15	71–79	71–79	ADV
ejpam-3545	602	16	.	.	PUNCT
ejpam-3545	603	1	the	the	DET
ejpam-3545	603	2	mathematical	mathematical	ADJ
ejpam-3545	603	3	society	society	NOUN
ejpam-3545	603	4	of	of	ADP
ejpam-3545	603	5	japan	japan	PROPN
ejpam-3545	603	6	,	,	PUNCT
ejpam-3545	603	7	1930	1930	NUM
ejpam-3545	603	8	.	.	PUNCT
ejpam-3545	604	1	[	[	X
ejpam-3545	604	2	62	62	NUM
ejpam-3545	604	3	]	]	X
ejpam-3545	604	4	c	c	PROPN
ejpam-3545	604	5	nieuwmeijer	nieuwmeijer	NOUN
ejpam-3545	604	6	.	.	PUNCT
ejpam-3545	605	1	1	1	NUM
ejpam-3545	605	2	+	+	NUM
ejpam-3545	605	3	1=	1=	NUM
ejpam-3545	605	4	3	3	NUM
ejpam-3545	605	5	:	:	PUNCT
ejpam-3545	605	6	the	the	DET
ejpam-3545	605	7	positive	positive	ADJ
ejpam-3545	605	8	effects	effect	NOUN
ejpam-3545	605	9	of	of	ADP
ejpam-3545	605	10	the	the	DET
ejpam-3545	605	11	synergy	synergy	NOUN
ejpam-3545	605	12	between	between	ADP
ejpam-3545	605	13	musician	musician	NOUN
ejpam-3545	605	14	and	and	CCONJ
ejpam-3545	605	15	classroom	classroom	NOUN
ejpam-3545	605	16	teacher	teacher	NOUN
ejpam-3545	605	17	on	on	ADP
ejpam-3545	605	18	young	young	ADJ
ejpam-3545	605	19	childrens	children	NOUN
ejpam-3545	605	20	free	free	ADJ
ejpam-3545	605	21	musical	musical	ADJ
ejpam-3545	605	22	play	play	NOUN
ejpam-3545	605	23	.	.	PUNCT
ejpam-3545	606	1	unpublished	unpublished	ADJ
ejpam-3545	606	2	masters	master	NOUN
ejpam-3545	606	3	thesis	thesis	NOUN
ejpam-3545	606	4	.	.	PUNCT
ejpam-3545	607	1	london	london	PROPN
ejpam-3545	607	2	:	:	PUNCT
ejpam-3545	607	3	roehampton	roehampton	PROPN
ejpam-3545	607	4	university	university	PROPN
ejpam-3545	607	5	,	,	PUNCT
ejpam-3545	607	6	2013	2013	NUM
ejpam-3545	607	7	.	.	PUNCT
ejpam-3545	608	1	[	[	X
ejpam-3545	608	2	63	63	NUM
ejpam-3545	608	3	]	]	PUNCT
ejpam-3545	608	4	snn	snn	PROPN
ejpam-3545	608	5	pandit	pandit	PROPN
ejpam-3545	608	6	.	.	PUNCT
ejpam-3545	609	1	a	a	DET
ejpam-3545	609	2	new	new	ADJ
ejpam-3545	609	3	matrix	matrix	NOUN
ejpam-3545	609	4	calculus	calculus	NOUN
ejpam-3545	609	5	.	.	PUNCT
ejpam-3545	610	1	journal	journal	NOUN
ejpam-3545	610	2	of	of	ADP
ejpam-3545	610	3	the	the	DET
ejpam-3545	610	4	society	society	NOUN
ejpam-3545	610	5	for	for	ADP
ejpam-3545	610	6	industrial	industrial	ADJ
ejpam-3545	610	7	and	and	CCONJ
ejpam-3545	610	8	applied	applied	ADJ
