id	sid	tid	token	lemma	pos
ejpam-3341	1	1	on	on	ADP
ejpam-3341	1	2	hoehnke	hoehnke	ADJ
ejpam-3341	1	3	ideal	ideal	NOUN
ejpam-3341	1	4	in	in	ADP
ejpam-3341	1	5	ordered	order	VERB
ejpam-3341	1	6	semigroups	semigroup	NOUN
ejpam-3341	1	7	european	european	PROPN
ejpam-3341	1	8	journal	journal	PROPN
ejpam-3341	1	9	of	of	ADP
ejpam-3341	1	10	pure	pure	ADJ
ejpam-3341	1	11	and	and	CCONJ
ejpam-3341	1	12	applied	apply	VERB
ejpam-3341	1	13	mathematics	mathematic	NOUN
ejpam-3341	1	14	vol	vol	NOUN
ejpam-3341	1	15	.	.	PUNCT
ejpam-3341	2	1	11	11	NUM
ejpam-3341	2	2	,	,	PUNCT
ejpam-3341	2	3	no	no	INTJ
ejpam-3341	2	4	.	.	NOUN
ejpam-3341	2	5	4	4	NUM
ejpam-3341	2	6	,	,	PUNCT
ejpam-3341	2	7	2018	2018	NUM
ejpam-3341	2	8	,	,	PUNCT
ejpam-3341	2	9	911	911	NUM
ejpam-3341	2	10	-	-	SYM
ejpam-3341	2	11	921	921	NUM
ejpam-3341	2	12	issn	issn	PROPN
ejpam-3341	2	13	1307	1307	NUM
ejpam-3341	2	14	-	-	SYM
ejpam-3341	2	15	5543	5543	NUM
ejpam-3341	2	16	–	–	PUNCT
ejpam-3341	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3341	2	18	published	publish	VERB
ejpam-3341	2	19	by	by	ADP
ejpam-3341	2	20	new	new	PROPN
ejpam-3341	2	21	york	york	PROPN
ejpam-3341	2	22	business	business	PROPN
ejpam-3341	2	23	global	global	ADJ
ejpam-3341	2	24	on	on	ADP
ejpam-3341	2	25	hoehnke	hoehnke	ADJ
ejpam-3341	2	26	ideal	ideal	NOUN
ejpam-3341	2	27	in	in	ADP
ejpam-3341	2	28	ordered	order	VERB
ejpam-3341	2	29	semigroups	semigroup	NOUN
ejpam-3341	2	30	niovi	niovi	PROPN
ejpam-3341	2	31	kehayopulu	kehayopulu	ADJ
ejpam-3341	2	32	abstract	abstract	NOUN
ejpam-3341	2	33	.	.	PUNCT
ejpam-3341	3	1	for	for	ADP
ejpam-3341	3	2	a	a	DET
ejpam-3341	3	3	proper	proper	ADJ
ejpam-3341	3	4	subset	subset	NOUN
ejpam-3341	3	5	a	a	PRON
ejpam-3341	3	6	of	of	ADP
ejpam-3341	3	7	an	an	DET
ejpam-3341	3	8	ordered	order	VERB
ejpam-3341	3	9	semigroup	semigroup	NOUN
ejpam-3341	3	10	s	s	PROPN
ejpam-3341	3	11	,	,	PUNCT
ejpam-3341	3	12	we	we	PRON
ejpam-3341	3	13	denote	denote	VERB
ejpam-3341	3	14	by	by	ADP
ejpam-3341	3	15	ha(s	ha(	NOUN
ejpam-3341	3	16	)	)	PUNCT
ejpam-3341	3	17	the	the	DET
ejpam-3341	3	18	subset	subset	NOUN
ejpam-3341	3	19	of	of	ADP
ejpam-3341	3	20	s	s	PRON
ejpam-3341	3	21	defined	define	VERB
ejpam-3341	3	22	by	by	ADP
ejpam-3341	3	23	ha(s	ha(	NOUN
ejpam-3341	3	24	)	)	PUNCT
ejpam-3341	3	25	:	:	PUNCT
ejpam-3341	4	1	=	=	SYM
ejpam-3341	4	2	{	{	PUNCT
ejpam-3341	4	3	h	h	NOUN
ejpam-3341	4	4	∈	∈	PROPN
ejpam-3341	4	5	s	s	VERB
ejpam-3341	4	6	such	such	ADJ
ejpam-3341	4	7	that	that	SCONJ
ejpam-3341	4	8	if	if	SCONJ
ejpam-3341	4	9	s	s	X
ejpam-3341	4	10	∈	∈	PROPN
ejpam-3341	4	11	s\a	s\a	NOUN
ejpam-3341	4	12	,	,	PUNCT
ejpam-3341	4	13	then	then	ADV
ejpam-3341	4	14	s	s	VERB
ejpam-3341	4	15	/∈	/∈	PUNCT
ejpam-3341	4	16	(	(	PUNCT
ejpam-3341	4	17	shs	shs	NOUN
ejpam-3341	4	18	]	]	PUNCT
ejpam-3341	4	19	}	}	PUNCT
ejpam-3341	4	20	.	.	PUNCT
ejpam-3341	5	1	we	we	PRON
ejpam-3341	5	2	prove	prove	VERB
ejpam-3341	5	3	,	,	PUNCT
ejpam-3341	5	4	among	among	ADP
ejpam-3341	5	5	others	other	NOUN
ejpam-3341	5	6	,	,	PUNCT
ejpam-3341	5	7	that	that	SCONJ
ejpam-3341	5	8	if	if	SCONJ
ejpam-3341	5	9	a	a	PRON
ejpam-3341	5	10	is	be	AUX
ejpam-3341	5	11	a	a	DET
ejpam-3341	5	12	right	right	ADJ
ejpam-3341	5	13	ideal	ideal	NOUN
ejpam-3341	5	14	of	of	ADP
ejpam-3341	5	15	s	s	PRON
ejpam-3341	5	16	and	and	CCONJ
ejpam-3341	5	17	the	the	DET
ejpam-3341	5	18	set	set	NOUN
ejpam-3341	5	19	ha(s	ha(	NOUN
ejpam-3341	5	20	)	)	PUNCT
ejpam-3341	5	21	is	be	AUX
ejpam-3341	5	22	nonempty	nonempty	ADJ
ejpam-3341	5	23	,	,	PUNCT
ejpam-3341	5	24	then	then	ADV
ejpam-3341	5	25	ha(s	ha(	NOUN
ejpam-3341	5	26	)	)	PUNCT
ejpam-3341	5	27	is	be	AUX
ejpam-3341	5	28	an	an	DET
ejpam-3341	5	29	ideal	ideal	NOUN
ejpam-3341	5	30	of	of	ADP
ejpam-3341	5	31	s	s	NOUN
ejpam-3341	5	32	;	;	PUNCT
ejpam-3341	5	33	in	in	ADP
ejpam-3341	5	34	particular	particular	ADJ
ejpam-3341	5	35	it	it	PRON
ejpam-3341	5	36	is	be	AUX
ejpam-3341	5	37	a	a	DET
ejpam-3341	5	38	semiprime	semiprime	NOUN
ejpam-3341	5	39	ideal	ideal	NOUN
ejpam-3341	5	40	of	of	ADP
ejpam-3341	5	41	s.	s.	PROPN
ejpam-3341	5	42	moreover	moreover	ADV
ejpam-3341	5	43	,	,	PUNCT
ejpam-3341	5	44	if	if	SCONJ
ejpam-3341	5	45	a	a	PRON
ejpam-3341	5	46	is	be	AUX
ejpam-3341	5	47	an	an	DET
ejpam-3341	5	48	ideal	ideal	NOUN
ejpam-3341	5	49	of	of	ADP
ejpam-3341	5	50	s	s	PROPN
ejpam-3341	5	51	,	,	PUNCT
ejpam-3341	5	52	then	then	ADV
ejpam-3341	5	53	a	a	DET
ejpam-3341	5	54	⊆	⊆	NUM
ejpam-3341	5	55	ha(s	ha(	NOUN
ejpam-3341	5	56	)	)	PUNCT
ejpam-3341	5	57	.	.	PUNCT
ejpam-3341	6	1	finally	finally	ADV
ejpam-3341	6	2	,	,	PUNCT
ejpam-3341	6	3	we	we	PRON
ejpam-3341	6	4	prove	prove	VERB
ejpam-3341	6	5	that	that	SCONJ
ejpam-3341	6	6	if	if	SCONJ
ejpam-3341	6	7	a	a	PRON
ejpam-3341	6	8	and	and	CCONJ
ejpam-3341	6	9	i	i	PRON
ejpam-3341	6	10	are	be	AUX
ejpam-3341	6	11	right	right	ADJ
ejpam-3341	6	12	ideals	ideal	NOUN
ejpam-3341	6	13	of	of	ADP
ejpam-3341	6	14	s	s	NOUN
ejpam-3341	6	15	,	,	PUNCT
ejpam-3341	6	16	then	then	ADV
ejpam-3341	6	17	i	i	PRON
ejpam-3341	6	18	⊆	⊆	NUM
ejpam-3341	6	19	ha(s	ha(	NOUN
ejpam-3341	6	20	)	)	PUNCT
ejpam-3341	7	1	if	if	SCONJ
ejpam-3341	7	2	and	and	CCONJ
ejpam-3341	7	3	only	only	ADV
ejpam-3341	7	4	if	if	SCONJ
ejpam-3341	7	5	s	s	X
ejpam-3341	7	6	/∈	/∈	INTJ
ejpam-3341	7	7	(	(	PUNCT
ejpam-3341	7	8	si	si	X
ejpam-3341	7	9	]	]	X
ejpam-3341	7	10	for	for	ADP
ejpam-3341	7	11	every	every	DET
ejpam-3341	7	12	s	s	PROPN
ejpam-3341	7	13	∈	∈	NOUN
ejpam-3341	7	14	s\a	s\a	NOUN
ejpam-3341	7	15	.	.	PUNCT
ejpam-3341	8	1	we	we	PRON
ejpam-3341	8	2	give	give	VERB
ejpam-3341	8	3	some	some	DET
ejpam-3341	8	4	examples	example	NOUN
ejpam-3341	8	5	that	that	PRON
ejpam-3341	8	6	illustrate	illustrate	VERB
ejpam-3341	8	7	our	our	PRON
ejpam-3341	8	8	results	result	NOUN
ejpam-3341	8	9	.	.	PUNCT
ejpam-3341	9	1	our	our	PRON
ejpam-3341	9	2	results	result	NOUN
ejpam-3341	9	3	generalize	generalize	VERB
ejpam-3341	9	4	the	the	DET
ejpam-3341	9	5	theorem	theorem	NOUN
ejpam-3341	9	6	2.4	2.4	NUM
ejpam-3341	9	7	in	in	ADP
ejpam-3341	9	8	semigroup	semigroup	PROPN
ejpam-3341	9	9	forum	forum	PROPN
ejpam-3341	9	10	96	96	NUM
ejpam-3341	9	11	(	(	PUNCT
ejpam-3341	9	12	2018	2018	NUM
ejpam-3341	9	13	)	)	PUNCT
ejpam-3341	9	14	,	,	PUNCT
ejpam-3341	9	15	523–535	523–535	NUM
ejpam-3341	9	16	.	.	PUNCT
ejpam-3341	10	1	2010	2010	NUM
ejpam-3341	10	2	mathematics	mathematic	NOUN
ejpam-3341	10	3	subject	subject	NOUN
ejpam-3341	10	4	classifications	classification	NOUN
ejpam-3341	10	5	:	:	PUNCT
ejpam-3341	10	6	06f05	06f05	NUM
ejpam-3341	10	7	,	,	PUNCT
ejpam-3341	10	8	20m10	20m10	NUM
ejpam-3341	10	9	key	key	ADJ
ejpam-3341	10	10	words	word	NOUN
ejpam-3341	10	11	and	and	CCONJ
ejpam-3341	10	12	phrases	phrase	NOUN
ejpam-3341	10	13	:	:	PUNCT
ejpam-3341	10	14	ordered	order	VERB
ejpam-3341	10	15	semigroup	semigroup	PROPN
ejpam-3341	10	16	,	,	PUNCT
ejpam-3341	10	17	semiprime	semiprime	NOUN
ejpam-3341	10	18	subset	subset	NOUN
ejpam-3341	10	19	(	(	PUNCT
ejpam-3341	10	20	right	right	ADV
ejpam-3341	10	21	ideal	ideal	NOUN
ejpam-3341	10	22	)	)	PUNCT
ejpam-3341	10	23	,	,	PUNCT
ejpam-3341	10	24	completely	completely	ADV
ejpam-3341	10	25	semiprime	semiprime	NOUN
ejpam-3341	10	26	ideal	ideal	NOUN
ejpam-3341	10	27	,	,	PUNCT
ejpam-3341	10	28	prime	prime	ADJ
ejpam-3341	10	29	subset	subset	NOUN
ejpam-3341	10	30	(	(	PUNCT
ejpam-3341	10	31	right	right	ADV
ejpam-3341	10	32	ideal	ideal	NOUN
ejpam-3341	10	33	)	)	PUNCT
ejpam-3341	10	34	,	,	PUNCT
ejpam-3341	10	35	completely	completely	ADV
ejpam-3341	10	36	prime	prime	ADJ
ejpam-3341	10	37	ideal	ideal	ADJ
ejpam-3341	10	38	,	,	PUNCT
ejpam-3341	10	39	hoehnke	hoehnke	ADJ
ejpam-3341	10	40	ideal	ideal	NOUN
ejpam-3341	10	41	1	1	NUM
ejpam-3341	10	42	.	.	PUNCT
ejpam-3341	10	43	introduction	introduction	NOUN
ejpam-3341	10	44	and	and	CCONJ
ejpam-3341	10	45	prerequisites	prerequisite	NOUN
ejpam-3341	10	46	regarding	regard	VERB
ejpam-3341	10	47	the	the	DET
ejpam-3341	10	48	prime	prime	ADJ
ejpam-3341	10	49	ideals	ideal	NOUN
ejpam-3341	11	1	,	,	PUNCT
ejpam-3341	11	2	clifford	clifford	PROPN
ejpam-3341	11	3	uses	use	VERB
ejpam-3341	11	4	the	the	DET
ejpam-3341	11	5	term	term	NOUN
ejpam-3341	11	6	“	"	PUNCT
ejpam-3341	11	7	prime	prime	ADJ
ejpam-3341	11	8	”	"	PUNCT
ejpam-3341	11	9	while	while	SCONJ
ejpam-3341	11	10	petrich	petrich	VERB
ejpam-3341	11	11	the	the	DET
ejpam-3341	11	12	term	term	NOUN
ejpam-3341	11	13	“	"	PUNCT
ejpam-3341	11	14	completely	completely	ADV
ejpam-3341	11	15	prime	prime	ADJ
ejpam-3341	11	16	”	"	PUNCT
ejpam-3341	11	17	.	.	PUNCT
ejpam-3341	12	1	clifford	clifford	PROPN
ejpam-3341	12	2	uses	use	VERB
ejpam-3341	12	3	the	the	DET
ejpam-3341	12	4	term	term	NOUN
ejpam-3341	12	5	“	"	PUNCT
ejpam-3341	12	6	semiprime	semiprime	NOUN
ejpam-3341	12	7	ideal	ideal	NOUN
ejpam-3341	12	8	”	"	PUNCT
ejpam-3341	12	9	and	and	CCONJ
ejpam-3341	12	10	petrich	petrich	VERB
ejpam-3341	12	11	the	the	DET
ejpam-3341	12	12	term	term	NOUN
ejpam-3341	12	13	“	"	PUNCT
ejpam-3341	12	14	completely	completely	ADV
ejpam-3341	12	15	semiprime	semiprime	NOUN
ejpam-3341	12	16	ideal	ideal	NOUN
ejpam-3341	12	17	(	(	PUNCT
ejpam-3341	12	18	subset	subset	NOUN
ejpam-3341	12	19	)	)	PUNCT
ejpam-3341	12	20	”	"	PUNCT
ejpam-3341	12	21	.	.	PUNCT
ejpam-3341	13	1	for	for	ADP
ejpam-3341	13	2	ordered	order	VERB
ejpam-3341	13	3	semigroups	semigroup	NOUN
ejpam-3341	13	4	i	i	PRON
ejpam-3341	13	5	adopted	adopt	VERB
ejpam-3341	13	6	the	the	DET
ejpam-3341	13	7	terminology	terminology	NOUN
ejpam-3341	13	8	due	due	ADP
ejpam-3341	13	9	to	to	ADP
ejpam-3341	13	10	clifford	clifford	PROPN
ejpam-3341	13	11	;	;	PUNCT
ejpam-3341	13	12	the	the	DET
ejpam-3341	13	13	authors	author	NOUN
ejpam-3341	13	14	in	in	ADP
ejpam-3341	13	15	[	[	X
ejpam-3341	13	16	2	2	NUM
ejpam-3341	13	17	]	]	PUNCT
ejpam-3341	13	18	the	the	DET
ejpam-3341	13	19	terminology	terminology	NOUN
ejpam-3341	13	20	by	by	ADP
ejpam-3341	13	21	petrich	petrich	PROPN
ejpam-3341	13	22	.	.	PUNCT
ejpam-3341	14	1	since	since	SCONJ
ejpam-3341	14	2	in	in	ADP
ejpam-3341	14	3	the	the	DET
ejpam-3341	14	4	present	present	ADJ
ejpam-3341	14	5	paper	paper	NOUN
ejpam-3341	14	6	we	we	PRON
ejpam-3341	14	7	refer	refer	VERB
ejpam-3341	14	8	to	to	ADP
ejpam-3341	14	9	[	[	X
ejpam-3341	14	10	2	2	NUM
ejpam-3341	14	11	]	]	PUNCT
ejpam-3341	14	12	,	,	PUNCT
ejpam-3341	14	13	for	for	ADP
ejpam-3341	14	14	the	the	DET
ejpam-3341	14	15	sake	sake	NOUN
ejpam-3341	14	16	of	of	ADP
ejpam-3341	14	17	completeness	completeness	NOUN
ejpam-3341	14	18	,	,	PUNCT
ejpam-3341	14	19	in	in	ADP
ejpam-3341	14	20	particular	particular	ADJ
ejpam-3341	14	21	for	for	ADP
ejpam-3341	14	22	this	this	DET
ejpam-3341	14	23	paper	paper	NOUN
ejpam-3341	14	24	,	,	PUNCT
ejpam-3341	14	25	we	we	PRON
ejpam-3341	14	26	will	will	AUX
ejpam-3341	14	27	use	use	VERB
ejpam-3341	14	28	the	the	DET
ejpam-3341	14	29	terms	term	NOUN
ejpam-3341	14	30	prime	prime	ADJ
ejpam-3341	14	31	,	,	PUNCT
ejpam-3341	14	32	semiprime	semiprime	NOUN
ejpam-3341	14	33	,	,	PUNCT
ejpam-3341	14	34	completely	completely	ADV
ejpam-3341	14	35	prime	prime	ADJ
ejpam-3341	14	36	,	,	PUNCT
ejpam-3341	14	37	completely	completely	ADV
ejpam-3341	14	38	semiprime	semiprime	NOUN
ejpam-3341	14	39	.	.	PUNCT
ejpam-3341	15	1	for	for	ADP
ejpam-3341	15	2	an	an	DET
ejpam-3341	15	3	ordered	order	VERB
ejpam-3341	15	4	semigroup	semigroup	NOUN
ejpam-3341	15	5	s	s	VERB
ejpam-3341	15	6	the	the	DET
ejpam-3341	15	7	zero	zero	NUM
ejpam-3341	15	8	of	of	ADP
ejpam-3341	15	9	s	s	PROPN
ejpam-3341	15	10	,	,	PUNCT
ejpam-3341	15	11	denoted	denote	VERB
ejpam-3341	15	12	by	by	ADP
ejpam-3341	15	13	0	0	NUM
ejpam-3341	15	14	,	,	PUNCT
ejpam-3341	15	15	is	be	AUX
ejpam-3341	15	16	an	an	DET
ejpam-3341	15	17	element	element	NOUN
ejpam-3341	15	18	of	of	ADP
ejpam-3341	15	19	s	s	PRON
ejpam-3341	15	20	such	such	ADJ
ejpam-3341	15	21	that	that	DET
ejpam-3341	15	22	0x	0x	NOUN
ejpam-3341	15	23	=	=	PUNCT
ejpam-3341	15	24	x0	x0	PROPN
ejpam-3341	15	25	=	=	PUNCT
ejpam-3341	15	26	0	0	NUM
ejpam-3341	15	27	and	and	CCONJ
ejpam-3341	15	28	0	0	NUM
ejpam-3341	15	29	≤	≤	NUM
ejpam-3341	15	30	x	x	PUNCT
ejpam-3341	15	31	for	for	ADP
ejpam-3341	15	32	every	every	DET
ejpam-3341	15	33	x	x	SYM
ejpam-3341	15	34	∈	∈	PROPN
ejpam-3341	15	35	s	s	PART
ejpam-3341	15	36	[	[	X
ejpam-3341	15	37	1	1	NUM
ejpam-3341	15	38	,	,	PUNCT
ejpam-3341	15	39	3	3	NUM
ejpam-3341	15	40	]	]	PUNCT
ejpam-3341	15	41	.	.	PUNCT
ejpam-3341	16	1	in	in	ADP