ejpam-3545	610	9	mathematics	mathematic	NOUN
ejpam-3545	610	10	,	,	PUNCT
ejpam-3545	610	11	9(4):632–639	9(4):632–639	NOUN
ejpam-3545	610	12	,	,	PUNCT
ejpam-3545	610	13	1961	1961	NUM
ejpam-3545	610	14	.	.	PUNCT
ejpam-3545	611	1	[	[	X
ejpam-3545	611	2	64	64	NUM
ejpam-3545	611	3	]	]	X
ejpam-3545	611	4	j	j	PROPN
ejpam-3545	611	5	phillips	phillips	PROPN
ejpam-3545	611	6	.	.	PUNCT
ejpam-3545	612	1	when	when	SCONJ
ejpam-3545	612	2	one	one	NUM
ejpam-3545	612	3	plus	plus	CCONJ
ejpam-3545	612	4	one	one	NUM
ejpam-3545	612	5	equals	equal	VERB
ejpam-3545	612	6	three	three	NUM
ejpam-3545	612	7	.	.	PUNCT
ejpam-3545	613	1	wellness	wellness	NOUN
ejpam-3545	613	2	universe	universe	NOUN
ejpam-3545	613	3	,	,	PUNCT
ejpam-3545	613	4	april	april	PROPN
ejpam-3545	613	5	10	10	NUM
ejpam-3545	613	6	,	,	PUNCT
ejpam-3545	613	7	2016	2016	NUM
ejpam-3545	613	8	.	.	PUNCT
ejpam-3545	614	1	[	[	X
ejpam-3545	614	2	65	65	NUM
ejpam-3545	614	3	]	]	X
ejpam-3545	614	4	jean	jean	PROPN
ejpam-3545	614	5	-	-	PUNCT
ejpam-3545	614	6	eric	eric	PROPN
ejpam-3545	614	7	pin	pin	PROPN
ejpam-3545	614	8	.	.	PUNCT
ejpam-3545	615	1	tropical	tropical	PROPN
ejpam-3545	615	2	semirings	semiring	NOUN
ejpam-3545	615	3	.	.	PUNCT
ejpam-3545	616	1	idempotency	idempotency	NOUN
ejpam-3545	616	2	.	.	PUNCT
ejpam-3545	617	1	publications	publication	NOUN
ejpam-3545	617	2	of	of	ADP
ejpam-3545	617	3	the	the	DET
ejpam-3545	617	4	newton	newton	PROPN
ejpam-3545	617	5	institute	institute	PROPN
ejpam-3545	617	6	,	,	PUNCT
ejpam-3545	617	7	11:50–69	11:50–69	NUM
ejpam-3545	617	8	,	,	PUNCT
ejpam-3545	617	9	1998	1998	NUM
ejpam-3545	617	10	.	.	PUNCT
ejpam-3545	618	1	[	[	X
ejpam-3545	618	2	66	66	NUM
ejpam-3545	618	3	]	]	PUNCT
ejpam-3545	618	4	pk	pk	NOUN
ejpam-3545	618	5	rashevskii	rashevskii	NOUN
ejpam-3545	618	6	.	.	PUNCT
ejpam-3545	619	1	on	on	ADP
ejpam-3545	619	2	the	the	DET
ejpam-3545	619	3	dogma	dogma	NOUN
ejpam-3545	619	4	of	of	ADP
ejpam-3545	619	5	the	the	DET
ejpam-3545	619	6	natural	natural	ADJ
ejpam-3545	619	7	numbers	number	NOUN
ejpam-3545	619	8	.	.	PUNCT
ejpam-3545	620	1	russian	russian	ADJ
ejpam-3545	620	2	mathematical	mathematical	ADJ
ejpam-3545	620	3	surveys	survey	NOUN
ejpam-3545	620	4	,	,	PUNCT
ejpam-3545	620	5	28(4):143–148	28(4):143–148	PROPN