ejpam-3341	16	2	an	an	DET
ejpam-3341	16	3	ordered	order	VERB
ejpam-3341	16	4	semigroup	semigroup	NOUN
ejpam-3341	16	5	,	,	PUNCT
ejpam-3341	16	6	the	the	DET
ejpam-3341	16	7	order	order	NOUN
ejpam-3341	16	8	plays	play	VERB
ejpam-3341	16	9	an	an	DET
ejpam-3341	16	10	essential	essential	ADJ
ejpam-3341	16	11	role	role	NOUN
ejpam-3341	16	12	and	and	CCONJ
ejpam-3341	16	13	a	a	DET
ejpam-3341	16	14	relation	relation	NOUN
ejpam-3341	16	15	between	between	ADP
ejpam-3341	16	16	the	the	DET
ejpam-3341	16	17	multiplication	multiplication	NOUN
ejpam-3341	16	18	and	and	CCONJ
ejpam-3341	16	19	the	the	DET
ejpam-3341	16	20	order	order	NOUN
ejpam-3341	16	21	is	be	AUX
ejpam-3341	16	22	needed	need	VERB
ejpam-3341	16	23	.	.	PUNCT
ejpam-3341	17	1	let	let	VERB
ejpam-3341	17	2	us	we	PRON
ejpam-3341	17	3	first	first	ADV
ejpam-3341	17	4	give	give	VERB
ejpam-3341	17	5	the	the	DET
ejpam-3341	17	6	following	follow	VERB
ejpam-3341	17	7	definitions	definition	NOUN
ejpam-3341	17	8	.	.	PUNCT
ejpam-3341	18	1	definition	definition	NOUN
ejpam-3341	18	2	1.1	1.1	NUM
ejpam-3341	18	3	.	.	PUNCT
ejpam-3341	19	1	[	[	X
ejpam-3341	19	2	5	5	NUM
ejpam-3341	19	3	;	;	PUNCT
ejpam-3341	19	4	definition	definition	NOUN
ejpam-3341	19	5	2	2	NUM
ejpam-3341	19	6	]	]	PUNCT
ejpam-3341	19	7	let	let	VERB
ejpam-3341	19	8	s	s	PRON
ejpam-3341	19	9	be	be	AUX
ejpam-3341	19	10	an	an	DET
ejpam-3341	19	11	ordered	order	VERB
ejpam-3341	19	12	semigroup	semigroup	NOUN
ejpam-3341	19	13	.	.	PUNCT
ejpam-3341	20	1	a	a	DET
ejpam-3341	20	2	subset	subset	NOUN
ejpam-3341	20	3	a	a	PRON
ejpam-3341	20	4	of	of	ADP
ejpam-3341	20	5	s	s	PRON
ejpam-3341	20	6	is	be	AUX
ejpam-3341	20	7	called	call	VERB
ejpam-3341	20	8	completely	completely	ADV
ejpam-3341	20	9	prime	prime	ADJ
ejpam-3341	20	10	if	if	SCONJ
ejpam-3341	20	11	for	for	ADP
ejpam-3341	20	12	any	any	DET
ejpam-3341	20	13	subsets	subset	NOUN
ejpam-3341	20	14	b	b	PROPN
ejpam-3341	20	15	,	,	PUNCT
ejpam-3341	20	16	c	c	NOUN
ejpam-3341	20	17	of	of	ADP
ejpam-3341	20	18	s	s	PRON
ejpam-3341	20	19	such	such	ADJ
ejpam-3341	20	20	that	that	SCONJ
ejpam-3341	20	21	bc	bc	PROPN
ejpam-3341	20	22	⊆	⊆	NUM
ejpam-3341	20	23	a	a	PRON
ejpam-3341	20	24	,	,	PUNCT
ejpam-3341	20	25	we	we	PRON
ejpam-3341	20	26	have	have	VERB
ejpam-3341	20	27	b	b	NUM
ejpam-3341	20	28	⊆	⊆	NUM
ejpam-3341	20	29	a	a	DET
ejpam-3341	20	30	or	or	CCONJ
ejpam-3341	20	31	c	c	NOUN
ejpam-3341	20	32	⊆	⊆	NUM
ejpam-3341	20	33	a.	a.	NOUN
ejpam-3341	20	34	equivalent	equivalent	ADJ
ejpam-3341	20	35	definition	definition	NOUN
ejpam-3341	20	36	:	:	PUNCT
ejpam-3341	20	37	if	if	SCONJ
ejpam-3341	20	38	x	x	X
ejpam-3341	20	39	,	,	PUNCT
ejpam-3341	20	40	y	y	PROPN
ejpam-3341	20	41	∈	∈	PROPN
ejpam-3341	20	42	s	s	VERB
ejpam-3341	20	43	such	such	ADJ
ejpam-3341	20	44	that	that	SCONJ
ejpam-3341	20	45	xy	xy	PROPN
ejpam-3341	20	46	∈	∈	PROPN
ejpam-3341	21	1	a	a	DET
ejpam-3341	21	2	,	,	PUNCT
ejpam-3341	21	3	then	then	ADV
ejpam-3341	21	4	x	x	PART
ejpam-3341	21	5	∈	∈	PROPN
ejpam-3341	21	6	a	a	PRON
ejpam-3341	21	7	of	of	ADP
ejpam-3341	21	8	y	y	PROPN
ejpam-3341	21	9	∈	∈	PROPN
ejpam-3341	21	10	a.	a.	NOUN
ejpam-3341	21	11	definition	definition	NOUN
ejpam-3341	21	12	1.2	1.2	NUM
ejpam-3341	21	13	.	.	PUNCT
ejpam-3341	22	1	[	[	X
ejpam-3341	22	2	5	5	NUM
ejpam-3341	22	3	;	;	PUNCT
ejpam-3341	22	4	definition	definition	NOUN
ejpam-3341	22	5	3	3	NUM
ejpam-3341	22	6	]	]	PUNCT
ejpam-3341	22	7	let	let	VERB
ejpam-3341	22	8	s	s	PRON
ejpam-3341	22	9	be	be	AUX
ejpam-3341	22	10	an	an	DET
ejpam-3341	22	11	ordered	order	VERB
ejpam-3341	22	12	semigroup	semigroup	NOUN
ejpam-3341	22	13	.	.	PUNCT
ejpam-3341	23	1	a	a	DET
ejpam-3341	23	2	subset	subset	NOUN
ejpam-3341	23	3	a	a	PRON
ejpam-3341	23	4	of	of	ADP
ejpam-3341	23	5	s	s	PRON
ejpam-3341	23	6	is	be	AUX
ejpam-3341	23	7	called	call	VERB
ejpam-3341	23	8	prime	prime	ADJ
ejpam-3341	23	9	if	if	SCONJ
ejpam-3341	23	10	for	for	ADP
ejpam-3341	23	11	any	any	DET
ejpam-3341	23	12	ideals	ideal	NOUN
ejpam-3341	23	13	b	b	NUM
ejpam-3341	23	14	,	,	PUNCT
ejpam-3341	23	15	c	c	NOUN
ejpam-3341	23	16	of	of	ADP
ejpam-3341	23	17	s	s	PRON
ejpam-3341	23	18	such	such	ADJ
ejpam-3341	23	19	that	that	SCONJ
ejpam-3341	23	20	bc	bc	PROPN
ejpam-3341	23	21	⊆	⊆	NUM
ejpam-3341	23	22	a	a	PRON
ejpam-3341	23	23	,	,	PUNCT
ejpam-3341	23	24	we	we	PRON
ejpam-3341	23	25	have	have	VERB
ejpam-3341	23	26	b	b	NUM
ejpam-3341	23	27	⊆	⊆	NUM
ejpam-3341	23	28	a	a	PRON
ejpam-3341	23	29	or	or	CCONJ
ejpam-3341	23	30	c	c	NOUN
ejpam-3341	23	31	⊆	⊆	NUM
ejpam-3341	23	32	a.	a.	NOUN
ejpam-3341	23	33	doi	doi	NOUN
ejpam-3341	23	34	:	:	PUNCT
ejpam-3341	23	35	https://doi.org/10.29020/nybg.ejpam.v11i4.3341	https://doi.org/10.29020/nybg.ejpam.v11i4.3341	NOUN
ejpam-3341	23	36	email	email	NOUN
ejpam-3341	23	37	address	address	NOUN
ejpam-3341	23	38	:	:	PUNCT
ejpam-3341	23	39	nkehayop@math.uoa.gr	nkehayop@math.uoa.gr	ADV
ejpam-3341	23	40	(	(	PUNCT
ejpam-3341	23	41	n.	n.	PROPN
ejpam-3341	23	42	kehayopulu	kehayopulu	PROPN
ejpam-3341	23	43	)	)	PUNCT
ejpam-3341	23	44	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3341	24	1	911	911	NUM
ejpam-3341	24	2	c	c	NOUN
ejpam-3341	24	3	©	©	PROPN
ejpam-3341	24	4	2018	2018	NUM
ejpam-3341	24	5	ejpam	ejpam	VERB
ejpam-3341	24	6	all	all	DET
ejpam-3341	24	7	rights	right	NOUN
ejpam-3341	24	8	reserved	reserve	VERB
ejpam-3341	24	9	.	.	PUNCT
ejpam-3341	25	1	n.	n.	PROPN
ejpam-3341	25	2	kehayopulu	kehayopulu	PROPN
ejpam-3341	25	3	/	/	SYM
ejpam-3341	25	4	eur	eur	PROPN
ejpam-3341	25	5	.	.	PUNCT
ejpam-3341	26	1	j.	j.	PROPN
ejpam-3341	26	2	pure	pure	PROPN
ejpam-3341	26	3	appl	appl	PROPN
ejpam-3341	26	4	.	.	PROPN
ejpam-3341	26	5	math	math	PROPN
ejpam-3341	26	6	,	,	PUNCT
ejpam-3341	26	7	11	11	NUM
ejpam-3341	26	8	(	(	PUNCT
ejpam-3341	26	9	4	4	NUM
ejpam-3341	26	10	)	)	PUNCT
ejpam-3341	26	11	(	(	PUNCT
ejpam-3341	26	12	2018	2018	NUM
ejpam-3341	26	13	)	)	PUNCT
ejpam-3341	26	14	,	,	PUNCT
ejpam-3341	26	15	911	911	NUM
ejpam-3341	26	16	-	-	SYM
ejpam-3341	26	17	921	921	NUM
ejpam-3341	26	18	912	912	NUM
ejpam-3341	26	19	definition	definition	NOUN
ejpam-3341	26	20	1.3	1.3	NUM
ejpam-3341	26	21	.	.	PUNCT
ejpam-3341	27	1	[	[	X
ejpam-3341	27	2	5	5	NUM
ejpam-3341	27	3	;	;	PUNCT
ejpam-3341	27	4	definition	definition	NOUN
ejpam-3341	27	5	4	4	NUM
ejpam-3341	27	6	]	]	PUNCT
ejpam-3341	27	7	let	let	VERB
ejpam-3341	27	8	s	s	PRON
ejpam-3341	27	9	be	be	AUX
ejpam-3341	27	10	an	an	DET
ejpam-3341	27	11	ordered	order	VERB
ejpam-3341	27	12	semigroup	semigroup	NOUN
ejpam-3341	27	13	.	.	PUNCT
ejpam-3341	28	1	a	a	DET
ejpam-3341	28	2	subset	subset	NOUN
ejpam-3341	28	3	a	a	PRON
ejpam-3341	28	4	of	of	ADP
ejpam-3341	28	5	s	s	PRON
ejpam-3341	28	6	is	be	AUX
ejpam-3341	28	7	called	call	VERB
ejpam-3341	28	8	completely	completely	ADV
ejpam-3341	28	9	semiprime	semiprime	NOUN
ejpam-3341	28	10	if	if	SCONJ
ejpam-3341	28	11	for	for	ADP
ejpam-3341	28	12	any	any	DET
ejpam-3341	28	13	subset	subset	NOUN
ejpam-3341	28	14	b	b	NOUN
ejpam-3341	28	15	of	of	ADP
ejpam-3341	28	16	s	s	PRON
ejpam-3341	28	17	such	such	ADJ
ejpam-3341	28	18	that	that	DET
ejpam-3341	28	19	b2	b2	NOUN
ejpam-3341	28	20	⊆	⊆	NUM
ejpam-3341	28	21	a	a	PRON
ejpam-3341	28	22	,	,	PUNCT
ejpam-3341	28	23	we	we	PRON
ejpam-3341	28	24	have	have	VERB
ejpam-3341	28	25	b	b	NUM
ejpam-3341	28	26	⊆	⊆	NUM
ejpam-3341	28	27	a.	a.	NOUN
ejpam-3341	28	28	equivalent	equivalent	ADJ
ejpam-3341	28	29	definition	definition	NOUN
ejpam-3341	28	30	:	:	PUNCT
ejpam-3341	28	31	for	for	SCONJ
ejpam-3341	28	32	every	every	DET
ejpam-3341	28	33	x	x	SYM
ejpam-3341	28	34	∈	∈	PROPN
ejpam-3341	28	35	s	s	VERB
ejpam-3341	28	36	such	such	ADJ
ejpam-3341	28	37	that	that	SCONJ
ejpam-3341	28	38	x2	x2	PROPN
ejpam-3341	28	39	∈	∈	PROPN
ejpam-3341	28	40	a	a	PRON
ejpam-3341	28	41	,	,	PUNCT
ejpam-3341	28	42	we	we	PRON
ejpam-3341	28	43	have	have	VERB
ejpam-3341	28	44	x	x	X
ejpam-3341	28	45	∈	∈	PROPN
ejpam-3341	28	46	a.	a.	NOUN
ejpam-3341	28	47	definition	definition	NOUN
ejpam-3341	28	48	1.4	1.4	NUM
ejpam-3341	28	49	.	.	PUNCT
ejpam-3341	29	1	[	[	X
ejpam-3341	29	2	4	4	NUM
ejpam-3341	29	3	;	;	PUNCT
ejpam-3341	29	4	remark	remark	NOUN
ejpam-3341	29	5	4	4	NUM
ejpam-3341	29	6	]	]	PUNCT
ejpam-3341	29	7	let	let	VERB
ejpam-3341	29	8	s	s	PRON
ejpam-3341	29	9	be	be	AUX
ejpam-3341	29	10	an	an	DET
ejpam-3341	29	11	ordered	order	VERB
ejpam-3341	29	12	semigroup	semigroup	NOUN
ejpam-3341	29	13	.	.	PUNCT
ejpam-3341	30	1	a	a	DET
ejpam-3341	30	2	subset	subset	NOUN
ejpam-3341	30	3	a	a	PRON
ejpam-3341	30	4	of	of	ADP
ejpam-3341	30	5	s	s	PRON
ejpam-3341	30	6	is	be	AUX
ejpam-3341	30	7	called	call	VERB
ejpam-3341	30	8	semiprime	semiprime	NOUN
ejpam-3341	30	9	if	if	SCONJ
ejpam-3341	30	10	for	for	ADP
ejpam-3341	30	11	any	any	DET
ejpam-3341	30	12	ideal	ideal	ADJ
ejpam-3341	30	13	b	b	PROPN
ejpam-3341	30	14	of	of	ADP
ejpam-3341	30	15	s	s	PRON
ejpam-3341	30	16	such	such	ADJ
ejpam-3341	30	17	that	that	DET
ejpam-3341	30	18	b2	b2	NOUN
ejpam-3341	30	19	⊆	⊆	NUM
ejpam-3341	30	20	a	a	PRON
ejpam-3341	30	21	,	,	PUNCT
ejpam-3341	30	22	we	we	PRON
ejpam-3341	30	23	have	have	VERB
ejpam-3341	30	24	b	b	NUM
ejpam-3341	30	25	⊆	⊆	NUM
ejpam-3341	30	26	a.	a.	NOUN
ejpam-3341	30	27	clearly	clearly	ADV
ejpam-3341	30	28	,	,	PUNCT
ejpam-3341	30	29	every	every	DET
ejpam-3341	30	30	completely	completely	ADV
ejpam-3341	30	31	prime	prime	ADJ
ejpam-3341	30	32	(	(	PUNCT
ejpam-3341	30	33	resp	resp	NOUN
ejpam-3341	30	34	.	.	PUNCT
ejpam-3341	31	1	completely	completely	ADV
ejpam-3341	31	2	semiprime	semiprime	NOUN
ejpam-3341	31	3	)	)	PUNCT
ejpam-3341	32	1	subset	subset	NOUN
ejpam-3341	32	2	of	of	ADP
ejpam-3341	32	3	s	s	PROPN
ejpam-3341	32	4	is	be	AUX
ejpam-3341	32	5	a	a	DET
ejpam-3341	32	6	prime	prime	ADJ
ejpam-3341	32	7	(	(	PUNCT
ejpam-3341	32	8	resp	resp	NOUN
ejpam-3341	32	9	.	.	PUNCT
ejpam-3341	32	10	semiprime	semiprime	NOUN
ejpam-3341	32	11	)	)	PUNCT
ejpam-3341	32	12	subset	subset	NOUN
ejpam-3341	32	13	.	.	PUNCT
ejpam-3341	33	1	the	the	DET
ejpam-3341	33	2	authors	author	NOUN
ejpam-3341	33	3	in	in	ADP
ejpam-3341	33	4	[	[	X
ejpam-3341	33	5	2	2	NUM
ejpam-3341	33	6	]	]	PUNCT
ejpam-3341	33	7	call	call	VERB
ejpam-3341	33	8	a	a	DET
ejpam-3341	33	9	right	right	ADJ
ejpam-3341	33	10	ideal	ideal	NOUN
ejpam-3341	33	11	i	i	PRON
ejpam-3341	33	12	of	of	ADP
ejpam-3341	33	13	an	an	DET
ejpam-3341	33	14	ordered	order	VERB
ejpam-3341	33	15	semigroup	semigroup	NOUN
ejpam-3341	33	16	s	s	VERB
ejpam-3341	33	17	prime	prime	NOUN
ejpam-3341	33	18	if	if	SCONJ
ejpam-3341	33	19	it	it	PRON
ejpam-3341	33	20	is	be	AUX
ejpam-3341	33	21	proper	proper	ADJ
ejpam-3341	33	22	and	and	CCONJ
ejpam-3341	33	23	for	for	ADP
ejpam-3341	33	24	any	any	DET
ejpam-3341	33	25	right	right	ADJ
ejpam-3341	33	26	ideals	ideal	NOUN
ejpam-3341	33	27	a	a	PRON
ejpam-3341	33	28	,	,	PUNCT
ejpam-3341	33	29	b	b	PROPN
ejpam-3341	33	30	of	of	ADP
ejpam-3341	33	31	s	s	PROPN
ejpam-3341	33	32	,	,	PUNCT
ejpam-3341	33	33	ab	ab	PROPN
ejpam-3341	33	34	⊆	⊆	NUM
ejpam-3341	33	35	i	i	PRON
ejpam-3341	33	36	implies	imply	VERB
ejpam-3341	33	37	a	a	DET
ejpam-3341	33	38	⊆	⊆	NUM
ejpam-3341	33	39	i	i	NOUN
ejpam-3341	33	40	or	or	CCONJ
ejpam-3341	33	41	b	b	NOUN
ejpam-3341	33	42	⊆	⊆	NUM
ejpam-3341	33	43	i.	i.	NOUN
ejpam-3341	33	44	they	they	PRON
ejpam-3341	33	45	call	call	VERB
ejpam-3341	33	46	a	a	DET
ejpam-3341	33	47	right	right	ADJ
ejpam-3341	33	48	ideal	ideal	NOUN
ejpam-3341	33	49	of	of	ADP
ejpam-3341	33	50	s	s	PRON
ejpam-3341	33	51	semiprime	semiprime	NOUN
ejpam-3341	33	52	if	if	SCONJ
ejpam-3341	33	53	it	it	PRON
ejpam-3341	33	54	is	be	AUX
ejpam-3341	33	55	proper	proper	ADJ
ejpam-3341	33	56	and	and	CCONJ
ejpam-3341	33	57	for	for	ADP
ejpam-3341	33	58	any	any	DET
ejpam-3341	33	59	right	right	ADJ
ejpam-3341	33	60	ideal	ideal	NOUN
ejpam-3341	33	61	a	a	PRON
ejpam-3341	33	62	of	of	ADP
ejpam-3341	33	63	s	s	PROPN
ejpam-3341	33	64	,	,	PUNCT
ejpam-3341	33	65	a2	a2	PROPN
ejpam-3341	33	66	⊆	⊆	NUM
ejpam-3341	33	67	i	i	PRON
ejpam-3341	33	68	implies	imply	VERB
ejpam-3341	33	69	a	a	DET
ejpam-3341	33	70	⊆	⊆	NUM
ejpam-3341	33	71	i.	i.	NOUN
ejpam-3341	33	72	their	their	PRON
ejpam-3341	33	73	definition	definition	NOUN
ejpam-3341	33	74	regarding	regard	VERB
ejpam-3341	33	75	the	the	DET
ejpam-3341	33	76	completely	completely	ADV
ejpam-3341	33	77	semiprime	semiprime	NOUN
ejpam-3341	33	78	right	right	ADJ
ejpam-3341	33	79	ideal	ideal	NOUN
ejpam-3341	33	80	is	be	AUX
ejpam-3341	33	81	the	the	DET
ejpam-3341	33	82	same	same	ADJ
ejpam-3341	33	83	with	with	ADP
ejpam-3341	33	84	the	the	DET
ejpam-3341	33	85	usual	usual	ADJ
ejpam-3341	33	86	one	one	NUM
ejpam-3341	33	87	in	in	ADP
ejpam-3341	33	88	rings	ring	NOUN
ejpam-3341	33	89	,	,	PUNCT
ejpam-3341	33	90	semigroups	semigroup	NOUN
ejpam-3341	33	91	,	,	PUNCT
ejpam-3341	33	92	ordered	order	VERB
ejpam-3341	33	93	semigroups	semigroup	NOUN
ejpam-3341	33	94	(	(	PUNCT
ejpam-3341	33	95	see	see	VERB
ejpam-3341	33	96	,	,	PUNCT
ejpam-3341	33	97	for	for	ADP
ejpam-3341	33	98	example	example	NOUN
ejpam-3341	33	99	[	[	X
ejpam-3341	33	100	8	8	NUM
ejpam-3341	33	101	]	]	PUNCT
ejpam-3341	33	102	)	)	PUNCT
ejpam-3341	33	103	with	with	ADP
ejpam-3341	33	104	the	the	DET
ejpam-3341	33	105	only	only	ADJ
ejpam-3341	33	106	difference	difference	NOUN
ejpam-3341	33	107	that	that	PRON
ejpam-3341	33	108	they	they	PRON
ejpam-3341	33	109	defined	define	VERB
ejpam-3341	33	110	it	it	PRON
ejpam-3341	33	111	as	as	ADP
ejpam-3341	33	112	“	"	PUNCT
ejpam-3341	33	113	proper	proper	ADJ
ejpam-3341	33	114	”	"	PUNCT
ejpam-3341	33	115	.	.	PUNCT
ejpam-3341	34	1	since	since	SCONJ
ejpam-3341	34	2	every	every	DET
ejpam-3341	34	3	ordered	order	VERB
ejpam-3341	34	4	semigroup	semigroup	NOUN
ejpam-3341	34	5	(	(	PUNCT
ejpam-3341	34	6	ring	ring	NOUN
ejpam-3341	34	7	,	,	PUNCT
ejpam-3341	34	8	semigroup	semigroup	PROPN
ejpam-3341	34	9	)	)	PUNCT
ejpam-3341	34	10	is	be	AUX
ejpam-3341	34	11	itself	itself	PRON
ejpam-3341	34	12	a	a	DET
ejpam-3341	34	13	completely	completely	ADV
ejpam-3341	34	14	prime	prime	ADJ
ejpam-3341	34	15	(	(	PUNCT
ejpam-3341	34	16	prime	prime	NOUN
ejpam-3341	34	17	)	)	PUNCT
ejpam-3341	34	18	or	or	CCONJ
ejpam-3341	34	19	completely	completely	ADV
ejpam-3341	34	20	semiprime	semiprime	NOUN
ejpam-3341	34	21	(	(	PUNCT
ejpam-3341	34	22	semiprime	semiprime	NOUN
ejpam-3341	34	23	)	)	PUNCT
ejpam-3341	34	24	subset	subset	NOUN
ejpam-3341	34	25	of	of	ADP
ejpam-3341	34	26	itself	itself	PRON
ejpam-3341	34	27	,	,	PUNCT
ejpam-3341	34	28	these	these	DET
ejpam-3341	34	29	concepts	concept	NOUN
ejpam-3341	34	30	have	have	AUX
ejpam-3341	34	31	been	be	AUX
ejpam-3341	34	32	never	never	ADV
ejpam-3341	34	33	defined	define	VERB
ejpam-3341	34	34	as	as	ADP
ejpam-3341	34	35	“	"	PUNCT
ejpam-3341	34	36	proper	proper	ADJ
ejpam-3341	34	37	”	"	PUNCT
ejpam-3341	34	38	in	in	ADP
ejpam-3341	34	39	the	the	DET
ejpam-3341	34	40	existed	exist	VERB
ejpam-3341	34	41	bibliography	bibliography	NOUN
ejpam-3341	34	42	(	(	PUNCT
ejpam-3341	34	43	so	so	ADV
ejpam-3341	34	44	in	in	ADP
ejpam-3341	34	45	proofs	proof	NOUN
ejpam-3341	34	46	,	,	PUNCT
ejpam-3341	34	47	as	as	ADV
ejpam-3341	34	48	well	well	ADV
ejpam-3341	34	49	)	)	PUNCT
ejpam-3341	34	50	.	.	PUNCT
ejpam-3341	35	1	for	for	ADP
ejpam-3341	35	2	an	an	DET
ejpam-3341	35	3	ordered	order	VERB
ejpam-3341	35	4	semigroup	semigroup	NOUN
ejpam-3341	35	5	(	(	PUNCT
ejpam-3341	35	6	s	s	PROPN
ejpam-3341	35	7	,	,	PUNCT
ejpam-3341	35	8	·	·	PUNCT
ejpam-3341	35	9	,	,	PUNCT
ejpam-3341	35	10	≤	≤	NUM
ejpam-3341	35	11	)	)	PUNCT
ejpam-3341	35	12	possessing	possess	VERB
ejpam-3341	35	13	a	a	DET
ejpam-3341	35	14	zero	zero	NUM
ejpam-3341	35	15	0	0	NUM
ejpam-3341	35	16	and	and	CCONJ
ejpam-3341	35	17	an	an	DET
ejpam-3341	35	18	identity	identity	NOUN
ejpam-3341	35	19	e	e	NOUN
ejpam-3341	35	20	of	of	ADP
ejpam-3341	35	21	(	(	PUNCT
ejpam-3341	35	22	s	s	PROPN
ejpam-3341	35	23	,	,	PUNCT
ejpam-3341	35	24	·	·	PUNCT
ejpam-3341	35	25	)	)	PUNCT
ejpam-3341	35	26	such	such	ADJ
ejpam-3341	35	27	that	that	SCONJ
ejpam-3341	35	28	e	e	NOUN
ejpam-3341	35	29	6=	6=	NUM
ejpam-3341	35	30	0	0	NUM
ejpam-3341	36	1	it	it	PRON
ejpam-3341	36	2	has	have	AUX
ejpam-3341	36	3	been	be	AUX
ejpam-3341	36	4	proved	prove	VERB
ejpam-3341	36	5	in	in	ADP
ejpam-3341	36	6	[	[	X
ejpam-3341	36	7	2	2	X
ejpam-3341	36	8	]	]	PUNCT
ejpam-3341	36	9	that	that	SCONJ
ejpam-3341	36	10	if	if	SCONJ
ejpam-3341	36	11	a	a	PRON
ejpam-3341	36	12	is	be	AUX
ejpam-3341	36	13	proper	proper	ADJ
ejpam-3341	36	14	right	right	ADJ
ejpam-3341	36	15	ideal	ideal	NOUN
ejpam-3341	36	16	of	of	ADP
ejpam-3341	36	17	s	s	PROPN
ejpam-3341	36	18	,	,	PUNCT
ejpam-3341	36	19	then	then	ADV
ejpam-3341	36	20	the	the	DET
ejpam-3341	36	21	set	set	NOUN
ejpam-3341	36	22	ha(s	ha(	NOUN
ejpam-3341	36	23	)	)	PUNCT
ejpam-3341	36	24	:	:	PUNCT
ejpam-3341	37	1	=	=	SYM
ejpam-3341	37	2	{	{	PUNCT
ejpam-3341	37	3	h	h	NOUN
ejpam-3341	37	4	∈	∈	PROPN
ejpam-3341	37	5	s	s	VERB
ejpam-3341	37	6	such	such	ADJ
ejpam-3341	37	7	that	that	SCONJ
ejpam-3341	37	8	if	if	SCONJ
ejpam-3341	37	9	s	s	X
ejpam-3341	37	10	∈	∈	NOUN
ejpam-3341	37	11	s\a	s\a	NOUN
ejpam-3341	37	12	then	then	ADV
ejpam-3341	37	13	s	s	VERB
ejpam-3341	37	14	/∈	/∈	PUNCT
ejpam-3341	38	1	(	(	PUNCT
ejpam-3341	38	2	shs	shs	PROPN
ejpam-3341	38	3	]	]	PUNCT
ejpam-3341	38	4	}	}	PUNCT
ejpam-3341	38	5	is	be	AUX
ejpam-3341	38	6	an	an	DET
ejpam-3341	38	7	interior	interior	ADJ
ejpam-3341	38	8	ideal	ideal	NOUN
ejpam-3341	38	9	of	of	ADP
ejpam-3341	38	10	s	s	NOUN
ejpam-3341	38	11	;	;	PUNCT
ejpam-3341	38	12	since	since	SCONJ
ejpam-3341	38	13	s	s	PRON
ejpam-3341	38	14	possess	possess	VERB
ejpam-3341	38	15	an	an	DET
ejpam-3341	38	16	identity	identity	NOUN
ejpam-3341	38	17	,	,	PUNCT
ejpam-3341	38	18	the	the	DET
ejpam-3341	38	19	interior	interior	ADJ
ejpam-3341	38	20	ideal	ideal	NOUN
ejpam-3341	38	21	ha(s	ha(	NOUN
ejpam-3341	38	22	)	)	PUNCT
ejpam-3341	38	23	is	be	AUX
ejpam-3341	38	24	also	also	ADV
ejpam-3341	38	25	an	an	DET
ejpam-3341	38	26	ideal	ideal	NOUN
ejpam-3341	38	27	of	of	ADP
ejpam-3341	38	28	s	s	PROPN
ejpam-3341	38	29	,	,	PUNCT
ejpam-3341	38	30	but	but	CCONJ
ejpam-3341	38	31	this	this	PRON
ejpam-3341	38	32	should	should	AUX
ejpam-3341	38	33	be	be	AUX
ejpam-3341	38	34	emphasized	emphasize	VERB
ejpam-3341	38	35	in	in	ADP
ejpam-3341	38	36	[	[	X
ejpam-3341	38	37	2	2	NUM
ejpam-3341	38	38	]	]	PUNCT
ejpam-3341	38	39	since	since	SCONJ
ejpam-3341	38	40	an	an	DET
ejpam-3341	38	41	interior	interior	ADJ
ejpam-3341	38	42	ideal	ideal	NOUN
ejpam-3341	38	43	is	be	AUX
ejpam-3341	38	44	not	not	PART
ejpam-3341	38	45	an	an	DET
ejpam-3341	38	46	ideal	ideal	NOUN
ejpam-3341	38	47	in	in	ADP
ejpam-3341	38	48	general	general	ADJ
ejpam-3341	38	49	.	.	PUNCT
ejpam-3341	39	1	then	then	ADV
ejpam-3341	39	2	the	the	DET
ejpam-3341	39	3	authors	author	NOUN
ejpam-3341	39	4	proved	prove	VERB
ejpam-3341	39	5	that	that	SCONJ
ejpam-3341	39	6	if	if	SCONJ
ejpam-3341	39	7	a	a	PRON
ejpam-3341	39	8	is	be	AUX
ejpam-3341	39	9	a	a	DET
ejpam-3341	39	10	proper	proper	ADJ
ejpam-3341	39	11	right	right	ADJ
ejpam-3341	39	12	ideal	ideal	NOUN
ejpam-3341	39	13	of	of	ADP
ejpam-3341	39	14	s	s	PRON
ejpam-3341	39	15	then	then	ADV
ejpam-3341	39	16	,	,	PUNCT
ejpam-3341	39	17	for	for	ADP
ejpam-3341	39	18	any	any	DET
ejpam-3341	39	19	right	right	ADJ
ejpam-3341	39	20	ideal	ideal	NOUN
ejpam-3341	39	21	i	i	PRON
ejpam-3341	39	22	of	of	ADP
ejpam-3341	39	23	s	s	PRON
ejpam-3341	39	24	we	we	PRON
ejpam-3341	39	25	have	have	AUX
ejpam-3341	39	26	i	i	PRON
ejpam-3341	39	27	⊆	⊆	NUM
ejpam-3341	39	28	ha(s	ha(	NOUN
ejpam-3341	39	29	)	)	PUNCT
ejpam-3341	40	1	if	if	SCONJ
ejpam-3341	40	2	and	and	CCONJ
ejpam-3341	40	3	only	only	ADV
ejpam-3341	40	4	if	if	SCONJ
ejpam-3341	40	5	s	s	AUX
ejpam-3341	40	6	/∈	/∈	INTJ
ejpam-3341	40	7	(	(	PUNCT
ejpam-3341	40	8	si	si	X
ejpam-3341	40	9	]	]	X
ejpam-3341	40	10	for	for	ADP
ejpam-3341	40	11	all	all	DET
ejpam-3341	40	12	s	s	PART
ejpam-3341	40	13	∈	∈	ADJ
ejpam-3341	40	14	s\a	s\a	NOUN
ejpam-3341	40	15	(	(	PUNCT
ejpam-3341	40	16	property	property	NOUN
ejpam-3341	40	17	(	(	PUNCT
ejpam-3341	40	18	2	2	NUM
ejpam-3341	40	19	)	)	PUNCT
ejpam-3341	40	20	in	in	ADP
ejpam-3341	40	21	[	[	X
ejpam-3341	40	22	2	2	NUM
ejpam-3341	40	23	;	;	PUNCT
ejpam-3341	40	24	theorem	theorem	VERB
ejpam-3341	40	25	2.4	2.4	NUM
ejpam-3341	40	26	]	]	PUNCT
ejpam-3341	40	27	)	)	PUNCT
ejpam-3341	40	28	and	and	CCONJ
ejpam-3341	40	29	using	use	VERB
ejpam-3341	40	30	this	this	DET
ejpam-3341	40	31	property	property	NOUN
ejpam-3341	40	32	they	they	PRON
ejpam-3341	40	33	proved	prove	VERB
ejpam-3341	40	34	that	that	SCONJ
ejpam-3341	40	35	if	if	SCONJ
ejpam-3341	40	36	a	a	PRON
ejpam-3341	40	37	is	be	AUX
ejpam-3341	40	38	a	a	DET
ejpam-3341	40	39	proper	proper	ADJ
ejpam-3341	40	40	ideal	ideal	NOUN
ejpam-3341	40	41	of	of	ADP
ejpam-3341	40	42	s	s	PROPN
ejpam-3341	40	43	,	,	PUNCT
ejpam-3341	40	44	then	then	ADV
ejpam-3341	40	45	a	a	DET
ejpam-3341	40	46	⊆	⊆	NUM
ejpam-3341	40	47	ha(s	ha(s	NUM
ejpam-3341	40	48	)	)	PUNCT
ejpam-3341	40	49	(	(	PUNCT
ejpam-3341	40	50	property	property	NOUN
ejpam-3341	40	51	(	(	PUNCT
ejpam-3341	40	52	3	3	NUM
ejpam-3341	40	53	)	)	PUNCT
ejpam-3341	40	54	in	in	ADP
ejpam-3341	40	55	[	[	X
ejpam-3341	40	56	2	2	NUM
ejpam-3341	40	57	;	;	PUNCT
ejpam-3341	40	58	theorem	theorem	VERB
ejpam-3341	40	59	2.4	2.4	NUM
ejpam-3341	40	60	]	]	PUNCT
ejpam-3341	40	61	)	)	PUNCT
ejpam-3341	40	62	and	and	CCONJ
ejpam-3341	40	63	that	that	SCONJ
ejpam-3341	40	64	ha(s	ha(s	PRON
ejpam-3341	40	65	)	)	PUNCT
ejpam-3341	40	66	is	be	AUX
ejpam-3341	40	67	a	a	DET
ejpam-3341	40	68	semiprime	semiprime	NOUN
ejpam-3341	40	69	ideal	ideal	NOUN
ejpam-3341	40	70	of	of	ADP
ejpam-3341	40	71	s	s	X
ejpam-3341	40	72	(	(	PUNCT
ejpam-3341	40	73	property	property	NOUN
ejpam-3341	40	74	(	(	PUNCT
ejpam-3341	40	75	1	1	NUM
ejpam-3341	40	76	)	)	PUNCT
ejpam-3341	40	77	in	in	ADP
ejpam-3341	40	78	the	the	DET
ejpam-3341	40	79	same	same	ADJ
ejpam-3341	40	80	theorem	theorem	NOUN
ejpam-3341	40	81	)	)	PUNCT
ejpam-3341	40	82	in	in	ADP
ejpam-3341	40	83	the	the	DET
ejpam-3341	40	84	sense	sense	NOUN
ejpam-3341	40	85	that	that	SCONJ
ejpam-3341	40	86	ha(s	ha(	NOUN
ejpam-3341	40	87	)	)	PUNCT
ejpam-3341	40	88	is	be	AUX
ejpam-3341	40	89	a	a	DET
ejpam-3341	40	90	proper	proper	ADJ
ejpam-3341	40	91	ideal	ideal	NOUN
ejpam-3341	40	92	of	of	ADP
ejpam-3341	40	93	s	s	PRON
ejpam-3341	40	94	and	and	CCONJ
ejpam-3341	40	95	for	for	ADP
ejpam-3341	40	96	any	any	DET
ejpam-3341	40	97	right	right	ADJ
ejpam-3341	40	98	ideal	ideal	NOUN
ejpam-3341	41	1	i	i	PRON
ejpam-3341	41	2	of	of	ADP
ejpam-3341	41	3	s	s	PRON
ejpam-3341	41	4	such	such	ADJ
ejpam-3341	41	5	that	that	DET
ejpam-3341	41	6	i2	i2	PROPN
ejpam-3341	41	7	⊆	⊆	NUM
ejpam-3341	41	8	ha(s	ha(	NOUN
ejpam-3341	41	9	)	)	PUNCT
ejpam-3341	41	10	we	we	PRON
ejpam-3341	41	11	have	have	VERB
ejpam-3341	41	12	i	i	PRON
ejpam-3341	41	13	⊆	⊆	NUM
ejpam-3341	41	14	ha(s	ha(	NOUN
ejpam-3341	41	15	)	)	PUNCT
ejpam-3341	41	16	.	.	PUNCT
ejpam-3341	42	1	that	that	PRON
ejpam-3341	42	2	is	be	AUX
ejpam-3341	42	3	,	,	PUNCT
ejpam-3341	42	4	it	it	PRON
ejpam-3341	42	5	has	have	AUX
ejpam-3341	42	6	been	be	AUX
ejpam-3341	42	7	proved	prove	VERB
ejpam-3341	42	8	that	that	SCONJ
ejpam-3341	42	9	(	(	PUNCT
ejpam-3341	42	10	2)⇒	2)⇒	NUM
ejpam-3341	42	11	(	(	PUNCT
ejpam-3341	42	12	1	1	NUM
ejpam-3341	42	13	)	)	PUNCT
ejpam-3341	42	14	and	and	CCONJ
ejpam-3341	42	15	(	(	PUNCT
ejpam-3341	42	16	3	3	NUM
ejpam-3341	42	17	)	)	PUNCT
ejpam-3341	42	18	.	.	PUNCT
ejpam-3341	43	1	the	the	DET
ejpam-3341	43	2	set	set	NOUN
ejpam-3341	43	3	ha(s	ha(	NOUN
ejpam-3341	43	4	)	)	PUNCT
ejpam-3341	43	5	has	have	AUX
ejpam-3341	43	6	been	be	AUX
ejpam-3341	43	7	called	call	VERB
ejpam-3341	43	8	“	"	PUNCT
ejpam-3341	43	9	hoehnke	hoehnke	ADJ
ejpam-3341	43	10	ideal	ideal	NOUN
ejpam-3341	43	11	”	"	PUNCT
ejpam-3341	43	12	in	in	ADP
ejpam-3341	43	13	[	[	X
ejpam-3341	43	14	2	2	NUM
ejpam-3341	43	15	]	]	PUNCT
ejpam-3341	43	16	.	.	PUNCT
ejpam-3341	44	1	in	in	ADP
ejpam-3341	44	2	the	the	DET
ejpam-3341	44	3	present	present	ADJ
ejpam-3341	44	4	paper	paper	NOUN
ejpam-3341	44	5	we	we	PRON
ejpam-3341	44	6	define	define	VERB
ejpam-3341	44	7	the	the	DET
ejpam-3341	44	8	ha(s	ha(	NOUN
ejpam-3341	44	9	)	)	PUNCT
ejpam-3341	44	10	for	for	ADP
ejpam-3341	44	11	any	any	DET
ejpam-3341	44	12	proper	proper	ADJ
ejpam-3341	44	13	subset	subset	NOUN
ejpam-3341	44	14	a	a	PRON
ejpam-3341	44	15	of	of	ADP
ejpam-3341	44	16	an	an	DET
ejpam-3341	44	17	ordered	order	VERB
ejpam-3341	44	18	semigroup	semigroup	PROPN
ejpam-3341	44	19	s.	s.	PROPN
ejpam-3341	44	20	we	we	PRON
ejpam-3341	44	21	keep	keep	VERB
ejpam-3341	44	22	the	the	DET
ejpam-3341	44	23	definitions	definition	NOUN
ejpam-3341	44	24	of	of	ADP
ejpam-3341	44	25	semiprime	semiprime	NOUN
ejpam-3341	44	26	and	and	CCONJ
ejpam-3341	44	27	prime	prime	ADJ
ejpam-3341	44	28	subsets	subset	NOUN
ejpam-3341	44	29	of	of	ADP