ejpam-3545	620	6	,	,	PUNCT
ejpam-3545	620	7	1973	1973	NUM
ejpam-3545	620	8	.	.	PUNCT
ejpam-3545	621	1	[	[	X
ejpam-3545	621	2	67	67	NUM
ejpam-3545	621	3	]	]	X
ejpam-3545	621	4	gilbert	gilbert	PROPN
ejpam-3545	621	5	ryle	ryle	PROPN
ejpam-3545	621	6	,	,	PUNCT
ejpam-3545	621	7	c	c	PROPN
ejpam-3545	621	8	lewy	lewy	PROPN
ejpam-3545	621	9	,	,	PUNCT
ejpam-3545	621	10	and	and	CCONJ
ejpam-3545	621	11	kr	kr	PROPN
ejpam-3545	621	12	popper	popper	NOUN
ejpam-3545	621	13	.	.	PUNCT
ejpam-3545	622	1	symposium	symposium	NOUN
ejpam-3545	622	2	:	:	PUNCT
ejpam-3545	622	3	why	why	SCONJ
ejpam-3545	622	4	are	be	AUX
ejpam-3545	622	5	the	the	DET
ejpam-3545	622	6	calculuses	calculus	NOUN
ejpam-3545	622	7	of	of	ADP
ejpam-3545	622	8	logic	logic	NOUN
ejpam-3545	622	9	and	and	CCONJ
ejpam-3545	622	10	arithmetic	arithmetic	ADJ
ejpam-3545	622	11	applicable	applicable	ADJ
ejpam-3545	622	12	to	to	ADP
ejpam-3545	622	13	reality	reality	NOUN
ejpam-3545	622	14	?	?	PUNCT
ejpam-3545	623	1	proceedings	proceeding	NOUN
ejpam-3545	623	2	of	of	ADP
ejpam-3545	623	3	the	the	DET
ejpam-3545	623	4	aristotelian	aristotelian	ADJ
ejpam-3545	623	5	society	society	NOUN
ejpam-3545	623	6	,	,	PUNCT
ejpam-3545	623	7	supplementary	supplementary	ADJ
ejpam-3545	623	8	volumes	volume	NOUN
ejpam-3545	623	9	,	,	PUNCT
ejpam-3545	623	10	20:20–60	20:20–60	PROPN
ejpam-3545	623	11	,	,	PUNCT
ejpam-3545	623	12	1946	1946	NUM
ejpam-3545	623	13	.	.	PUNCT
ejpam-3545	624	1	[	[	X
ejpam-3545	624	2	68	68	NUM
ejpam-3545	624	3	]	]	PUNCT
ejpam-3545	624	4	claude	claude	PROPN
ejpam-3545	624	5	elwood	elwood	PROPN
ejpam-3545	624	6	shannon	shannon	PROPN
ejpam-3545	624	7	.	.	PUNCT
ejpam-3545	625	1	a	a	DET
ejpam-3545	625	2	mathematical	mathematical	ADJ
ejpam-3545	625	3	theory	theory	NOUN
ejpam-3545	625	4	of	of	ADP
ejpam-3545	625	5	communication	communication	NOUN
ejpam-3545	625	6	.	.	PUNCT
ejpam-3545	626	1	bell	bell	NOUN
ejpam-3545	626	2	system	system	PROPN
ejpam-3545	626	3	technical	technical	PROPN
ejpam-3545	626	4	journal	journal	PROPN
ejpam-3545	626	5	,	,	PUNCT
ejpam-3545	626	6	27(3):379–423	27(3):379–423	PROPN
ejpam-3545	626	7	,	,	PUNCT
ejpam-3545	626	8	1948	1948	NUM
ejpam-3545	626	9	.	.	PUNCT
ejpam-3545	627	1	[	[	X
ejpam-3545	627	2	69	69	NUM
ejpam-3545	627	3	]	]	X