ejpam-3341	44	30	ordered	order	VERB
ejpam-3341	44	31	semigroups	semigroup	NOUN
ejpam-3341	44	32	given	give	VERB
ejpam-3341	44	33	above	above	ADV
ejpam-3341	44	34	,	,	PUNCT
ejpam-3341	44	35	and	and	CCONJ
ejpam-3341	44	36	we	we	PRON
ejpam-3341	44	37	first	first	ADV
ejpam-3341	44	38	prove	prove	VERB
ejpam-3341	44	39	that	that	SCONJ
ejpam-3341	44	40	the	the	DET
ejpam-3341	44	41	set	set	NOUN
ejpam-3341	44	42	ha(s	ha(	NOUN
ejpam-3341	44	43	)	)	PUNCT
ejpam-3341	44	44	is	be	AUX
ejpam-3341	44	45	a	a	DET
ejpam-3341	44	46	semiprime	semiprime	NOUN
ejpam-3341	44	47	subset	subset	NOUN
ejpam-3341	44	48	of	of	ADP
ejpam-3341	44	49	s.	s.	PROPN
ejpam-3341	44	50	then	then	ADV
ejpam-3341	44	51	we	we	PRON
ejpam-3341	44	52	prove	prove	VERB
ejpam-3341	44	53	that	that	SCONJ
ejpam-3341	44	54	,	,	PUNCT
ejpam-3341	44	55	if	if	SCONJ
ejpam-3341	44	56	a	a	PRON
ejpam-3341	44	57	is	be	AUX
ejpam-3341	44	58	a	a	DET
ejpam-3341	44	59	proper	proper	ADJ
ejpam-3341	44	60	ideal	ideal	NOUN
ejpam-3341	44	61	of	of	ADP
ejpam-3341	44	62	s	s	PROPN
ejpam-3341	44	63	,	,	PUNCT
ejpam-3341	44	64	then	then	ADV
ejpam-3341	44	65	a	a	PRON
ejpam-3341	44	66	is	be	AUX
ejpam-3341	44	67	a	a	DET
ejpam-3341	44	68	subset	subset	NOUN
ejpam-3341	44	69	of	of	ADP
ejpam-3341	44	70	ha(s	ha(	NOUN
ejpam-3341	44	71	)	)	PUNCT
ejpam-3341	44	72	.	.	PUNCT
ejpam-3341	45	1	we	we	PRON
ejpam-3341	45	2	show	show	VERB
ejpam-3341	45	3	,	,	PUNCT
ejpam-3341	45	4	among	among	ADP
ejpam-3341	45	5	others	other	NOUN
ejpam-3341	45	6	,	,	PUNCT
ejpam-3341	45	7	that	that	SCONJ
ejpam-3341	45	8	if	if	SCONJ
ejpam-3341	45	9	a	a	PRON
ejpam-3341	45	10	is	be	AUX
ejpam-3341	45	11	a	a	DET
ejpam-3341	45	12	right	right	ADJ
ejpam-3341	45	13	ideal	ideal	NOUN
ejpam-3341	45	14	of	of	ADP
ejpam-3341	45	15	s	s	PRON
ejpam-3341	45	16	and	and	CCONJ
ejpam-3341	45	17	the	the	DET
ejpam-3341	45	18	set	set	NOUN
ejpam-3341	45	19	ha(s	ha(	NOUN
ejpam-3341	45	20	)	)	PUNCT
ejpam-3341	45	21	is	be	AUX
ejpam-3341	45	22	nonempty	nonempty	ADJ
ejpam-3341	45	23	,	,	PUNCT
ejpam-3341	45	24	then	then	ADV
ejpam-3341	45	25	ha(s	ha(	NOUN
ejpam-3341	45	26	)	)	PUNCT
ejpam-3341	45	27	is	be	AUX
ejpam-3341	45	28	an	an	DET
ejpam-3341	45	29	ideal	ideal	NOUN
ejpam-3341	45	30	of	of	ADP
ejpam-3341	45	31	s	s	PROPN
ejpam-3341	45	32	;	;	PUNCT
ejpam-3341	45	33	and	and	CCONJ
ejpam-3341	45	34	hence	hence	ADV
ejpam-3341	45	35	a	a	DET
ejpam-3341	45	36	semiprime	semiprime	NOUN
ejpam-3341	45	37	ideal	ideal	NOUN
ejpam-3341	45	38	of	of	ADP
ejpam-3341	45	39	s.	s.	PROPN
ejpam-3341	45	40	finally	finally	ADV
ejpam-3341	45	41	,	,	PUNCT
ejpam-3341	45	42	we	we	PRON
ejpam-3341	45	43	prove	prove	VERB
ejpam-3341	45	44	that	that	SCONJ
ejpam-3341	45	45	if	if	SCONJ
ejpam-3341	45	46	a	a	PRON
ejpam-3341	45	47	and	and	CCONJ
ejpam-3341	45	48	i	i	PRON
ejpam-3341	45	49	are	be	AUX
ejpam-3341	45	50	right	right	ADJ
ejpam-3341	45	51	ideals	ideal	NOUN
ejpam-3341	45	52	of	of	ADP
ejpam-3341	45	53	an	an	DET
ejpam-3341	45	54	ordered	order	VERB
ejpam-3341	45	55	semigroup	semigroup	PROPN
ejpam-3341	45	56	s	s	PROPN
ejpam-3341	45	57	,	,	PUNCT
ejpam-3341	45	58	then	then	ADV
ejpam-3341	45	59	we	we	PRON
ejpam-3341	45	60	have	have	VERB
ejpam-3341	45	61	i	i	PRON
ejpam-3341	45	62	⊆	⊆	NUM
ejpam-3341	45	63	ha(s	ha(	NOUN
ejpam-3341	45	64	)	)	PUNCT
ejpam-3341	46	1	if	if	SCONJ
ejpam-3341	46	2	and	and	CCONJ
ejpam-3341	46	3	only	only	ADV
ejpam-3341	46	4	if	if	SCONJ
ejpam-3341	46	5	s	s	X
ejpam-3341	46	6	/∈	/∈	INTJ
ejpam-3341	46	7	(	(	PUNCT
ejpam-3341	46	8	si	si	X
ejpam-3341	46	9	]	]	X
ejpam-3341	46	10	for	for	ADP
ejpam-3341	46	11	every	every	DET
ejpam-3341	46	12	s	s	PROPN
ejpam-3341	46	13	∈	∈	PROPN
ejpam-3341	46	14	s\a	s\a	NOUN
ejpam-3341	46	15	.	.	PUNCT
ejpam-3341	47	1	unlike	unlike	ADP
ejpam-3341	47	2	in	in	ADP
ejpam-3341	47	3	[	[	X
ejpam-3341	47	4	2	2	NUM
ejpam-3341	47	5	]	]	PUNCT
ejpam-3341	47	6	,	,	PUNCT
ejpam-3341	47	7	we	we	PRON
ejpam-3341	47	8	have	have	AUX
ejpam-3341	47	9	not	not	PART
ejpam-3341	47	10	used	use	VERB
ejpam-3341	47	11	this	this	DET
ejpam-3341	47	12	last	last	ADJ
ejpam-3341	47	13	property	property	NOUN
ejpam-3341	47	14	to	to	PART
ejpam-3341	47	15	prove	prove	VERB
ejpam-3341	47	16	that	that	SCONJ
ejpam-3341	47	17	ha(s	ha(	NOUN
ejpam-3341	47	18	)	)	PUNCT
ejpam-3341	47	19	is	be	AUX
ejpam-3341	47	20	semiprime	semiprime	NOUN
ejpam-3341	47	21	and	and	CCONJ
ejpam-3341	47	22	that	that	SCONJ
ejpam-3341	47	23	a	a	DET
ejpam-3341	47	24	⊆	⊆	NUM
ejpam-3341	47	25	ha(s	ha(	NOUN
ejpam-3341	47	26	)	)	PUNCT
ejpam-3341	47	27	;	;	PUNCT
ejpam-3341	47	28	each	each	PRON
ejpam-3341	47	29	of	of	ADP
ejpam-3341	47	30	the	the	DET
ejpam-3341	47	31	three	three	NUM
ejpam-3341	47	32	properties	property	NOUN
ejpam-3341	47	33	have	have	AUX
ejpam-3341	47	34	been	be	AUX
ejpam-3341	47	35	proved	prove	VERB
ejpam-3341	47	36	independently	independently	ADV
ejpam-3341	47	37	and	and	CCONJ
ejpam-3341	47	38	the	the	DET
ejpam-3341	47	39	proof	proof	NOUN
ejpam-3341	47	40	of	of	ADP
ejpam-3341	47	41	theorem	theorem	ADJ
ejpam-3341	47	42	2.4	2.4	NUM
ejpam-3341	47	43	in	in	ADP
ejpam-3341	47	44	[	[	X
ejpam-3341	47	45	2	2	NUM
ejpam-3341	47	46	]	]	PUNCT
ejpam-3341	47	47	can	can	AUX
ejpam-3341	47	48	be	be	AUX
ejpam-3341	47	49	also	also	ADV
ejpam-3341	47	50	given	give	VERB
ejpam-3341	47	51	in	in	ADP
ejpam-3341	47	52	the	the	DET
ejpam-3341	47	53	same	same	ADJ
ejpam-3341	47	54	way	way	NOUN
ejpam-3341	47	55	.	.	PUNCT
ejpam-3341	48	1	in	in	ADP
ejpam-3341	48	2	[	[	X
ejpam-3341	48	3	2	2	NUM
ejpam-3341	48	4	]	]	PUNCT
ejpam-3341	48	5	only	only	ADV
ejpam-3341	48	6	the	the	DET
ejpam-3341	48	7	definition	definition	NOUN
ejpam-3341	48	8	of	of	ADP
ejpam-3341	48	9	semiprime	semiprime	NOUN
ejpam-3341	48	10	right	right	PRON
ejpam-3341	48	11	ideal	ideal	NOUN
ejpam-3341	48	12	is	be	AUX
ejpam-3341	48	13	given	give	VERB
ejpam-3341	48	14	,	,	PUNCT
ejpam-3341	48	15	there	there	PRON
ejpam-3341	48	16	is	be	VERB
ejpam-3341	48	17	no	no	DET
ejpam-3341	48	18	the	the	DET
ejpam-3341	48	19	definition	definition	NOUN
ejpam-3341	48	20	of	of	ADP
ejpam-3341	48	21	semiprime	semiprime	NOUN
ejpam-3341	48	22	ideal	ideal	NOUN
ejpam-3341	48	23	in	in	ADP
ejpam-3341	48	24	the	the	DET
ejpam-3341	48	25	paper	paper	NOUN
ejpam-3341	48	26	.	.	PUNCT
ejpam-3341	49	1	however	however	ADV
ejpam-3341	49	2	,	,	PUNCT
ejpam-3341	49	3	according	accord	VERB
ejpam-3341	49	4	to	to	ADP
ejpam-3341	49	5	the	the	DET
ejpam-3341	49	6	proof	proof	NOUN
ejpam-3341	49	7	of	of	ADP
ejpam-3341	49	8	theorem	theorem	ADJ
ejpam-3341	49	9	2.4	2.4	NUM
ejpam-3341	49	10	,	,	PUNCT
ejpam-3341	49	11	the	the	DET
ejpam-3341	49	12	authors	author	NOUN
ejpam-3341	49	13	call	call	VERB
ejpam-3341	49	14	an	an	DET
ejpam-3341	49	15	ideal	ideal	NOUN
ejpam-3341	49	16	a	a	PRON
ejpam-3341	49	17	of	of	ADP
ejpam-3341	49	18	an	an	DET
ejpam-3341	49	19	ordered	order	VERB
ejpam-3341	49	20	semigroup	semigroup	NOUN
ejpam-3341	49	21	s	s	PART
ejpam-3341	49	22	semiprime	semiprime	NOUN
ejpam-3341	49	23	if	if	SCONJ
ejpam-3341	49	24	it	it	PRON
ejpam-3341	49	25	is	be	AUX
ejpam-3341	49	26	proper	proper	ADJ
ejpam-3341	49	27	and	and	CCONJ
ejpam-3341	49	28	for	for	ADP
ejpam-3341	49	29	any	any	DET
ejpam-3341	49	30	n.	n.	NOUN
ejpam-3341	49	31	kehayopulu	kehayopulu	ADJ
ejpam-3341	49	32	/	/	SYM
ejpam-3341	49	33	eur	eur	PROPN
ejpam-3341	49	34	.	.	PUNCT
ejpam-3341	50	1	j.	j.	PROPN
ejpam-3341	50	2	pure	pure	PROPN
ejpam-3341	50	3	appl	appl	PROPN
ejpam-3341	50	4	.	.	PROPN
ejpam-3341	50	5	math	math	PROPN
ejpam-3341	50	6	,	,	PUNCT
ejpam-3341	50	7	11	11	NUM
ejpam-3341	50	8	(	(	PUNCT
ejpam-3341	50	9	4	4	NUM
ejpam-3341	50	10	)	)	PUNCT
ejpam-3341	50	11	(	(	PUNCT
ejpam-3341	50	12	2018	2018	NUM
ejpam-3341	50	13	)	)	PUNCT
ejpam-3341	50	14	,	,	PUNCT
ejpam-3341	50	15	911	911	NUM
ejpam-3341	50	16	-	-	SYM
ejpam-3341	50	17	921	921	NUM
ejpam-3341	50	18	913	913	NUM
ejpam-3341	50	19	right	right	ADJ
ejpam-3341	50	20	ideal	ideal	NOUN
ejpam-3341	50	21	i	i	PRON
ejpam-3341	50	22	of	of	ADP
ejpam-3341	50	23	s	s	PROPN
ejpam-3341	50	24	,	,	PUNCT
ejpam-3341	50	25	i2	i2	PROPN
ejpam-3341	50	26	⊆	⊆	NUM
ejpam-3341	50	27	a	a	DET
ejpam-3341	50	28	implies	implie	NOUN
ejpam-3341	50	29	i	i	PRON
ejpam-3341	50	30	⊆	⊆	NUM
ejpam-3341	50	31	a.	a.	NOUN
ejpam-3341	50	32	in	in	ADP
ejpam-3341	50	33	case	case	NOUN
ejpam-3341	50	34	of	of	ADP
ejpam-3341	50	35	ideals	ideal	NOUN
ejpam-3341	50	36	,	,	PUNCT
ejpam-3341	50	37	this	this	DET
ejpam-3341	50	38	definition	definition	NOUN
ejpam-3341	50	39	is	be	AUX
ejpam-3341	50	40	equivalent	equivalent	ADJ
ejpam-3341	50	41	to	to	ADP
ejpam-3341	50	42	our	our	PRON
ejpam-3341	50	43	definition	definition	NOUN
ejpam-3341	50	44	1.4	1.4	NUM
ejpam-3341	50	45	.	.	PUNCT
ejpam-3341	51	1	so	so	ADV
ejpam-3341	51	2	the	the	DET
ejpam-3341	51	3	results	result	NOUN
ejpam-3341	51	4	of	of	ADP
ejpam-3341	51	5	the	the	DET
ejpam-3341	51	6	present	present	ADJ
ejpam-3341	51	7	paper	paper	NOUN
ejpam-3341	51	8	generalize	generalize	VERB
ejpam-3341	51	9	the	the	DET
ejpam-3341	51	10	theorem	theorem	NOUN
ejpam-3341	51	11	2.4	2.4	NUM
ejpam-3341	51	12	in	in	ADP
ejpam-3341	51	13	[	[	X
ejpam-3341	51	14	2	2	NUM
ejpam-3341	51	15	]	]	PUNCT
ejpam-3341	51	16	.	.	PUNCT
ejpam-3341	52	1	on	on	ADP
ejpam-3341	52	2	this	this	DET
ejpam-3341	52	3	occasion	occasion	NOUN
ejpam-3341	52	4	some	some	DET
ejpam-3341	52	5	information	information	NOUN
ejpam-3341	52	6	concerning	concern	VERB
ejpam-3341	52	7	the	the	DET
ejpam-3341	52	8	associate	associate	ADJ
ejpam-3341	52	9	prime	prime	ADJ
ejpam-3341	52	10	ideal	ideal	NOUN
ejpam-3341	52	11	has	have	AUX
ejpam-3341	52	12	been	be	AUX
ejpam-3341	52	13	also	also	ADV
ejpam-3341	52	14	given	give	VERB
ejpam-3341	52	15	.	.	PUNCT
ejpam-3341	53	1	we	we	PRON
ejpam-3341	53	2	give	give	VERB
ejpam-3341	53	3	some	some	DET
ejpam-3341	53	4	examples	example	NOUN
ejpam-3341	53	5	that	that	PRON
ejpam-3341	53	6	illustrate	illustrate	VERB
ejpam-3341	53	7	our	our	PRON
ejpam-3341	53	8	results	result	NOUN
ejpam-3341	53	9	.	.	PUNCT
ejpam-3341	54	1	2	2	X
ejpam-3341	54	2	.	.	X
ejpam-3341	54	3	main	main	ADJ
ejpam-3341	54	4	results	result	NOUN
ejpam-3341	54	5	let	let	VERB
ejpam-3341	54	6	(	(	PUNCT
ejpam-3341	54	7	s	s	X
ejpam-3341	54	8	,	,	PUNCT
ejpam-3341	54	9	·	·	PUNCT
ejpam-3341	54	10	,	,	PUNCT
ejpam-3341	54	11	≤	≤	NUM
ejpam-3341	54	12	)	)	PUNCT
ejpam-3341	54	13	be	be	VERB
ejpam-3341	54	14	an	an	DET
ejpam-3341	54	15	ordered	order	VERB
ejpam-3341	54	16	semigroup	semigroup	NOUN
ejpam-3341	54	17	.	.	PUNCT
ejpam-3341	55	1	a	a	DET
ejpam-3341	55	2	nonempty	nonempty	NOUN
ejpam-3341	55	3	subset	subset	VERB
ejpam-3341	55	4	a	a	PRON
ejpam-3341	55	5	of	of	ADP
ejpam-3341	55	6	s	s	PRON
ejpam-3341	55	7	is	be	AUX
ejpam-3341	55	8	called	call	VERB
ejpam-3341	55	9	a	a	DET
ejpam-3341	55	10	right	right	NOUN
ejpam-3341	55	11	(	(	PUNCT
ejpam-3341	55	12	resp	resp	NOUN
ejpam-3341	55	13	.	.	PUNCT
ejpam-3341	56	1	left	left	ADJ
ejpam-3341	56	2	)	)	PUNCT
ejpam-3341	56	3	ideal	ideal	NOUN
ejpam-3341	56	4	of	of	ADP
ejpam-3341	56	5	s	s	PRON
ejpam-3341	56	6	if	if	SCONJ
ejpam-3341	56	7	(	(	PUNCT
ejpam-3341	56	8	1	1	NUM
ejpam-3341	56	9	)	)	PUNCT
ejpam-3341	56	10	as	as	ADP
ejpam-3341	56	11	⊆	⊆	X
ejpam-3341	56	12	a	a	DET
ejpam-3341	56	13	(	(	PUNCT
ejpam-3341	56	14	resp	resp	NOUN
ejpam-3341	56	15	.	.	PUNCT
ejpam-3341	57	1	sa	sa	PROPN
ejpam-3341	57	2	⊆	⊆	NUM
ejpam-3341	57	3	a	a	NOUN
ejpam-3341	57	4	)	)	PUNCT
ejpam-3341	57	5	and	and	CCONJ
ejpam-3341	57	6	(	(	PUNCT
ejpam-3341	57	7	2	2	X
ejpam-3341	57	8	)	)	PUNCT
ejpam-3341	57	9	if	if	SCONJ
ejpam-3341	57	10	a	a	DET
ejpam-3341	57	11	∈	∈	PROPN
ejpam-3341	57	12	a	a	PRON
ejpam-3341	57	13	and	and	CCONJ
ejpam-3341	57	14	s	s	PROPN
ejpam-3341	57	15	3	3	NUM
ejpam-3341	57	16	b	b	NOUN
ejpam-3341	57	17	≤	≤	NUM
ejpam-3341	57	18	a	a	DET
ejpam-3341	57	19	,	,	PUNCT
ejpam-3341	57	20	then	then	ADV
ejpam-3341	57	21	b	b	X
ejpam-3341	57	22	∈	∈	PROPN
ejpam-3341	57	23	a	a	PRON
ejpam-3341	58	1	[	[	X
ejpam-3341	58	2	4	4	NUM
ejpam-3341	58	3	,	,	PUNCT
ejpam-3341	58	4	5	5	NUM
ejpam-3341	58	5	]	]	PUNCT
ejpam-3341	58	6	.	.	PUNCT
ejpam-3341	59	1	for	for	ADP
ejpam-3341	59	2	a	a	DET
ejpam-3341	59	3	subset	subset	NOUN
ejpam-3341	59	4	a	a	PRON
ejpam-3341	59	5	of	of	ADP
ejpam-3341	59	6	an	an	DET
ejpam-3341	59	7	ordered	order	VERB
ejpam-3341	59	8	semigroup	semigroup	NOUN
ejpam-3341	59	9	(	(	PUNCT
ejpam-3341	59	10	s	s	PROPN
ejpam-3341	59	11	,	,	PUNCT
ejpam-3341	59	12	·	·	PUNCT
ejpam-3341	59	13	,	,	PUNCT