ejpam-3545	627	4	yoshinori	yoshinori	PROPN
ejpam-3545	627	5	shiozawa	shiozawa	PROPN
ejpam-3545	627	6	.	.	PUNCT
ejpam-3545	628	1	international	international	ADJ
ejpam-3545	628	2	trade	trade	NOUN
ejpam-3545	628	3	theory	theory	NOUN
ejpam-3545	628	4	and	and	CCONJ
ejpam-3545	628	5	exotic	exotic	ADJ
ejpam-3545	628	6	algebras	algebra	NOUN
ejpam-3545	628	7	.	.	PUNCT
ejpam-3545	629	1	evolutionary	evolutionary	ADJ
ejpam-3545	629	2	and	and	CCONJ
ejpam-3545	629	3	institutional	institutional	ADJ
ejpam-3545	629	4	economics	economic	NOUN
ejpam-3545	629	5	review	review	NOUN
ejpam-3545	629	6	,	,	PUNCT
ejpam-3545	629	7	12(1):177–212	12(1):177–212	NUM
ejpam-3545	629	8	,	,	PUNCT
ejpam-3545	629	9	2015	2015	NUM
ejpam-3545	629	10	.	.	PUNCT
ejpam-3545	630	1	[	[	X
ejpam-3545	630	2	70	70	X
ejpam-3545	630	3	]	]	X
ejpam-3545	630	4	david	david	PROPN
ejpam-3545	630	5	speyer	speyer	PROPN
ejpam-3545	630	6	and	and	CCONJ
ejpam-3545	630	7	bernd	bernd	PROPN
ejpam-3545	630	8	sturmfels	sturmfel	NOUN
ejpam-3545	630	9	.	.	PUNCT
ejpam-3545	631	1	tropical	tropical	ADJ
ejpam-3545	631	2	mathematics	mathematic	NOUN
ejpam-3545	631	3	.	.	PUNCT
ejpam-3545	632	1	mathematics	mathematic	NOUN
ejpam-3545	632	2	magazine	magazine	NOUN
ejpam-3545	632	3	,	,	PUNCT
ejpam-3545	632	4	82(3):163–173	82(3):163–173	PROPN
ejpam-3545	632	5	,	,	PUNCT
ejpam-3545	632	6	2009	2009	NUM
ejpam-3545	632	7	.	.	PUNCT
ejpam-3545	633	1	[	[	X
ejpam-3545	633	2	71	71	NUM
ejpam-3545	633	3	]	]	PUNCT
ejpam-3545	633	4	a	a	DET
ejpam-3545	633	5	trabacca	trabacca	NOUN
ejpam-3545	633	6	,	,	PUNCT
ejpam-3545	633	7	g	g	PROPN
ejpam-3545	633	8	moro	moro	X
ejpam-3545	633	9	,	,	PUNCT
ejpam-3545	633	10	l	l	PROPN
ejpam-3545	633	11	gennaro	gennaro	NOUN
ejpam-3545	633	12	,	,	PUNCT
ejpam-3545	633	13	and	and	CCONJ
ejpam-3545	633	14	l	l	PROPN
ejpam-3545	633	15	russo	russo	NOUN
ejpam-3545	633	16	.	.	PUNCT
ejpam-3545	634	1	when	when	SCONJ
ejpam-3545	634	2	one	one	NUM
ejpam-3545	634	3	plus	plus	CCONJ
ejpam-3545	634	4	one	one	NUM
ejpam-3545	634	5	equals	equal	VERB
ejpam-3545	634	6	three	three	NUM
ejpam-3545	634	7	:	:	PUNCT
ejpam-3545	634	8	the	the	DET
ejpam-3545	634	9	icf	icf	PROPN
ejpam-3545	634	10	perspective	perspective	NOUN
ejpam-3545	634	11	of	of	ADP
ejpam-3545	634	12	health	health	NOUN
ejpam-3545	634	13	and	and	CCONJ
ejpam-3545	634	14	disability	disability	NOUN
ejpam-3545	634	15	in	in	ADP
ejpam-3545	634	16	the	the	DET
ejpam-3545	634	17	third	third	ADJ
ejpam-3545	634	18	millennium	millennium	NOUN
ejpam-3545	634	19	.	.	PUNCT
ejpam-3545	635	1	european	european	PROPN
ejpam-3545	635	2	journal	journal	PROPN
ejpam-3545	635	3	of	of	ADP
ejpam-3545	635	4	physical	physical	ADJ
ejpam-3545	635	5	and	and	CCONJ
ejpam-3545	635	6	rehabilitation	rehabilitation	NOUN
ejpam-3545	635	7	medicine	medicine	NOUN
ejpam-3545	635	8	,	,	PUNCT
ejpam-3545	635	9	48(4):709–710	48(4):709–710	PROPN
ejpam-3545	635	10	,	,	PUNCT
ejpam-3545	635	11	2012	2012	NUM
ejpam-3545	635	12	.	.	PUNCT
ejpam-3545	636	1	[	[	X
ejpam-3545	636	2	72	72	NUM
ejpam-3545	636	3	]	]	X
ejpam-3545	636	4	dave	dave	PROPN
ejpam-3545	636	5	trott	trott	PROPN
ejpam-3545	636	6	.	.	PUNCT
ejpam-3545	637	1	one	one	NUM
ejpam-3545	637	2	plus	plus	CCONJ
ejpam-3545	637	3	one	one	NUM
ejpam-3545	637	4	equals	equal	VERB
ejpam-3545	637	5	three	three	NUM
ejpam-3545	637	6	:	:	PUNCT
ejpam-3545	637	7	a	a	DET
ejpam-3545	637	8	masterclass	masterclass	NOUN
ejpam-3545	637	9	in	in	ADP
ejpam-3545	637	10	creative	creative	ADJ
ejpam-3545	637	11	thinking	thinking	NOUN
ejpam-3545	637	12	.	.	PUNCT
ejpam-3545	638	1	macmillan	macmillan	PROPN
ejpam-3545	638	2	publishing	publishing	PROPN
ejpam-3545	638	3	company	company	NOUN
ejpam-3545	638	4	,	,	PUNCT
ejpam-3545	638	5	new	new	PROPN
ejpam-3545	638	6	york	york	PROPN
ejpam-3545	638	7	,	,	PUNCT
ejpam-3545	638	8	2015	2015	NUM
ejpam-3545	638	9	.	.	PUNCT
ejpam-3545	639	1	references	reference	NOUN
ejpam-3545	639	2	1810	1810	NUM
ejpam-3545	640	1	[	[	X
ejpam-3545	640	2	73	73	NUM
ejpam-3545	640	3	]	]	PUNCT
ejpam-3545	640	4	hermann	hermann	PROPN
ejpam-3545	640	5	von	von	PROPN
ejpam-3545	640	6	helmholtz	helmholtz	PROPN
ejpam-3545	640	7	.	.	PUNCT
ejpam-3545	641	1	zahlen	zahlen	PROPN
ejpam-3545	641	2	und	und	PROPN
ejpam-3545	641	3	messen	messen	PROPN
ejpam-3545	641	4	.	.	PUNCT
ejpam-3545	642	1	philosophische	philosophische	PROPN
ejpam-3545	642	2	aufsatze	aufsatze	PROPN
ejpam-3545	642	3	,	,	PUNCT
ejpam-3545	642	4	fues	fues	PROPN
ejpam-3545	642	5	’s	’s	PART
ejpam-3545	642	6	verlag	verlag	PROPN
ejpam-3545	642	7	,	,	PUNCT
ejpam-3545	642	8	leipzig	leipzig	PROPN