ejpam-3341	59	14	≤	≤	NUM
ejpam-3341	59	15	)	)	PUNCT
ejpam-3341	59	16	,	,	PUNCT
ejpam-3341	59	17	we	we	PRON
ejpam-3341	59	18	denote	denote	VERB
ejpam-3341	59	19	by	by	ADP
ejpam-3341	59	20	(	(	PUNCT
ejpam-3341	59	21	a	a	X
ejpam-3341	59	22	]	]	X
ejpam-3341	59	23	the	the	DET
ejpam-3341	59	24	subset	subset	NOUN
ejpam-3341	59	25	of	of	ADP
ejpam-3341	59	26	s	s	PRON
ejpam-3341	59	27	defined	define	VERB
ejpam-3341	59	28	by	by	ADP
ejpam-3341	59	29	(	(	PUNCT
ejpam-3341	59	30	a	a	X
ejpam-3341	59	31	]	]	X
ejpam-3341	59	32	:	:	PUNCT
ejpam-3341	59	33	=	=	SYM
ejpam-3341	59	34	{	{	PUNCT
ejpam-3341	59	35	t	t	NOUN
ejpam-3341	59	36	∈	∈	PROPN
ejpam-3341	59	37	s	s	AUX
ejpam-3341	59	38	|	|	NOUN
ejpam-3341	59	39	t	t	X
ejpam-3341	59	40	≤	≤	NOUN
ejpam-3341	59	41	a	a	PRON
ejpam-3341	59	42	for	for	ADP
ejpam-3341	59	43	some	some	DET
ejpam-3341	59	44	a	a	DET
ejpam-3341	59	45	∈	∈	PROPN
ejpam-3341	59	46	a	a	PRON
ejpam-3341	59	47	}	}	PUNCT
ejpam-3341	59	48	[	[	X
ejpam-3341	59	49	4	4	NUM
ejpam-3341	59	50	,	,	PUNCT
ejpam-3341	59	51	5	5	NUM
ejpam-3341	59	52	]	]	PUNCT
ejpam-3341	59	53	.	.	PUNCT
ejpam-3341	60	1	if	if	SCONJ
ejpam-3341	60	2	s	s	PROPN
ejpam-3341	60	3	is	be	AUX
ejpam-3341	60	4	a	a	DET
ejpam-3341	60	5	right	right	ADJ
ejpam-3341	60	6	ideal	ideal	NOUN
ejpam-3341	60	7	,	,	PUNCT
ejpam-3341	60	8	left	leave	VERB
ejpam-3341	60	9	ideal	ideal	NOUN
ejpam-3341	60	10	or	or	CCONJ
ejpam-3341	60	11	an	an	DET
ejpam-3341	60	12	ideal	ideal	NOUN
ejpam-3341	60	13	of	of	ADP
ejpam-3341	60	14	an	an	DET
ejpam-3341	60	15	ordered	order	VERB
ejpam-3341	60	16	semigroup	semigroup	NOUN
ejpam-3341	60	17	s	s	PROPN
ejpam-3341	60	18	,	,	PUNCT
ejpam-3341	60	19	then	then	ADV
ejpam-3341	60	20	(	(	PUNCT
ejpam-3341	60	21	a	a	X
ejpam-3341	60	22	]	]	X
ejpam-3341	60	23	=	=	PUNCT
ejpam-3341	60	24	a.	a.	NOUN
ejpam-3341	60	25	for	for	ADP
ejpam-3341	60	26	a	a	DET
ejpam-3341	60	27	proper	proper	ADJ
ejpam-3341	60	28	subset	subset	NOUN
ejpam-3341	60	29	a	a	PRON
ejpam-3341	60	30	of	of	ADP
ejpam-3341	60	31	s	s	PRON
ejpam-3341	60	32	we	we	PRON
ejpam-3341	60	33	denote	denote	VERB
ejpam-3341	60	34	by	by	ADP
ejpam-3341	60	35	ha(s	ha(	NOUN
ejpam-3341	60	36	)	)	PUNCT
ejpam-3341	60	37	the	the	DET
ejpam-3341	60	38	subset	subset	NOUN
ejpam-3341	60	39	of	of	ADP
ejpam-3341	60	40	s	s	PRON
ejpam-3341	60	41	defined	define	VERB
ejpam-3341	60	42	by	by	ADP
ejpam-3341	60	43	ha(s	ha(	NOUN
ejpam-3341	60	44	)	)	PUNCT
ejpam-3341	60	45	:	:	PUNCT
ejpam-3341	60	46	=	=	SYM
ejpam-3341	60	47	{	{	PUNCT
ejpam-3341	60	48	h	h	NOUN
ejpam-3341	60	49	∈	∈	PROPN
ejpam-3341	60	50	s	s	VERB
ejpam-3341	60	51	such	such	ADJ
ejpam-3341	60	52	that	that	SCONJ
ejpam-3341	60	53	if	if	SCONJ
ejpam-3341	60	54	s	s	X
ejpam-3341	60	55	∈	∈	PROPN
ejpam-3341	60	56	s\a	s\a	NOUN
ejpam-3341	60	57	,	,	PUNCT
ejpam-3341	60	58	then	then	ADV
ejpam-3341	60	59	s	s	AUX
ejpam-3341	60	60	/∈	/∈	PUNCT
ejpam-3341	60	61	(	(	PUNCT
ejpam-3341	60	62	shs	shs	NOUN
ejpam-3341	60	63	]	]	X
ejpam-3341	60	64	}	}	PUNCT
ejpam-3341	60	65	[	[	X
ejpam-3341	60	66	2	2	NUM
ejpam-3341	60	67	]	]	PUNCT
ejpam-3341	60	68	.	.	PUNCT
ejpam-3341	61	1	clearly	clearly	ADV
ejpam-3341	61	2	,	,	PUNCT
ejpam-3341	61	3	ha(s	ha(s	X
ejpam-3341	61	4	)	)	PUNCT
ejpam-3341	61	5	=	=	SYM
ejpam-3341	61	6	∅	∅	NOUN
ejpam-3341	61	7	or	or	CCONJ
ejpam-3341	61	8	ha(s	ha(	NOUN
ejpam-3341	61	9	)	)	PUNCT
ejpam-3341	61	10	6=	6=	ADP
ejpam-3341	61	11	∅.	∅.	ADV
ejpam-3341	61	12	let	let	VERB
ejpam-3341	61	13	us	we	PRON
ejpam-3341	61	14	give	give	VERB
ejpam-3341	61	15	an	an	DET
ejpam-3341	61	16	example	example	NOUN
ejpam-3341	61	17	for	for	ADP
ejpam-3341	61	18	which	which	PRON
ejpam-3341	61	19	ha(s	ha(s	NUM
ejpam-3341	61	20	)	)	PUNCT
ejpam-3341	61	21	=	=	PUNCT
ejpam-3341	61	22	∅.	∅.	PRON
ejpam-3341	61	23	example	example	NOUN
ejpam-3341	61	24	2.1	2.1	NUM
ejpam-3341	61	25	.	.	PUNCT
ejpam-3341	62	1	for	for	ADP
ejpam-3341	62	2	the	the	DET
ejpam-3341	62	3	ordered	order	VERB
ejpam-3341	62	4	semigroup	semigroup	NOUN
ejpam-3341	62	5	s	s	PART
ejpam-3341	62	6	=	=	PUNCT
ejpam-3341	62	7	{	{	PUNCT
ejpam-3341	62	8	a	a	DET
ejpam-3341	62	9	,	,	PUNCT
ejpam-3341	62	10	b	b	NOUN
ejpam-3341	62	11	,	,	PUNCT
ejpam-3341	62	12	c	c	NOUN
ejpam-3341	62	13	}	}	PUNCT
ejpam-3341	62	14	defined	define	VERB
ejpam-3341	62	15	by	by	ADP
ejpam-3341	62	16	table	table	NOUN
ejpam-3341	62	17	2	2	NUM
ejpam-3341	62	18	and	and	CCONJ
ejpam-3341	62	19	figure	figure	NOUN
ejpam-3341	62	20	2	2	NUM
ejpam-3341	62	21	and	and	CCONJ
ejpam-3341	62	22	the	the	DET
ejpam-3341	62	23	subset	subset	NOUN
ejpam-3341	62	24	a	a	X
ejpam-3341	62	25	=	=	X
ejpam-3341	62	26	{	{	PUNCT
ejpam-3341	62	27	a	a	PROPN
ejpam-3341	62	28	,	,	PUNCT
ejpam-3341	62	29	b	b	NOUN
ejpam-3341	62	30	}	}	PUNCT
ejpam-3341	62	31	of	of	ADP
ejpam-3341	62	32	s	s	PROPN
ejpam-3341	62	33	,	,	PUNCT
ejpam-3341	62	34	we	we	PRON
ejpam-3341	62	35	have	have	VERB
ejpam-3341	62	36	ha(s	ha(	NOUN
ejpam-3341	62	37	)	)	PUNCT
ejpam-3341	63	1	=	=	PUNCT
ejpam-3341	63	2	∅.	∅.	VERB
ejpam-3341	63	3	for	for	ADP
ejpam-3341	63	4	a	a	PRON
ejpam-3341	63	5	=	=	SYM
ejpam-3341	63	6	{	{	PUNCT
ejpam-3341	63	7	b	b	NOUN
ejpam-3341	63	8	,	,	PUNCT
ejpam-3341	63	9	c	c	AUX
ejpam-3341	63	10	}	}	PUNCT
ejpam-3341	63	11	we	we	PRON
ejpam-3341	63	12	also	also	ADV
ejpam-3341	63	13	have	have	VERB
ejpam-3341	63	14	ha(s	ha(	NOUN
ejpam-3341	63	15	)	)	PUNCT
ejpam-3341	64	1	=	=	PUNCT
ejpam-3341	64	2	∅.	∅.	X
ejpam-3341	64	3	·	·	PUNCT
ejpam-3341	64	4	a	a	DET
ejpam-3341	64	5	b	b	NOUN
ejpam-3341	64	6	c	c	X
ejpam-3341	64	7	a	a	DET
ejpam-3341	64	8	a	a	DET
ejpam-3341	64	9	b	b	NOUN
ejpam-3341	64	10	a	a	DET
ejpam-3341	64	11	b	b	NOUN
ejpam-3341	64	12	a	a	DET
ejpam-3341	64	13	b	b	NOUN
ejpam-3341	64	14	a	a	DET
ejpam-3341	64	15	c	c	NOUN
ejpam-3341	64	16	a	a	DET
ejpam-3341	64	17	b	b	PROPN
ejpam-3341	64	18	c	c	NOUN
ejpam-3341	64	19	table	table	NOUN
ejpam-3341	64	20	2	2	NUM
ejpam-3341	64	21	.	.	PUNCT
ejpam-3341	64	22	c	c	PROPN
ejpam-3341	64	23	b	b	PROPN
ejpam-3341	64	24	a	a	DET
ejpam-3341	64	25	figure	figure	NOUN
ejpam-3341	64	26	2	2	NUM
ejpam-3341	64	27	.	.	PUNCT
ejpam-3341	64	28	proposition	proposition	NOUN
ejpam-3341	64	29	2.2	2.2	NUM
ejpam-3341	64	30	.	.	PUNCT
ejpam-3341	65	1	(	(	PUNCT
ejpam-3341	65	2	see	see	VERB
ejpam-3341	65	3	also	also	ADV
ejpam-3341	65	4	[	[	X
ejpam-3341	65	5	2	2	NUM
ejpam-3341	65	6	;	;	PUNCT
ejpam-3341	65	7	theorem	theorem	VERB
ejpam-3341	65	8	2.4(1	2.4(1	NOUN
ejpam-3341	65	9	)	)	PUNCT
ejpam-3341	65	10	]	]	PUNCT
ejpam-3341	65	11	)	)	PUNCT
ejpam-3341	65	12	if	if	SCONJ
ejpam-3341	65	13	s	s	NOUN
ejpam-3341	65	14	is	be	AUX
ejpam-3341	65	15	an	an	DET
ejpam-3341	65	16	ordered	order	VERB
ejpam-3341	65	17	semigroup	semigroup	NOUN
ejpam-3341	65	18	,	,	PUNCT
ejpam-3341	65	19	then	then	ADV
ejpam-3341	65	20	the	the	DET
ejpam-3341	65	21	set	set	NOUN
ejpam-3341	65	22	ha(s	ha(	NOUN
ejpam-3341	65	23	)	)	PUNCT
ejpam-3341	65	24	is	be	AUX
ejpam-3341	65	25	a	a	DET
ejpam-3341	65	26	semiprime	semiprime	NOUN
ejpam-3341	65	27	subset	subset	NOUN
ejpam-3341	65	28	of	of	ADP
ejpam-3341	65	29	s.	s.	PROPN
ejpam-3341	65	30	proof	proof	PROPN
ejpam-3341	65	31	.	.	PUNCT
ejpam-3341	66	1	let	let	VERB
ejpam-3341	66	2	i	i	PRON
ejpam-3341	66	3	be	be	AUX
ejpam-3341	66	4	an	an	DET
ejpam-3341	66	5	ideal	ideal	NOUN
ejpam-3341	66	6	of	of	ADP
ejpam-3341	66	7	s	s	PRON
ejpam-3341	66	8	such	such	ADJ
ejpam-3341	66	9	that	that	DET
ejpam-3341	66	10	i2	i2	PROPN
ejpam-3341	66	11	⊆	⊆	NUM
ejpam-3341	66	12	ha(s	ha(	NOUN
ejpam-3341	66	13	)	)	PUNCT
ejpam-3341	66	14	.	.	PUNCT
ejpam-3341	67	1	then	then	ADV
ejpam-3341	67	2	i	i	PRON
ejpam-3341	67	3	⊆	⊆	NUM
ejpam-3341	67	4	ha(s	ha(	NOUN
ejpam-3341	67	5	)	)	PUNCT
ejpam-3341	67	6	.	.	PUNCT
ejpam-3341	68	1	indeed	indeed	ADV
ejpam-3341	68	2	:	:	PUNCT
ejpam-3341	68	3	let	let	VERB
ejpam-3341	68	4	h	h	PRON
ejpam-3341	68	5	∈	∈	PROPN
ejpam-3341	68	6	i.	i.	NOUN
ejpam-3341	68	7	we	we	PRON
ejpam-3341	68	8	have	have	VERB
ejpam-3341	68	9	to	to	PART
ejpam-3341	68	10	prove	prove	VERB
ejpam-3341	68	11	that	that	SCONJ
ejpam-3341	68	12	h	h	NOUN
ejpam-3341	68	13	∈	∈	PROPN
ejpam-3341	68	14	ha(s	ha(	NOUN
ejpam-3341	68	15	)	)	PUNCT
ejpam-3341	68	16	that	that	PRON
ejpam-3341	68	17	is	be	AUX
ejpam-3341	68	18	,	,	PUNCT
ejpam-3341	68	19	if	if	SCONJ
ejpam-3341	68	20	s	s	X
ejpam-3341	68	21	∈	∈	PROPN
ejpam-3341	68	22	s\a	s\a	NOUN
ejpam-3341	68	23	,	,	PUNCT
ejpam-3341	68	24	then	then	ADV
ejpam-3341	68	25	s	s	VERB
ejpam-3341	68	26	/∈	/∈	PUNCT
ejpam-3341	68	27	(	(	PUNCT
ejpam-3341	68	28	shs	shs	PROPN
ejpam-3341	68	29	]	]	PUNCT
ejpam-3341	68	30	.	.	PUNCT
ejpam-3341	69	1	suppose	suppose	VERB
ejpam-3341	69	2	s	s	X
ejpam-3341	69	3	∈	∈	PROPN
ejpam-3341	69	4	s\a	s\a	PROPN
ejpam-3341	69	5	and	and	CCONJ
ejpam-3341	69	6	s	s	PROPN
ejpam-3341	69	7	∈	∈	PROPN
ejpam-3341	69	8	(	(	PUNCT
ejpam-3341	69	9	shs	shs	NOUN
ejpam-3341	69	10	]	]	PUNCT
ejpam-3341	69	11	.	.	PUNCT
ejpam-3341	70	1	since	since	SCONJ
ejpam-3341	70	2	h	h	PROPN
ejpam-3341	70	3	∈	∈	PROPN
ejpam-3341	70	4	i	i	PRON
ejpam-3341	70	5	and	and	CCONJ
ejpam-3341	70	6	i	i	PRON
ejpam-3341	70	7	is	be	AUX
ejpam-3341	70	8	an	an	DET
ejpam-3341	70	9	ideal	ideal	NOUN
ejpam-3341	70	10	of	of	ADP
ejpam-3341	70	11	s	s	PROPN
ejpam-3341	70	12	,	,	PUNCT
ejpam-3341	70	13	we	we	PRON
ejpam-3341	70	14	have	have	VERB
ejpam-3341	70	15	s	s	X
ejpam-3341	70	16	∈	∈	NOUN
ejpam-3341	70	17	(	(	PUNCT
ejpam-3341	70	18	s(is	s(i	NOUN
ejpam-3341	70	19	)	)	PUNCT
ejpam-3341	70	20	]	]	PUNCT
ejpam-3341	71	1	⊆	⊆	NUM
ejpam-3341	71	2	(	(	PUNCT
ejpam-3341	71	3	si	si	NOUN
ejpam-3341	71	4	]	]	X
ejpam-3341	71	5	⊆	⊆	NUM
ejpam-3341	71	6	(	(	PUNCT
ejpam-3341	71	7	si	si	NOUN
ejpam-3341	71	8	]	]	X
ejpam-3341	71	9	⊆	⊆	NUM
ejpam-3341	71	10	(	(	PUNCT
ejpam-3341	71	11	i	i	NOUN
ejpam-3341	71	12	]	]	X
ejpam-3341	71	13	=	=	SYM
ejpam-3341	71	14	i	i	PROPN
ejpam-3341	71	15	,	,	PUNCT
ejpam-3341	71	16	n.	n.	PROPN
ejpam-3341	71	17	kehayopulu	kehayopulu	PROPN
ejpam-3341	71	18	/	/	SYM
ejpam-3341	71	19	eur	eur	PROPN
ejpam-3341	71	20	.	.	PUNCT
ejpam-3341	72	1	j.	j.	PROPN
ejpam-3341	72	2	pure	pure	PROPN
ejpam-3341	72	3	appl	appl	PROPN
ejpam-3341	72	4	.	.	PROPN
ejpam-3341	72	5	math	math	PROPN
ejpam-3341	72	6	,	,	PUNCT
ejpam-3341	72	7	11	11	NUM
ejpam-3341	72	8	(	(	PUNCT
ejpam-3341	72	9	4	4	NUM
ejpam-3341	72	10	)	)	PUNCT
ejpam-3341	72	11	(	(	PUNCT
ejpam-3341	72	12	2018	2018	NUM
ejpam-3341	72	13	)	)	PUNCT
ejpam-3341	72	14	,	,	PUNCT
ejpam-3341	72	15	911	911	NUM
ejpam-3341	72	16	-	-	SYM
ejpam-3341	72	17	921	921	NUM
ejpam-3341	72	18	914	914	NUM
ejpam-3341	72	19	then	then	ADV
ejpam-3341	72	20	s2	s2	PROPN
ejpam-3341	72	21	∈	∈	PROPN
ejpam-3341	72	22	i2	i2	PROPN
ejpam-3341	72	23	⊆	⊆	NUM
ejpam-3341	72	24	ha(s	ha(	NOUN
ejpam-3341	72	25	)	)	PUNCT
ejpam-3341	72	26	.	.	PUNCT
ejpam-3341	73	1	since	since	SCONJ
ejpam-3341	73	2	s2	s2	PROPN
ejpam-3341	73	3	∈	∈	PROPN
ejpam-3341	73	4	ha(s	ha(	NOUN
ejpam-3341	73	5	)	)	PUNCT
ejpam-3341	73	6	and	and	CCONJ
ejpam-3341	73	7	s	s	NOUN
ejpam-3341	73	8	∈	∈	PROPN
ejpam-3341	73	9	s\a	s\a	NOUN
ejpam-3341	73	10	,	,	PUNCT
ejpam-3341	73	11	we	we	PRON
ejpam-3341	73	12	have	have	VERB
ejpam-3341	73	13	s	s	PRON
ejpam-3341	73	14	/∈	/∈	PUNCT
ejpam-3341	73	15	(	(	PUNCT
ejpam-3341	73	16	ss2s	ss2s	PROPN
ejpam-3341	73	17	]	]	X
ejpam-3341	73	18	=	=	PUNCT
ejpam-3341	74	1	(	(	PUNCT
ejpam-3341	74	2	s	s	X
ejpam-3341	74	3	]	]	X
ejpam-3341	74	4	=	=	SYM
ejpam-3341	74	5	s	s	X
ejpam-3341	74	6	which	which	PRON
ejpam-3341	74	7	is	be	AUX
ejpam-3341	74	8	impossible	impossible	ADJ
ejpam-3341	74	9	.	.	PUNCT
ejpam-3341	75	1	�	�	PROPN
ejpam-3341	75	2	proposition	proposition	NOUN
ejpam-3341	75	3	2.3	2.3	NUM
ejpam-3341	75	4	.	.	PUNCT
ejpam-3341	76	1	(	(	PUNCT
ejpam-3341	76	2	see	see	VERB
ejpam-3341	76	3	also	also	ADV
ejpam-3341	76	4	[	[	X
ejpam-3341	76	5	2	2	NUM
ejpam-3341	76	6	;	;	PUNCT
ejpam-3341	76	7	theorem	theorem	VERB
ejpam-3341	76	8	2.4(3	2.4(3	NUM
ejpam-3341	76	9	)	)	PUNCT
ejpam-3341	76	10	]	]	PUNCT
ejpam-3341	76	11	let	let	VERB
ejpam-3341	76	12	s	s	PRON
ejpam-3341	76	13	be	be	AUX
ejpam-3341	76	14	an	an	DET
ejpam-3341	76	15	ordered	order	VERB
ejpam-3341	76	16	semigroup	semigroup	NOUN
ejpam-3341	76	17	.	.	PUNCT
ejpam-3341	77	1	then	then	ADV
ejpam-3341	77	2	we	we	PRON
ejpam-3341	77	3	have	have	VERB
ejpam-3341	77	4	the	the	DET
ejpam-3341	77	5	following	following	NOUN
ejpam-3341	77	6	:	:	PUNCT
ejpam-3341	77	7	if	if	SCONJ
ejpam-3341	77	8	a	a	PRON
ejpam-3341	77	9	is	be	AUX