ejpam-3545	642	9	,	,	PUNCT
ejpam-3545	642	10	pages	page	NOUN
ejpam-3545	642	11	17–52	17–52	NUM
ejpam-3545	642	12	,	,	PUNCT
ejpam-3545	642	13	1887	1887	NUM
ejpam-3545	642	14	(	(	PUNCT
ejpam-3545	642	15	translated	translate	VERB
ejpam-3545	642	16	by	by	ADP
ejpam-3545	642	17	c.l	c.l	PROPN
ejpam-3545	642	18	.	.	PROPN
ejpam-3545	642	19	bryan	bryan	PROPN
ejpam-3545	642	20	,	,	PUNCT
ejpam-3545	642	21	“	"	PUNCT
ejpam-3545	642	22	counting	count	VERB
ejpam-3545	642	23	and	and	CCONJ
ejpam-3545	642	24	measuring	measure	VERB
ejpam-3545	642	25	”	"	PUNCT
ejpam-3545	642	26	,	,	PUNCT
ejpam-3545	642	27	van	van	PROPN
ejpam-3545	642	28	nostrand	nostrand	PROPN
ejpam-3545	642	29	,	,	PUNCT
ejpam-3545	642	30	1930	1930	NUM
ejpam-3545	642	31	)	)	PUNCT
ejpam-3545	642	32	.	.	PUNCT
ejpam-3545	643	1	[	[	X
ejpam-3545	643	2	74	74	NUM
ejpam-3545	643	3	]	]	PUNCT
ejpam-3545	643	4	nn	nn	X
ejpam-3545	643	5	vorobjev	vorobjev	NOUN
ejpam-3545	643	6	.	.	PUNCT
ejpam-3545	644	1	the	the	DET
ejpam-3545	644	2	extremal	extremal	ADJ
ejpam-3545	644	3	matrix	matrix	NOUN
ejpam-3545	644	4	algebra	algebra	NOUN
ejpam-3545	644	5	.	.	PUNCT
ejpam-3545	645	1	soviet	soviet	ADJ
ejpam-3545	645	2	math	math	PROPN
ejpam-3545	645	3	.	.	PUNCT
ejpam-3545	646	1	dokl	dokl	NOUN
ejpam-3545	646	2	,	,	PUNCT
ejpam-3545	646	3	4:1220–1223	4:1220–1223	PROPN
ejpam-3545	646	4	,	,	PUNCT
ejpam-3545	646	5	1963	1963	NUM
ejpam-3545	646	6	.	.	PUNCT
ejpam-3545	647	1	[	[	X
ejpam-3545	647	2	75	75	NUM
ejpam-3545	647	3	]	]	PUNCT
ejpam-3545	647	4	uwe	uwe	PROPN
ejpam-3545	647	5	zimmermann	zimmermann	PROPN
ejpam-3545	647	6	.	.	PUNCT
ejpam-3545	648	1	linear	linear	PROPN
ejpam-3545	648	2	and	and	CCONJ
ejpam-3545	648	3	combinatorial	combinatorial	ADJ
ejpam-3545	648	4	optimization	optimization	NOUN
ejpam-3545	648	5	in	in	ADP
ejpam-3545	648	6	ordered	order	VERB
ejpam-3545	648	7	algebraic	algebraic	ADJ
ejpam-3545	648	8	structures	structure	NOUN
ejpam-3545	648	9	.	.	PUNCT
ejpam-3545	649	1	ann	ann	PROPN
ejpam-3545	649	2	.	.	PROPN
ejpam-3545	649	3	discrete	discrete	ADJ
ejpam-3545	649	4	math	math	NOUN
ejpam-3545	649	5	.	.	PUNCT
ejpam-3545	649	6	,	,	PUNCT
ejpam-3545	649	7	10:1–38	10:1–38	NUM
ejpam-3545	649	8	,	,	PUNCT
ejpam-3545	649	9	1981	1981	NUM
ejpam-3545	649	10	.	.	PUNCT