ejpam-3341	77	10	a	a	DET
ejpam-3341	77	11	(	(	PUNCT
ejpam-3341	77	12	proper	proper	ADJ
ejpam-3341	77	13	)	)	PUNCT
ejpam-3341	77	14	ideal	ideal	NOUN
ejpam-3341	77	15	of	of	ADP
ejpam-3341	77	16	s	s	PROPN
ejpam-3341	77	17	,	,	PUNCT
ejpam-3341	77	18	then	then	ADV
ejpam-3341	77	19	a	a	DET
ejpam-3341	77	20	⊆	⊆	NUM
ejpam-3341	77	21	ha(s	ha(	NOUN
ejpam-3341	77	22	)	)	PUNCT
ejpam-3341	77	23	.	.	PUNCT
ejpam-3341	78	1	proof	proof	NOUN
ejpam-3341	78	2	.	.	PUNCT
ejpam-3341	79	1	let	let	VERB
ejpam-3341	79	2	h	h	PRON
ejpam-3341	79	3	∈	∈	PROPN
ejpam-3341	79	4	a.	a.	NOUN
ejpam-3341	80	1	then	then	ADV
ejpam-3341	80	2	h	h	PROPN
ejpam-3341	80	3	∈	∈	PROPN
ejpam-3341	80	4	ha(s	ha(	NOUN
ejpam-3341	80	5	)	)	PUNCT
ejpam-3341	80	6	.	.	PUNCT
ejpam-3341	81	1	indeed	indeed	ADV
ejpam-3341	81	2	:	:	PUNCT
ejpam-3341	81	3	first	first	ADV
ejpam-3341	81	4	of	of	ADP
ejpam-3341	81	5	all	all	PRON
ejpam-3341	81	6	,	,	PUNCT
ejpam-3341	81	7	since	since	SCONJ
ejpam-3341	81	8	a	a	DET
ejpam-3341	81	9	⊆	⊆	NUM
ejpam-3341	81	10	s	s	NOUN
ejpam-3341	81	11	,	,	PUNCT
ejpam-3341	81	12	we	we	PRON
ejpam-3341	81	13	have	have	VERB
ejpam-3341	81	14	h	h	PROPN
ejpam-3341	81	15	∈	∈	PROPN
ejpam-3341	81	16	s.	s.	PROPN
ejpam-3341	81	17	let	let	VERB
ejpam-3341	81	18	now	now	ADV
ejpam-3341	81	19	s	s	VERB
ejpam-3341	81	20	∈	∈	ADJ
ejpam-3341	81	21	s\a	s\a	NOUN
ejpam-3341	81	22	.	.	PUNCT
ejpam-3341	82	1	then	then	ADV
ejpam-3341	82	2	s	s	VERB
ejpam-3341	82	3	/∈	/∈	PUNCT
ejpam-3341	82	4	(	(	PUNCT
ejpam-3341	82	5	shs	shs	NOUN
ejpam-3341	82	6	]	]	PUNCT
ejpam-3341	82	7	.	.	PUNCT
ejpam-3341	83	1	in	in	ADP
ejpam-3341	83	2	fact	fact	NOUN
ejpam-3341	83	3	:	:	PUNCT
ejpam-3341	83	4	if	if	SCONJ
ejpam-3341	83	5	s	s	X
ejpam-3341	83	6	∈	∈	PROPN
ejpam-3341	83	7	(	(	PUNCT
ejpam-3341	83	8	shs	shs	PROPN
ejpam-3341	83	9	]	]	PUNCT
ejpam-3341	83	10	then	then	ADV
ejpam-3341	83	11	,	,	PUNCT
ejpam-3341	83	12	since	since	SCONJ
ejpam-3341	83	13	a	a	PRON
ejpam-3341	83	14	is	be	AUX
ejpam-3341	83	15	an	an	DET
ejpam-3341	83	16	ideal	ideal	NOUN
ejpam-3341	83	17	of	of	ADP
ejpam-3341	83	18	s	s	PROPN
ejpam-3341	83	19	,	,	PUNCT
ejpam-3341	83	20	we	we	PRON
ejpam-3341	83	21	have	have	VERB
ejpam-3341	83	22	s	s	X
ejpam-3341	83	23	∈	∈	NOUN
ejpam-3341	83	24	(	(	PUNCT
ejpam-3341	83	25	s(hs	s(hs	PROPN
ejpam-3341	83	26	)	)	PUNCT
ejpam-3341	83	27	]	]	PUNCT
ejpam-3341	84	1	⊆	⊆	X
ejpam-3341	84	2	(	(	PUNCT
ejpam-3341	84	3	s(as	s(a	NOUN
ejpam-3341	84	4	)	)	PUNCT
ejpam-3341	84	5	]	]	PUNCT
ejpam-3341	85	1	⊆	⊆	NUM
ejpam-3341	85	2	(	(	PUNCT
ejpam-3341	85	3	sa	sa	X
ejpam-3341	85	4	]	]	X
ejpam-3341	85	5	⊆	⊆	NUM
ejpam-3341	85	6	(	(	PUNCT
ejpam-3341	85	7	sa	sa	X
ejpam-3341	85	8	]	]	X
ejpam-3341	85	9	⊆	⊆	NUM
ejpam-3341	85	10	(	(	PUNCT
ejpam-3341	85	11	a	a	X
ejpam-3341	85	12	]	]	X
ejpam-3341	85	13	=	=	X
ejpam-3341	85	14	a	a	PRON
ejpam-3341	85	15	which	which	PRON
ejpam-3341	85	16	is	be	AUX
ejpam-3341	85	17	impossible	impossible	ADJ
ejpam-3341	85	18	.	.	PUNCT
ejpam-3341	86	1	since	since	SCONJ
ejpam-3341	86	2	h	h	PROPN
ejpam-3341	86	3	∈	∈	PROPN
ejpam-3341	86	4	s	s	PROPN
ejpam-3341	86	5	,	,	PUNCT
ejpam-3341	86	6	s	s	PART
ejpam-3341	86	7	∈	∈	X
ejpam-3341	86	8	s\a	s\a	PROPN
ejpam-3341	86	9	and	and	CCONJ
ejpam-3341	86	10	s	s	PROPN
ejpam-3341	86	11	/∈	/∈	PUNCT
ejpam-3341	86	12	(	(	PUNCT
ejpam-3341	86	13	shs	shs	PROPN
ejpam-3341	86	14	]	]	PUNCT
ejpam-3341	86	15	,	,	PUNCT
ejpam-3341	86	16	we	we	PRON
ejpam-3341	86	17	have	have	VERB
ejpam-3341	86	18	h	h	NOUN
ejpam-3341	86	19	∈	∈	PROPN
ejpam-3341	86	20	ha(s	ha(	NOUN
ejpam-3341	86	21	)	)	PUNCT
ejpam-3341	86	22	.	.	PUNCT
ejpam-3341	87	1	�	�	PROPN
ejpam-3341	87	2	corollary	corollary	ADJ
ejpam-3341	87	3	2.4	2.4	NUM
ejpam-3341	87	4	.	.	PUNCT
ejpam-3341	88	1	if	if	SCONJ
ejpam-3341	88	2	a	a	PRON
ejpam-3341	88	3	is	be	AUX
ejpam-3341	88	4	a	a	DET
ejpam-3341	88	5	(	(	PUNCT
ejpam-3341	88	6	proper	proper	ADJ
ejpam-3341	88	7	)	)	PUNCT
ejpam-3341	88	8	ideal	ideal	NOUN
ejpam-3341	88	9	of	of	ADP
ejpam-3341	88	10	s	s	PROPN
ejpam-3341	88	11	,	,	PUNCT
ejpam-3341	88	12	then	then	ADV
ejpam-3341	88	13	ha(s	ha(	NOUN
ejpam-3341	88	14	)	)	PUNCT
ejpam-3341	88	15	6=	6=	ADP
ejpam-3341	88	16	∅.	∅.	VERB
ejpam-3341	88	17	in	in	ADP
ejpam-3341	88	18	proposition	proposition	NOUN
ejpam-3341	88	19	2.3	2.3	NUM
ejpam-3341	88	20	and	and	CCONJ
ejpam-3341	88	21	corollary	corollary	ADJ
ejpam-3341	88	22	2.4	2.4	NUM
ejpam-3341	88	23	is	be	AUX
ejpam-3341	88	24	not	not	PART
ejpam-3341	88	25	necessary	necessary	ADJ
ejpam-3341	88	26	to	to	PART
ejpam-3341	88	27	assume	assume	VERB
ejpam-3341	88	28	that	that	SCONJ
ejpam-3341	88	29	the	the	DET
ejpam-3341	88	30	ideal	ideal	NOUN
ejpam-3341	88	31	a	a	PRON
ejpam-3341	88	32	is	be	AUX
ejpam-3341	88	33	a	a	DET
ejpam-3341	88	34	“	"	PUNCT
ejpam-3341	88	35	proper	proper	ADJ
ejpam-3341	88	36	”	"	PUNCT
ejpam-3341	88	37	ideal	ideal	NOUN
ejpam-3341	88	38	of	of	ADP
ejpam-3341	88	39	s	s	PRON
ejpam-3341	88	40	;	;	PUNCT
ejpam-3341	88	41	this	this	PRON
ejpam-3341	88	42	is	be	AUX
ejpam-3341	88	43	because	because	SCONJ
ejpam-3341	88	44	,	,	PUNCT
ejpam-3341	88	45	by	by	ADP
ejpam-3341	88	46	writing	write	VERB
ejpam-3341	88	47	ha(s	ha(	NOUN
ejpam-3341	88	48	)	)	PUNCT
ejpam-3341	88	49	,	,	PUNCT
ejpam-3341	88	50	we	we	PRON
ejpam-3341	88	51	already	already	ADV
ejpam-3341	88	52	accepted	accept	VERB
ejpam-3341	88	53	that	that	SCONJ
ejpam-3341	88	54	a	a	PRON
ejpam-3341	88	55	is	be	AUX
ejpam-3341	88	56	a	a	DET
ejpam-3341	88	57	proper	proper	ADJ
ejpam-3341	88	58	subset	subset	NOUN
ejpam-3341	88	59	of	of	ADP
ejpam-3341	88	60	s.	s.	PROPN
ejpam-3341	88	61	proposition	proposition	PROPN
ejpam-3341	88	62	2.5	2.5	NUM
ejpam-3341	88	63	.	.	PUNCT
ejpam-3341	89	1	let	let	VERB
ejpam-3341	89	2	(	(	PUNCT
ejpam-3341	89	3	s	s	X
ejpam-3341	89	4	,	,	PUNCT
ejpam-3341	89	5	·	·	PUNCT
ejpam-3341	89	6	,	,	PUNCT
ejpam-3341	89	7	≤	≤	NUM
ejpam-3341	89	8	)	)	PUNCT
ejpam-3341	89	9	be	be	AUX
ejpam-3341	89	10	an	an	DET
ejpam-3341	89	11	ordered	order	VERB
ejpam-3341	89	12	semigroup	semigroup	NOUN
ejpam-3341	89	13	.	.	PUNCT
ejpam-3341	90	1	then	then	ADV
ejpam-3341	90	2	if	if	SCONJ
ejpam-3341	90	3	ha(s	ha(	NOUN
ejpam-3341	90	4	)	)	PUNCT
ejpam-3341	90	5	6=	6=	ADP
ejpam-3341	90	6	∅	∅	NOUN
ejpam-3341	90	7	,	,	PUNCT
ejpam-3341	90	8	then	then	ADV
ejpam-3341	90	9	ha(s	ha(	NOUN
ejpam-3341	90	10	)	)	PUNCT
ejpam-3341	90	11	is	be	AUX
ejpam-3341	90	12	a	a	DET
ejpam-3341	90	13	right	right	ADJ
ejpam-3341	90	14	ideal	ideal	NOUN
ejpam-3341	90	15	of	of	ADP
ejpam-3341	90	16	s.	s.	PROPN
ejpam-3341	90	17	proof	proof	PROPN
ejpam-3341	90	18	.	.	PUNCT
ejpam-3341	91	1	by	by	ADP
ejpam-3341	91	2	hypothesis	hypothesis	NOUN
ejpam-3341	91	3	,	,	PUNCT
ejpam-3341	91	4	ha(s	ha(s	X
ejpam-3341	91	5	)	)	PUNCT
ejpam-3341	91	6	is	be	AUX
ejpam-3341	91	7	a	a	DET
ejpam-3341	91	8	nonempty	nonempty	ADJ
ejpam-3341	91	9	subset	subset	NOUN
ejpam-3341	91	10	of	of	ADP
ejpam-3341	91	11	s.	s.	PROPN
ejpam-3341	91	12	let	let	VERB
ejpam-3341	91	13	h	h	PROPN
ejpam-3341	91	14	∈	∈	PROPN
ejpam-3341	91	15	ha(s	ha(s	X
ejpam-3341	91	16	)	)	PUNCT
ejpam-3341	91	17	and	and	CCONJ
ejpam-3341	91	18	t	t	PROPN
ejpam-3341	91	19	∈	∈	PROPN
ejpam-3341	91	20	s.	s.	PROPN
ejpam-3341	91	21	then	then	ADV
ejpam-3341	91	22	ht	ht	PROPN
ejpam-3341	91	23	∈	∈	PROPN
ejpam-3341	91	24	ha(s	ha(	NOUN
ejpam-3341	91	25	)	)	PUNCT
ejpam-3341	91	26	.	.	PUNCT
ejpam-3341	92	1	in	in	ADP
ejpam-3341	92	2	fact	fact	NOUN
ejpam-3341	92	3	:	:	PUNCT
ejpam-3341	92	4	first	first	ADV
ejpam-3341	92	5	of	of	ADP
ejpam-3341	92	6	all	all	PRON
ejpam-3341	92	7	,	,	PUNCT
ejpam-3341	92	8	ht	ht	PROPN
ejpam-3341	92	9	∈	∈	PROPN
ejpam-3341	92	10	s.	s.	PROPN
ejpam-3341	92	11	let	let	VERB
ejpam-3341	92	12	now	now	ADV
ejpam-3341	92	13	s	s	VERB
ejpam-3341	92	14	∈	∈	ADJ
ejpam-3341	92	15	s\a	s\a	NOUN
ejpam-3341	92	16	.	.	PUNCT
ejpam-3341	93	1	then	then	ADV
ejpam-3341	93	2	s	s	VERB
ejpam-3341	93	3	/∈	/∈	PUNCT
ejpam-3341	93	4	(	(	PUNCT
ejpam-3341	93	5	shts	sht	NOUN
ejpam-3341	93	6	]	]	PUNCT
ejpam-3341	93	7	.	.	PUNCT
ejpam-3341	94	1	indeed	indeed	ADV
ejpam-3341	94	2	:	:	PUNCT
ejpam-3341	94	3	if	if	SCONJ
ejpam-3341	94	4	s	s	X
ejpam-3341	94	5	∈	∈	PROPN
ejpam-3341	94	6	(	(	PUNCT
ejpam-3341	94	7	sh(ts	sh(t	NOUN
ejpam-3341	94	8	)	)	PUNCT
ejpam-3341	94	9	]	]	PUNCT
ejpam-3341	94	10	,	,	PUNCT
ejpam-3341	94	11	then	then	ADV
ejpam-3341	94	12	s	s	VERB
ejpam-3341	94	13	∈	∈	PROPN
ejpam-3341	94	14	(	(	PUNCT
ejpam-3341	94	15	shs	shs	NOUN
ejpam-3341	94	16	]	]	PUNCT
ejpam-3341	94	17	.	.	PUNCT
ejpam-3341	95	1	on	on	ADP
ejpam-3341	95	2	the	the	DET
ejpam-3341	95	3	other	other	ADJ
ejpam-3341	95	4	hand	hand	NOUN
ejpam-3341	95	5	,	,	PUNCT
ejpam-3341	95	6	since	since	SCONJ
ejpam-3341	95	7	h	h	PROPN
ejpam-3341	95	8	∈	∈	PROPN
ejpam-3341	95	9	ha(s	ha(s	X
ejpam-3341	95	10	)	)	PUNCT
ejpam-3341	95	11	and	and	CCONJ
ejpam-3341	95	12	s	s	NOUN
ejpam-3341	95	13	∈	∈	PROPN
ejpam-3341	95	14	s\a	s\a	NOUN
ejpam-3341	95	15	,	,	PUNCT
ejpam-3341	95	16	we	we	PRON
ejpam-3341	95	17	have	have	VERB
ejpam-3341	95	18	s	s	PRON
ejpam-3341	95	19	/∈	/∈	PUNCT
ejpam-3341	95	20	(	(	PUNCT
ejpam-3341	95	21	shs	shs	PROPN
ejpam-3341	95	22	]	]	PUNCT
ejpam-3341	95	23	,	,	PUNCT
ejpam-3341	95	24	we	we	PRON
ejpam-3341	95	25	get	get	VERB
ejpam-3341	95	26	a	a	DET
ejpam-3341	95	27	contradiction	contradiction	NOUN
ejpam-3341	95	28	.	.	PUNCT
ejpam-3341	96	1	let	let	VERB
ejpam-3341	96	2	now	now	ADV
ejpam-3341	96	3	h	h	NOUN
ejpam-3341	96	4	∈	∈	PROPN
ejpam-3341	96	5	ha(s	ha(s	X
ejpam-3341	96	6	)	)	PUNCT
ejpam-3341	96	7	and	and	CCONJ
ejpam-3341	96	8	s	s	VERB
ejpam-3341	96	9	3	3	NUM
ejpam-3341	96	10	g	g	PROPN
ejpam-3341	96	11	≤	≤	NOUN
ejpam-3341	96	12	h.	h.	NOUN
ejpam-3341	97	1	then	then	ADV
ejpam-3341	97	2	g	g	PROPN
ejpam-3341	97	3	∈	∈	PROPN
ejpam-3341	97	4	ha(s	ha(	NOUN
ejpam-3341	97	5	)	)	PUNCT
ejpam-3341	97	6	.	.	PUNCT
ejpam-3341	98	1	indeed	indeed	ADV
ejpam-3341	98	2	:	:	PUNCT
ejpam-3341	98	3	let	let	VERB
ejpam-3341	98	4	s	s	PRON
ejpam-3341	98	5	∈	∈	NOUN
ejpam-3341	98	6	s\a	s\a	PROPN
ejpam-3341	98	7	.	.	PUNCT
ejpam-3341	99	1	since	since	SCONJ
ejpam-3341	99	2	h	h	PROPN
ejpam-3341	99	3	∈	∈	PROPN
ejpam-3341	99	4	ha(s	ha(s	X
ejpam-3341	99	5	)	)	PUNCT
ejpam-3341	99	6	and	and	CCONJ
ejpam-3341	99	7	s	s	NOUN
ejpam-3341	99	8	∈	∈	PROPN
ejpam-3341	99	9	s\a	s\a	NOUN
ejpam-3341	99	10	,	,	PUNCT
ejpam-3341	99	11	we	we	PRON
ejpam-3341	99	12	have	have	VERB
ejpam-3341	99	13	s	s	PRON
ejpam-3341	99	14	/∈	/∈	PUNCT
ejpam-3341	99	15	(	(	PUNCT
ejpam-3341	99	16	shs	shs	NOUN
ejpam-3341	99	17	]	]	PUNCT
ejpam-3341	99	18	.	.	PUNCT
ejpam-3341	100	1	since	since	SCONJ
ejpam-3341	100	2	g	g	PROPN
ejpam-3341	100	3	≤	≤	NUM
ejpam-3341	100	4	h	h	NOUN
ejpam-3341	100	5	,	,	PUNCT
ejpam-3341	100	6	we	we	PRON
ejpam-3341	100	7	have	have	VERB
ejpam-3341	100	8	(	(	PUNCT
ejpam-3341	100	9	sgs	sgs	PROPN
ejpam-3341	100	10	]	]	PUNCT
ejpam-3341	100	11	⊆	⊆	NUM
ejpam-3341	100	12	(	(	PUNCT
ejpam-3341	100	13	shs	shs	PROPN
ejpam-3341	100	14	]	]	PUNCT
ejpam-3341	100	15	.	.	PUNCT
ejpam-3341	101	1	then	then	ADV
ejpam-3341	101	2	we	we	PRON
ejpam-3341	101	3	get	get	VERB
ejpam-3341	101	4	s	s	PRON
ejpam-3341	101	5	/∈	/∈	PUNCT
ejpam-3341	101	6	(	(	PUNCT
ejpam-3341	101	7	sgs	sgs	PROPN
ejpam-3341	101	8	]	]	PUNCT
ejpam-3341	101	9	.	.	PUNCT
ejpam-3341	102	1	since	since	SCONJ
ejpam-3341	102	2	s	s	PROPN
ejpam-3341	102	3	∈	∈	PROPN
ejpam-3341	102	4	s\a	s\a	PROPN
ejpam-3341	102	5	and	and	CCONJ
ejpam-3341	102	6	s	s	PROPN
ejpam-3341	102	7	/∈	/∈	PUNCT
ejpam-3341	102	8	(	(	PUNCT
ejpam-3341	102	9	sgs	sgs	PROPN
ejpam-3341	102	10	]	]	PUNCT
ejpam-3341	102	11	,	,	PUNCT
ejpam-3341	102	12	we	we	PRON
ejpam-3341	102	13	have	have	VERB
ejpam-3341	102	14	g	g	PROPN
ejpam-3341	102	15	∈	∈	PROPN
ejpam-3341	102	16	ha(s	ha(	NOUN
ejpam-3341	102	17	)	)	PUNCT
ejpam-3341	102	18	.	.	PUNCT
ejpam-3341	103	1	�	�	PROPN
ejpam-3341	103	2	proposition	proposition	NOUN
ejpam-3341	103	3	2.6	2.6	NUM
ejpam-3341	103	4	.	.	PUNCT
ejpam-3341	104	1	let	let	VERB
ejpam-3341	104	2	(	(	PUNCT
ejpam-3341	104	3	s	s	X
ejpam-3341	104	4	,	,	PUNCT
ejpam-3341	104	5	·	·	PUNCT
ejpam-3341	104	6	,	,	PUNCT
ejpam-3341	104	7	≤	≤	NUM
ejpam-3341	104	8	)	)	PUNCT
ejpam-3341	104	9	be	be	AUX
ejpam-3341	104	10	an	an	DET
ejpam-3341	104	11	ordered	order	VERB
ejpam-3341	104	12	semigroup	semigroup	NOUN
ejpam-3341	104	13	.	.	PUNCT
ejpam-3341	105	1	then	then	ADV
ejpam-3341	105	2	if	if	SCONJ
ejpam-3341	105	3	a	a	PRON
ejpam-3341	105	4	is	be	AUX
ejpam-3341	105	5	a	a	DET
ejpam-3341	105	6	right	right	ADJ
ejpam-3341	105	7	ideal	ideal	NOUN
ejpam-3341	105	8	of	of	ADP
ejpam-3341	105	9	s	s	PRON
ejpam-3341	105	10	and	and	CCONJ
ejpam-3341	105	11	ha(s	ha(	NOUN
ejpam-3341	105	12	)	)	PUNCT
ejpam-3341	105	13	6=	6=	ADP
ejpam-3341	105	14	∅	∅	NOUN
ejpam-3341	105	15	,	,	PUNCT
ejpam-3341	105	16	then	then	ADV
ejpam-3341	105	17	ha(s	ha(	NOUN
ejpam-3341	105	18	)	)	PUNCT
ejpam-3341	105	19	is	be	AUX
ejpam-3341	105	20	a	a	DET
ejpam-3341	105	21	left	left	ADJ
ejpam-3341	105	22	ideal	ideal	NOUN
ejpam-3341	105	23	of	of	ADP
ejpam-3341	105	24	s.	s.	PROPN
ejpam-3341	105	25	proof	proof	PROPN
ejpam-3341	105	26	.	.	PUNCT
ejpam-3341	106	1	by	by	ADP
ejpam-3341	106	2	hypothesis	hypothesis	NOUN
ejpam-3341	106	3	,	,	PUNCT
ejpam-3341	106	4	ha(s	ha(s	X
ejpam-3341	106	5	)	)	PUNCT
ejpam-3341	106	6	is	be	AUX
ejpam-3341	106	7	a	a	DET
ejpam-3341	106	8	nonempty	nonempty	ADJ
ejpam-3341	106	9	subset	subset	NOUN
ejpam-3341	106	10	of	of	ADP
ejpam-3341	106	11	s.	s.	PROPN
ejpam-3341	106	12	let	let	VERB
ejpam-3341	106	13	t	t	PROPN
ejpam-3341	106	14	∈	∈	PROPN
ejpam-3341	106	15	s	s	PART
ejpam-3341	106	16	and	and	CCONJ
ejpam-3341	106	17	h	h	NOUN
ejpam-3341	106	18	∈	∈	PROPN
ejpam-3341	106	19	ha(s	ha(	NOUN
ejpam-3341	106	20	)	)	PUNCT
ejpam-3341	106	21	.	.	PUNCT
ejpam-3341	107	1	then	then	ADV
ejpam-3341	107	2	th	th	X
ejpam-3341	107	3	∈	∈	PROPN
ejpam-3341	107	4	ha(s	ha(	NOUN
ejpam-3341	107	5	)	)	PUNCT
ejpam-3341	107	6	.	.	PUNCT
ejpam-3341	108	1	indeed	indeed	ADV
ejpam-3341	108	2	:	:	PUNCT
ejpam-3341	108	3	let	let	VERB
ejpam-3341	108	4	s	s	PRON
ejpam-3341	108	5	∈	∈	NOUN
ejpam-3341	108	6	s\a	s\a	NOUN
ejpam-3341	108	7	.	.	PUNCT
ejpam-3341	109	1	we	we	PRON
ejpam-3341	109	2	have	have	VERB
ejpam-3341	109	3	to	to	PART
ejpam-3341	109	4	prove	prove	VERB
ejpam-3341	109	5	that	that	PRON
ejpam-3341	109	6	s	s	VERB
ejpam-3341	109	7	/∈	/∈	PUNCT
ejpam-3341	109	8	(	(	PUNCT
ejpam-3341	109	9	sths	sth	NOUN
ejpam-3341	109	10	]	]	PUNCT
ejpam-3341	109	11	.	.	PUNCT
ejpam-3341	110	1	suppose	suppose	VERB
ejpam-3341	110	2	s	s	X
ejpam-3341	110	3	∈	∈	PROPN
ejpam-3341	110	4	(	(	PUNCT
ejpam-3341	110	5	sths	sth	NOUN
ejpam-3341	110	6	]	]	PUNCT
ejpam-3341	110	7	.	.	PUNCT
ejpam-3341	111	1	then	then	ADV
ejpam-3341	111	2	we	we	PRON
ejpam-3341	111	3	have	have	VERB
ejpam-3341	111	4	st	st	PROPN
ejpam-3341	111	5	∈	∈	PROPN
ejpam-3341	111	6	(	(	PUNCT
ejpam-3341	111	7	sths](s	sths](s	NOUN
ejpam-3341	111	8	]	]	X
ejpam-3341	111	9	⊆	⊆	NUM
ejpam-3341	111	10	(	(	PUNCT
ejpam-3341	111	11	sths2	sths2	PROPN
ejpam-3341	111	12	]	]	X
ejpam-3341	111	13	⊆	⊆	NUM
ejpam-3341	111	14	(	(	PUNCT
ejpam-3341	111	15	sths	sth	NOUN
ejpam-3341	111	16	]	]	PUNCT
ejpam-3341	111	17	(	(	PUNCT
ejpam-3341	111	18	1	1	X
ejpam-3341	111	19	)	)	PUNCT
ejpam-3341	111	20	on	on	ADP
ejpam-3341	111	21	the	the	DET
ejpam-3341	111	22	other	other	ADJ
ejpam-3341	111	23	hand	hand	NOUN
ejpam-3341	111	24	,	,	PUNCT
ejpam-3341	111	25	since	since	SCONJ
ejpam-3341	111	26	h	h	PROPN
ejpam-3341	111	27	∈	∈	PROPN
ejpam-3341	111	28	ha(s	ha(	NOUN
ejpam-3341	111	29	)	)	PUNCT
ejpam-3341	111	30	,	,	PUNCT
ejpam-3341	111	31	we	we	PRON
ejpam-3341	111	32	have	have	VERB
ejpam-3341	111	33	st	st	PROPN
ejpam-3341	111	34	∈	∈	PROPN
ejpam-3341	111	35	a.	a.	NOUN
ejpam-3341	111	36	indeed	indeed	ADV
ejpam-3341	111	37	:	:	PUNCT
ejpam-3341	111	38	let	let	VERB
ejpam-3341	111	39	st	st	PROPN
ejpam-3341	111	40	∈	∈	PROPN
ejpam-3341	111	41	s\a	s\a	PROPN
ejpam-3341	111	42	.	.	PUNCT
ejpam-3341	112	1	since	since	SCONJ
ejpam-3341	112	2	h	h	PROPN
ejpam-3341	112	3	∈	∈	PROPN
ejpam-3341	112	4	ha(s	ha(s	X
ejpam-3341	112	5	)	)	PUNCT
ejpam-3341	112	6	and	and	CCONJ
ejpam-3341	112	7	st	st	PROPN
ejpam-3341	112	8	∈	∈	PROPN
ejpam-3341	112	9	s\a	s\a	PROPN
ejpam-3341	112	10	,	,	PUNCT
ejpam-3341	112	11	we	we	PRON
ejpam-3341	112	12	have	have	VERB
ejpam-3341	112	13	st	st	PROPN
ejpam-3341	112	14	/∈	/∈	PROPN
ejpam-3341	112	15	(	(	PUNCT
ejpam-3341	112	16	sths	sth	NOUN
ejpam-3341	112	17	]	]	PUNCT
ejpam-3341	112	18	which	which	PRON
ejpam-3341	112	19	is	be	AUX
ejpam-3341	112	20	impossible	impossible	ADJ
ejpam-3341	112	21	by	by	ADP
ejpam-3341	112	22	(	(	PUNCT
ejpam-3341	112	23	1	1	NUM
ejpam-3341	112	24	)	)	PUNCT
ejpam-3341	112	25	.	.	PUNCT
ejpam-3341	113	1	since	since	SCONJ
ejpam-3341	113	2	s	s	PROPN
ejpam-3341	113	3	∈	∈	PROPN
ejpam-3341	113	4	(	(	PUNCT
ejpam-3341	113	5	sths	sth	NOUN
ejpam-3341	113	6	]	]	PUNCT
ejpam-3341	113	7	and	and	CCONJ
ejpam-3341	113	8	st	st	PROPN
ejpam-3341	113	9	∈	∈	PROPN
ejpam-3341	113	10	a	a	X
ejpam-3341	113	11	,	,	PUNCT
ejpam-3341	113	12	we	we	PRON
ejpam-3341	113	13	have	have	VERB
ejpam-3341	113	14	s	s	X
ejpam-3341	113	15	∈	∈	NOUN
ejpam-3341	113	16	(	(	PUNCT
ejpam-3341	113	17	(	(	PUNCT
ejpam-3341	113	18	st)hs	st)hs	NOUN
ejpam-3341	113	19	]	]	X
ejpam-3341	113	20	⊆	⊆	NUM
ejpam-3341	113	21	(	(	PUNCT
ejpam-3341	113	22	ahs	ahs	INTJ
ejpam-3341	113	23	]	]	PUNCT
ejpam-3341	113	24	⊆	⊆	NUM
ejpam-3341	113	25	(	(	PUNCT
ejpam-3341	113	26	as	as	ADP
ejpam-3341	113	27	]	]	PUNCT
ejpam-3341	113	28	⊆	⊆	NUM
ejpam-3341	113	29	(	(	PUNCT
ejpam-3341	113	30	a	a	X
ejpam-3341	113	31	]	]	X
ejpam-3341	113	32	=	=	SYM
ejpam-3341	113	33	a	a	NOUN
ejpam-3341	113	34	,	,	PUNCT
ejpam-3341	113	35	so	so	SCONJ
ejpam-3341	113	36	s	s	NOUN
ejpam-3341	113	37	∈	∈	PROPN
ejpam-3341	113	38	a	a	DET
ejpam-3341	113	39	which	which	PRON
ejpam-3341	113	40	is	be	AUX
ejpam-3341	113	41	impossible	impossible	ADJ
ejpam-3341	113	42	.	.	PUNCT
ejpam-3341	114	1	finally	finally	ADV
ejpam-3341	114	2	,	,	PUNCT
ejpam-3341	114	3	as	as	ADP
ejpam-3341	114	4	in	in	ADP
ejpam-3341	114	5	proposition	proposition	NOUN
ejpam-3341	114	6	2.5	2.5	NUM
ejpam-3341	114	7	,	,	PUNCT
ejpam-3341	114	8	h	h	NOUN
ejpam-3341	114	9	∈	∈	PROPN
ejpam-3341	114	10	ha(s	ha(s	X
ejpam-3341	114	11	)	)	PUNCT
ejpam-3341	114	12	and	and	CCONJ
ejpam-3341	114	13	s	s	VERB
ejpam-3341	114	14	3	3	NUM
ejpam-3341	114	15	g	g	NOUN
ejpam-3341	114	16	≤	≤	NUM
ejpam-3341	114	17	h	h	NOUN
ejpam-3341	114	18	imply	imply	VERB
ejpam-3341	114	19	g	g	PROPN
ejpam-3341	114	20	∈	∈	PROPN
ejpam-3341	114	21	ha(s	ha(	NOUN
ejpam-3341	114	22	)	)	PUNCT
ejpam-3341	114	23	;	;	PUNCT
ejpam-3341	114	24	thus	thus	ADV
ejpam-3341	114	25	ha(s	ha(	NOUN
ejpam-3341	114	26	)	)	PUNCT
ejpam-3341	114	27	is	be	AUX
ejpam-3341	114	28	a	a	DET
ejpam-3341	114	29	left	left	ADJ
ejpam-3341	114	30	ideal	ideal	NOUN
ejpam-3341	114	31	of	of	ADP
ejpam-3341	114	32	s.	s.	PROPN
ejpam-3341	114	33	�	�	PROPN
ejpam-3341	114	34	corollary	corollary	ADJ
ejpam-3341	114	35	2.7	2.7	NUM
ejpam-3341	114	36	.	.	PUNCT
ejpam-3341	115	1	if	if	SCONJ
ejpam-3341	115	2	s	s	NOUN
ejpam-3341	115	3	is	be	AUX
ejpam-3341	115	4	an	an	DET
ejpam-3341	115	5	ordered	order	VERB
ejpam-3341	115	6	semigroup	semigroup	NOUN
ejpam-3341	115	7	,	,	PUNCT
ejpam-3341	115	8	a	a	DET
ejpam-3341	115	9	a	a	DET
ejpam-3341	115	10	right	right	ADJ
ejpam-3341	115	11	ideal	ideal	NOUN
ejpam-3341	115	12	of	of	ADP
ejpam-3341	115	13	s	s	PRON
ejpam-3341	115	14	and	and	CCONJ
ejpam-3341	115	15	ha(s	ha(	NOUN
ejpam-3341	115	16	)	)	PUNCT
ejpam-3341	115	17	6=	6=	ADP
ejpam-3341	115	18	∅	∅	NOUN
ejpam-3341	115	19	,	,	PUNCT
ejpam-3341	115	20	then	then	ADV
ejpam-3341	115	21	ha(s	ha(	NOUN
ejpam-3341	115	22	)	)	PUNCT
ejpam-3341	115	23	is	be	AUX
ejpam-3341	115	24	an	an	DET
ejpam-3341	115	25	ideal	ideal	NOUN
ejpam-3341	115	26	of	of	ADP
ejpam-3341	115	27	s.	s.	PROPN
ejpam-3341	115	28	n.	n.	PROPN
ejpam-3341	115	29	kehayopulu	kehayopulu	PROPN
ejpam-3341	115	30	/	/	SYM
ejpam-3341	115	31	eur	eur	PROPN
ejpam-3341	115	32	.	.	PUNCT
ejpam-3341	116	1	j.	j.	PROPN
ejpam-3341	116	2	pure	pure	PROPN
ejpam-3341	116	3	appl	appl	PROPN
ejpam-3341	116	4	.	.	PROPN
ejpam-3341	116	5	math	math	PROPN
ejpam-3341	116	6	,	,	PUNCT
ejpam-3341	116	7	11	11	NUM
ejpam-3341	116	8	(	(	PUNCT
ejpam-3341	116	9	4	4	NUM
ejpam-3341	116	10	)	)	PUNCT
ejpam-3341	116	11	(	(	PUNCT
ejpam-3341	116	12	2018	2018	NUM
ejpam-3341	116	13	)	)	PUNCT
ejpam-3341	116	14	,	,	PUNCT
ejpam-3341	116	15	911	911	NUM
ejpam-3341	116	16	-	-	SYM
ejpam-3341	116	17	921	921	NUM
ejpam-3341	116	18	915	915	NUM
ejpam-3341	116	19	proof	proof	NOUN
ejpam-3341	116	20	.	.	PUNCT
ejpam-3341	117	1	since	since	SCONJ
ejpam-3341	117	2	ha(s	ha(	NOUN
ejpam-3341	117	3	)	)	PUNCT
ejpam-3341	117	4	6=	6=	ADP
ejpam-3341	117	5	∅	∅	NOUN
ejpam-3341	117	6	,	,	PUNCT
ejpam-3341	117	7	by	by	ADP
ejpam-3341	117	8	proposition	proposition	NOUN
ejpam-3341	117	9	2.5	2.5	NUM
ejpam-3341	117	10	,	,	PUNCT
ejpam-3341	117	11	ha(s	ha(	NOUN
ejpam-3341	117	12	)	)	PUNCT
ejpam-3341	117	13	is	be	AUX
ejpam-3341	117	14	a	a	DET
ejpam-3341	117	15	right	right	ADJ
ejpam-3341	117	16	ideal	ideal	NOUN
ejpam-3341	117	17	of	of	ADP
ejpam-3341	117	18	s.	s.	PROPN
ejpam-3341	117	19	since	since	SCONJ
ejpam-3341	117	20	a	a	DET
ejpam-3341	117	21	a	a	DET
ejpam-3341	117	22	right	right	ADJ
ejpam-3341	117	23	ideal	ideal	NOUN
ejpam-3341	117	24	of	of	ADP
ejpam-3341	117	25	s	s	PRON
ejpam-3341	117	26	and	and	CCONJ
ejpam-3341	117	27	ha(s	ha(	NOUN
ejpam-3341	117	28	)	)	PUNCT
ejpam-3341	117	29	6=	6=	ADP
ejpam-3341	117	30	∅	∅	NOUN
ejpam-3341	117	31	,	,	PUNCT
ejpam-3341	117	32	by	by	ADP
ejpam-3341	117	33	proposition	proposition	NOUN
ejpam-3341	117	34	2.6	2.6	NUM
ejpam-3341	117	35	,	,	PUNCT
ejpam-3341	117	36	ha(s	ha(s	NUM
ejpam-3341	117	37	)	)	PUNCT
ejpam-3341	117	38	is	be	AUX
ejpam-3341	117	39	a	a	DET
ejpam-3341	117	40	left	left	ADJ
ejpam-3341	117	41	ideal	ideal	NOUN
ejpam-3341	117	42	of	of	ADP
ejpam-3341	117	43	s	s	PROPN
ejpam-3341	117	44	;	;	PUNCT
ejpam-3341	117	45	and	and	CCONJ
ejpam-3341	117	46	so	so	ADV
ejpam-3341	117	47	ha(s	ha(	NOUN
ejpam-3341	117	48	)	)	PUNCT
ejpam-3341	117	49	is	be	AUX
ejpam-3341	117	50	an	an	DET
ejpam-3341	117	51	ideal	ideal	NOUN
ejpam-3341	117	52	of	of	ADP
ejpam-3341	117	53	s.	s.	PROPN
ejpam-3341	117	54	�	�	PROPN
ejpam-3341	117	55	corollary	corollary	PROPN
ejpam-3341	117	56	2.8	2.8	NUM
ejpam-3341	117	57	.	.	PUNCT
ejpam-3341	118	1	(	(	PUNCT
ejpam-3341	118	2	see	see	VERB
ejpam-3341	118	3	also	also	ADV
ejpam-3341	118	4	[	[	X
ejpam-3341	118	5	2	2	NUM
ejpam-3341	118	6	;	;	PUNCT
ejpam-3341	118	7	theorem	theorem	VERB
ejpam-3341	118	8	2.4(1	2.4(1	NOUN
ejpam-3341	118	9	)	)	PUNCT
ejpam-3341	118	10	]	]	PUNCT
ejpam-3341	118	11	)	)	PUNCT
ejpam-3341	118	12	if	if	SCONJ
ejpam-3341	118	13	s	s	NOUN
ejpam-3341	118	14	is	be	AUX
ejpam-3341	118	15	an	an	DET
ejpam-3341	118	16	ordered	order	VERB
ejpam-3341	118	17	semigroup	semigroup	NOUN
ejpam-3341	118	18	,	,	PUNCT
ejpam-3341	118	19	a	a	DET
ejpam-3341	118	20	a	a	DET
ejpam-3341	118	21	right	right	ADJ
ejpam-3341	118	22	ideal	ideal	NOUN
ejpam-3341	118	23	of	of	ADP
ejpam-3341	118	24	s	s	PRON
ejpam-3341	118	25	and	and	CCONJ
ejpam-3341	118	26	ha(s	ha(	NOUN
ejpam-3341	118	27	)	)	PUNCT
ejpam-3341	118	28	6=	6=	ADP
ejpam-3341	118	29	∅	∅	NOUN
ejpam-3341	118	30	,	,	PUNCT
ejpam-3341	118	31	then	then	ADV
ejpam-3341	118	32	ha(s	ha(	NOUN
ejpam-3341	118	33	)	)	PUNCT
ejpam-3341	118	34	is	be	AUX
ejpam-3341	118	35	a	a	DET
ejpam-3341	118	36	semiprime	semiprime	NOUN
ejpam-3341	118	37	ideal	ideal	NOUN
ejpam-3341	118	38	of	of	ADP
ejpam-3341	118	39	s.	s.	PROPN
ejpam-3341	118	40	proof	proof	PROPN
ejpam-3341	118	41	.	.	PUNCT
ejpam-3341	119	1	since	since	SCONJ
ejpam-3341	119	2	a	a	PRON
ejpam-3341	119	3	is	be	AUX
ejpam-3341	119	4	a	a	DET
ejpam-3341	119	5	right	right	ADJ
ejpam-3341	119	6	ideal	ideal	NOUN
ejpam-3341	119	7	of	of	ADP
ejpam-3341	119	8	s	s	PRON
ejpam-3341	119	9	and	and	CCONJ
ejpam-3341	119	10	ha(s	ha(	NOUN
ejpam-3341	119	11	)	)	PUNCT
ejpam-3341	119	12	6=	6=	ADP
ejpam-3341	119	13	∅	∅	NOUN
ejpam-3341	119	14	,	,	PUNCT
ejpam-3341	119	15	by	by	ADP
ejpam-3341	119	16	corollary	corollary	ADJ
ejpam-3341	119	17	2.7	2.7	NUM
ejpam-3341	119	18	,	,	PUNCT
ejpam-3341	119	19	ha(s	ha(s	NUM
ejpam-3341	119	20	)	)	PUNCT
ejpam-3341	119	21	is	be	AUX
ejpam-3341	119	22	an	an	DET
ejpam-3341	119	23	ideal	ideal	NOUN
ejpam-3341	119	24	of	of	ADP
ejpam-3341	119	25	s.	s.	PROPN
ejpam-3341	119	26	on	on	ADP
ejpam-3341	119	27	the	the	DET
ejpam-3341	119	28	other	other	ADJ
ejpam-3341	119	29	hand	hand	NOUN
ejpam-3341	119	30	,	,	PUNCT
ejpam-3341	119	31	by	by	ADP
ejpam-3341	119	32	proposition	proposition	NOUN
ejpam-3341	119	33	2.2	2.2	NUM
ejpam-3341	119	34	,	,	PUNCT
ejpam-3341	119	35	ha(s	ha(	NOUN
ejpam-3341	119	36	)	)	PUNCT
ejpam-3341	119	37	is	be	AUX
ejpam-3341	119	38	a	a	DET
ejpam-3341	119	39	semiprime	semiprime	NOUN
ejpam-3341	119	40	subset	subset	NOUN
ejpam-3341	119	41	of	of	ADP
ejpam-3341	119	42	s.	s.	PROPN
ejpam-3341	119	43	thus	thus	ADV
ejpam-3341	119	44	ha(s	ha(	NOUN
ejpam-3341	119	45	)	)	PUNCT
ejpam-3341	119	46	is	be	AUX
ejpam-3341	119	47	a	a	DET
ejpam-3341	119	48	semiprime	semiprime	NOUN
ejpam-3341	119	49	ideal	ideal	NOUN
ejpam-3341	119	50	of	of	ADP
ejpam-3341	119	51	s.	s.	PROPN
ejpam-3341	119	52	�	�	PROPN
ejpam-3341	119	53	proposition	proposition	PROPN
ejpam-3341	119	54	2.9	2.9	NUM
ejpam-3341	119	55	.	.	PUNCT
ejpam-3341	120	1	let	let	VERB
ejpam-3341	120	2	(	(	PUNCT
ejpam-3341	120	3	s	s	X
ejpam-3341	120	4	,	,	PUNCT
ejpam-3341	120	5	·	·	PUNCT
ejpam-3341	120	6	,	,	PUNCT
ejpam-3341	120	7	≤	≤	NUM
ejpam-3341	120	8	)	)	PUNCT
ejpam-3341	120	9	be	be	AUX
ejpam-3341	120	10	an	an	DET
ejpam-3341	120	11	ordered	order	VERB
ejpam-3341	120	12	semigroup	semigroup	NOUN
ejpam-3341	120	13	and	and	CCONJ
ejpam-3341	120	14	i	i	PRON
ejpam-3341	120	15	a	a	DET
ejpam-3341	120	16	right	right	ADJ
ejpam-3341	120	17	ideal	ideal	NOUN
ejpam-3341	120	18	of	of	ADP
ejpam-3341	120	19	the	the	DET
ejpam-3341	120	20	semigroup	semigroup	NOUN
ejpam-3341	120	21	(	(	PUNCT
ejpam-3341	120	22	s	s	PROPN
ejpam-3341	120	23	,	,	PUNCT
ejpam-3341	120	24	·	·	PUNCT
ejpam-3341	120	25	)	)	PUNCT
ejpam-3341	120	26	.	.	PUNCT
ejpam-3341	121	1	if	if	SCONJ
ejpam-3341	121	2	s	s	PRON
ejpam-3341	121	3	/∈	/∈	INTJ
ejpam-3341	121	4	(	(	PUNCT
ejpam-3341	121	5	si	si	X
ejpam-3341	121	6	]	]	X
ejpam-3341	121	7	for	for	ADP
ejpam-3341	121	8	every	every	DET
ejpam-3341	121	9	s	s	PROPN
ejpam-3341	121	10	∈	∈	PROPN
ejpam-3341	121	11	s\a	s\a	NOUN
ejpam-3341	121	12	,	,	PUNCT
ejpam-3341	121	13	then	then	ADV
ejpam-3341	121	14	i	i	PRON
ejpam-3341	121	15	⊆	⊆	NUM
ejpam-3341	121	16	ha(s	ha(	NOUN
ejpam-3341	121	17	)	)	PUNCT
ejpam-3341	121	18	.	.	PUNCT
ejpam-3341	122	1	proof	proof	NOUN
ejpam-3341	122	2	.	.	PUNCT
ejpam-3341	123	1	let	let	VERB
ejpam-3341	123	2	h	h	PRON
ejpam-3341	123	3	∈	∈	PROPN
ejpam-3341	123	4	i.	i.	NOUN
ejpam-3341	124	1	then	then	ADV
ejpam-3341	124	2	h	h	PROPN
ejpam-3341	124	3	∈	∈	PROPN
ejpam-3341	124	4	ha(s	ha(	NOUN
ejpam-3341	124	5	)	)	PUNCT
ejpam-3341	124	6	,	,	PUNCT
ejpam-3341	124	7	that	that	PRON
ejpam-3341	124	8	is	be	AUX
ejpam-3341	124	9	if	if	SCONJ
ejpam-3341	124	10	s	s	X
ejpam-3341	124	11	∈	∈	PROPN
ejpam-3341	124	12	s\a	s\a	NOUN
ejpam-3341	124	13	,	,	PUNCT
ejpam-3341	124	14	then	then	ADV
ejpam-3341	124	15	s	s	VERB
ejpam-3341	124	16	/∈	/∈	PUNCT
ejpam-3341	124	17	(	(	PUNCT
ejpam-3341	124	18	shs	shs	PROPN
ejpam-3341	124	19	]	]	PUNCT
ejpam-3341	124	20	.	.	PUNCT
ejpam-3341	125	1	indeed	indeed	ADV
ejpam-3341	125	2	:	:	PUNCT
ejpam-3341	125	3	let	let	VERB
ejpam-3341	125	4	s	s	PRON
ejpam-3341	125	5	∈	∈	NOUN
ejpam-3341	125	6	s\a	s\a	PROPN
ejpam-3341	125	7	and	and	CCONJ
ejpam-3341	125	8	s	s	PROPN
ejpam-3341	125	9	∈	∈	PROPN
ejpam-3341	125	10	(	(	PUNCT
ejpam-3341	125	11	shs	shs	NOUN
ejpam-3341	125	12	]	]	PUNCT
ejpam-3341	125	13	.	.	PUNCT
ejpam-3341	126	1	then	then	ADV
ejpam-3341	126	2	we	we	PRON
ejpam-3341	126	3	have	have	VERB
ejpam-3341	126	4	s	s	X
ejpam-3341	126	5	∈	∈	NOUN
ejpam-3341	126	6	(	(	PUNCT
ejpam-3341	126	7	s(is	s(i	NOUN
ejpam-3341	126	8	)	)	PUNCT
ejpam-3341	126	9	]	]	PUNCT
ejpam-3341	127	1	⊆	⊆	NUM
ejpam-3341	127	2	(	(	PUNCT
ejpam-3341	127	3	si	si	X
ejpam-3341	127	4	]	]	X
ejpam-3341	127	5	,	,	PUNCT
ejpam-3341	127	6	we	we	PRON
ejpam-3341	127	7	get	get	VERB
ejpam-3341	127	8	a	a	DET
ejpam-3341	127	9	contradiction	contradiction	NOUN
ejpam-3341	127	10	.	.	PUNCT
ejpam-3341	128	1	�	�	PROPN
ejpam-3341	128	2	proposition	proposition	PROPN
ejpam-3341	128	3	2.10	2.10	NUM
ejpam-3341	128	4	.	.	PUNCT
ejpam-3341	129	1	let	let	VERB
ejpam-3341	129	2	s	s	PRON
ejpam-3341	129	3	be	be	AUX
ejpam-3341	129	4	an	an	DET
ejpam-3341	129	5	ordered	order	VERB
ejpam-3341	129	6	semigroup	semigroup	NOUN
ejpam-3341	129	7	,	,	PUNCT
ejpam-3341	129	8	ha(s	ha(	NOUN
ejpam-3341	129	9	)	)	PUNCT
ejpam-3341	129	10	a	a	DET
ejpam-3341	129	11	left	left	ADJ
ejpam-3341	129	12	ideal	ideal	NOUN
ejpam-3341	129	13	of	of	ADP
ejpam-3341	129	14	s	s	PRON
ejpam-3341	130	1	and	and	CCONJ
ejpam-3341	130	2	i	i	PRON
ejpam-3341	130	3	be	be	VERB
ejpam-3341	130	4	a	a	DET
ejpam-3341	130	5	subset	subset	NOUN
ejpam-3341	130	6	of	of	ADP
ejpam-3341	130	7	s	s	PRON
ejpam-3341	130	8	such	such	ADJ
ejpam-3341	130	9	that	that	SCONJ
ejpam-3341	130	10	i	i	PRON
ejpam-3341	130	11	⊆	⊆	NUM
ejpam-3341	130	12	ha(s	ha(	NOUN
ejpam-3341	130	13	)	)	PUNCT
ejpam-3341	130	14	.	.	PUNCT
ejpam-3341	131	1	then	then	ADV
ejpam-3341	131	2	s	s	VERB
ejpam-3341	131	3	/∈	/∈	PUNCT
ejpam-3341	131	4	(	(	PUNCT
ejpam-3341	131	5	si	si	X
ejpam-3341	131	6	]	]	X
ejpam-3341	131	7	for	for	ADP
ejpam-3341	131	8	every	every	DET
ejpam-3341	131	9	s	s	PROPN
ejpam-3341	131	10	∈	∈	PROPN
ejpam-3341	131	11	s\a	s\a	NOUN
ejpam-3341	131	12	.	.	PUNCT
ejpam-3341	132	1	proof	proof	NOUN
ejpam-3341	132	2	.	.	PUNCT
ejpam-3341	133	1	let	let	VERB
ejpam-3341	133	2	s	s	PRON
ejpam-3341	133	3	∈	∈	NOUN
ejpam-3341	133	4	s\a	s\a	NOUN
ejpam-3341	133	5	such	such	ADJ
ejpam-3341	133	6	that	that	PRON
ejpam-3341	133	7	s	s	VERB
ejpam-3341	133	8	∈	∈	PROPN
ejpam-3341	133	9	(	(	PUNCT
ejpam-3341	133	10	si	si	X
ejpam-3341	133	11	]	]	X
ejpam-3341	133	12	.	.	PUNCT
ejpam-3341	134	1	then	then	ADV
ejpam-3341	134	2	s	s	VERB
ejpam-3341	134	3	∈	∈	PROPN
ejpam-3341	134	4	(	(	PUNCT
ejpam-3341	134	5	si	si	X
ejpam-3341	134	6	]	]	X
ejpam-3341	134	7	⊆	⊆	NUM
ejpam-3341	134	8	(	(	PUNCT
ejpam-3341	134	9	sha(s	sha(s	PROPN
ejpam-3341	134	10	)	)	PUNCT
ejpam-3341	134	11	]	]	PUNCT
ejpam-3341	135	1	⊆	⊆	NUM
ejpam-3341	135	2	(	(	PUNCT
ejpam-3341	135	3	sha(s	sha(s	PROPN
ejpam-3341	135	4	)	)	PUNCT
ejpam-3341	135	5	]	]	PUNCT
ejpam-3341	136	1	⊆	⊆	NUM
ejpam-3341	136	2	(	(	PUNCT
ejpam-3341	136	3	ha(s	ha(	NOUN
ejpam-3341	136	4	)	)	PUNCT
ejpam-3341	136	5	]	]	PUNCT
ejpam-3341	136	6	=	=	PUNCT
ejpam-3341	136	7	ha(s	ha(s	X
ejpam-3341	136	8	)	)	PUNCT
ejpam-3341	136	9	since	since	SCONJ
ejpam-3341	136	10	ha(s	ha(	NOUN
ejpam-3341	136	11	)	)	PUNCT
ejpam-3341	136	12	is	be	AUX
ejpam-3341	136	13	a	a	DET
ejpam-3341	136	14	left	left	ADJ
ejpam-3341	136	15	ideal	ideal	NOUN
ejpam-3341	136	16	of	of	ADP
ejpam-3341	136	17	s.	s.	PROPN
ejpam-3341	136	18	we	we	PRON
ejpam-3341	136	19	have	have	VERB
ejpam-3341	136	20	s	s	NOUN
ejpam-3341	136	21	∈	∈	ADJ
ejpam-3341	136	22	s\a	s\a	PROPN
ejpam-3341	136	23	and	and	CCONJ
ejpam-3341	136	24	s	s	NOUN
ejpam-3341	136	25	∈	∈	NOUN
ejpam-3341	136	26	ha(s	ha(	NOUN
ejpam-3341	136	27	)	)	PUNCT
ejpam-3341	136	28	,	,	PUNCT
ejpam-3341	136	29	so	so	SCONJ
ejpam-3341	136	30	s	s	AUX
ejpam-3341	136	31	/∈	/∈	PUNCT
ejpam-3341	136	32	(	(	PUNCT
ejpam-3341	136	33	sss	sss	PROPN
ejpam-3341	136	34	]	]	X
ejpam-3341	136	35	=	=	PUNCT
ejpam-3341	136	36	(	(	PUNCT
ejpam-3341	136	37	s	s	X
ejpam-3341	136	38	]	]	X
ejpam-3341	136	39	=	=	SYM
ejpam-3341	136	40	s	s	X
ejpam-3341	136	41	which	which	PRON
ejpam-3341	136	42	is	be	AUX
ejpam-3341	136	43	impossible	impossible	ADJ
ejpam-3341	136	44	.	.	PUNCT
ejpam-3341	137	1	�	�	PROPN
ejpam-3341	137	2	corollary	corollary	NOUN
ejpam-3341	137	3	2.11	2.11	NUM
ejpam-3341	137	4	.	.	PUNCT
ejpam-3341	138	1	let	let	VERB
ejpam-3341	138	2	s	s	PRON
ejpam-3341	138	3	be	be	AUX
ejpam-3341	138	4	an	an	DET
ejpam-3341	138	5	ordered	order	VERB
ejpam-3341	138	6	semigroup	semigroup	NOUN
ejpam-3341	138	7	,	,	PUNCT
ejpam-3341	138	8	a	a	DET
ejpam-3341	138	9	a	a	DET
ejpam-3341	138	10	right	right	ADJ
ejpam-3341	138	11	ideal	ideal	NOUN
ejpam-3341	138	12	of	of	ADP
ejpam-3341	138	13	s	s	PROPN
ejpam-3341	138	14	,	,	PUNCT
ejpam-3341	138	15	ha(s	ha(s	X
ejpam-3341	138	16	)	)	PUNCT
ejpam-3341	138	17	6=	6=	ADP
ejpam-3341	138	18	∅	∅	NOUN
ejpam-3341	138	19	and	and	CCONJ
ejpam-3341	138	20	i	i	PRON
ejpam-3341	138	21	a	a	DET
ejpam-3341	138	22	subset	subset	NOUN
ejpam-3341	138	23	of	of	ADP
ejpam-3341	138	24	s	s	PRON
ejpam-3341	138	25	such	such	ADJ
ejpam-3341	138	26	that	that	SCONJ
ejpam-3341	138	27	i	i	PRON
ejpam-3341	138	28	⊆	⊆	NUM
ejpam-3341	138	29	ha(s	ha(	NOUN
ejpam-3341	138	30	)	)	PUNCT
ejpam-3341	138	31	.	.	PUNCT
ejpam-3341	139	1	then	then	ADV
ejpam-3341	139	2	s	s	VERB
ejpam-3341	139	3	/∈	/∈	PUNCT
ejpam-3341	139	4	(	(	PUNCT
ejpam-3341	139	5	si	si	X
ejpam-3341	139	6	]	]	X
ejpam-3341	139	7	for	for	ADP
ejpam-3341	139	8	every	every	DET
ejpam-3341	139	9	s	s	PROPN
ejpam-3341	139	10	∈	∈	PROPN
ejpam-3341	139	11	s\a	s\a	NOUN
ejpam-3341	139	12	.	.	PUNCT
ejpam-3341	140	1	proof	proof	NOUN
ejpam-3341	140	2	.	.	PUNCT
ejpam-3341	141	1	since	since	SCONJ
ejpam-3341	141	2	a	a	PRON
ejpam-3341	141	3	is	be	AUX
ejpam-3341	141	4	a	a	DET
ejpam-3341	141	5	right	right	ADJ
ejpam-3341	141	6	ideal	ideal	NOUN
ejpam-3341	141	7	of	of	ADP
ejpam-3341	141	8	s	s	PRON
ejpam-3341	141	9	and	and	CCONJ
ejpam-3341	141	10	ha(s	ha(	NOUN
ejpam-3341	141	11	)	)	PUNCT
ejpam-3341	141	12	6=	6=	ADP
ejpam-3341	141	13	∅	∅	NOUN
ejpam-3341	141	14	,	,	PUNCT
ejpam-3341	141	15	by	by	ADP
ejpam-3341	141	16	proposition	proposition	NOUN
ejpam-3341	141	17	2.6	2.6	NUM
ejpam-3341	141	18	,	,	PUNCT
ejpam-3341	141	19	ha(s	ha(s	NUM
ejpam-3341	141	20	)	)	PUNCT
ejpam-3341	141	21	is	be	AUX
ejpam-3341	141	22	a	a	DET
ejpam-3341	141	23	left	left	ADJ
ejpam-3341	141	24	ideal	ideal	NOUN
ejpam-3341	141	25	of	of	ADP
ejpam-3341	141	26	s.	s.	PROPN
ejpam-3341	141	27	since	since	SCONJ
ejpam-3341	141	28	ha(s	ha(	NOUN
ejpam-3341	141	29	)	)	PUNCT
ejpam-3341	141	30	is	be	AUX
ejpam-3341	141	31	a	a	DET
ejpam-3341	141	32	left	left	ADJ
ejpam-3341	141	33	ideal	ideal	NOUN
ejpam-3341	141	34	of	of	ADP
ejpam-3341	141	35	s	s	PRON
ejpam-3341	142	1	and	and	CCONJ
ejpam-3341	142	2	i	i	PRON
ejpam-3341	142	3	a	a	DET
ejpam-3341	142	4	subset	subset	NOUN
ejpam-3341	142	5	of	of	ADP
ejpam-3341	142	6	s	s	PRON
ejpam-3341	142	7	such	such	ADJ
ejpam-3341	142	8	that	that	SCONJ
ejpam-3341	142	9	i	i	PRON
ejpam-3341	142	10	⊆	⊆	NUM
ejpam-3341	142	11	ha(s	ha(	NOUN
ejpam-3341	142	12	)	)	PUNCT
ejpam-3341	142	13	,	,	PUNCT
ejpam-3341	142	14	by	by	ADP
ejpam-3341	142	15	proposition	proposition	NOUN
ejpam-3341	142	16	2.10	2.10	NUM
ejpam-3341	142	17	,	,	PUNCT
ejpam-3341	142	18	s	s	PART
ejpam-3341	142	19	/∈	/∈	PUNCT
ejpam-3341	142	20	(	(	PUNCT
ejpam-3341	142	21	si	si	X
ejpam-3341	142	22	]	]	X
ejpam-3341	142	23	for	for	ADP
ejpam-3341	142	24	every	every	DET
ejpam-3341	142	25	s	s	PROPN
ejpam-3341	142	26	∈	∈	PROPN
ejpam-3341	142	27	s\a	s\a	PROPN
ejpam-3341	142	28	.	.	PUNCT
ejpam-3341	143	1	�	�	PROPN
ejpam-3341	143	2	corollary	corollary	ADJ
ejpam-3341	143	3	2.12	2.12	NUM
ejpam-3341	143	4	.	.	PUNCT
ejpam-3341	144	1	(	(	PUNCT
ejpam-3341	144	2	see	see	VERB
ejpam-3341	144	3	also	also	ADV
ejpam-3341	144	4	[	[	X
ejpam-3341	144	5	2	2	NUM
ejpam-3341	144	6	;	;	PUNCT
ejpam-3341	144	7	theorem	theorem	ADJ
ejpam-3341	144	8	2.4(2	2.4(2	NUM
ejpam-3341	144	9	)	)	PUNCT
ejpam-3341	144	10	]	]	PUNCT
ejpam-3341	144	11	)	)	PUNCT
ejpam-3341	144	12	let	let	VERB
ejpam-3341	144	13	(	(	PUNCT
ejpam-3341	144	14	s	s	X
ejpam-3341	144	15	,	,	PUNCT
ejpam-3341	144	16	·	·	PUNCT
ejpam-3341	144	17	,	,	PUNCT
ejpam-3341	144	18	≤	≤	NUM
ejpam-3341	144	19	)	)	PUNCT
ejpam-3341	144	20	be	be	VERB
ejpam-3341	144	21	an	an	DET
ejpam-3341	144	22	ordered	order	VERB
ejpam-3341	144	23	semigroup	semigroup	NOUN
ejpam-3341	144	24	and	and	CCONJ
ejpam-3341	144	25	a	a	DET
ejpam-3341	144	26	,	,	PUNCT
ejpam-3341	144	27	i	i	PRON
ejpam-3341	144	28	right	right	ADJ
ejpam-3341	144	29	ideals	ideal	NOUN
ejpam-3341	144	30	of	of	ADP
ejpam-3341	144	31	(	(	PUNCT
ejpam-3341	144	32	s	s	X
ejpam-3341	144	33	,	,	PUNCT
ejpam-3341	144	34	·	·	PUNCT
ejpam-3341	144	35	,	,	PUNCT
ejpam-3341	144	36	≤	≤	NUM
ejpam-3341	144	37	)	)	PUNCT
ejpam-3341	144	38	.	.	PUNCT
ejpam-3341	145	1	then	then	ADV
ejpam-3341	145	2	i	i	PRON
ejpam-3341	145	3	⊆	⊆	NUM
ejpam-3341	145	4	ha(s	ha(	NOUN
ejpam-3341	145	5	)	)	PUNCT
ejpam-3341	145	6	if	if	SCONJ
ejpam-3341	145	7	and	and	CCONJ
ejpam-3341	145	8	only	only	ADV
ejpam-3341	145	9	if	if	SCONJ
ejpam-3341	145	10	s	s	X
ejpam-3341	145	11	/∈	/∈	INTJ
ejpam-3341	145	12	(	(	PUNCT
ejpam-3341	145	13	si	si	X
ejpam-3341	145	14	]	]	X
ejpam-3341	145	15	for	for	ADP
ejpam-3341	145	16	every	every	DET
ejpam-3341	145	17	s	s	PROPN
ejpam-3341	145	18	∈	∈	PROPN
ejpam-3341	145	19	s\a	s\a	NOUN
ejpam-3341	145	20	.	.	PUNCT
ejpam-3341	146	1	proof	proof	NOUN
ejpam-3341	146	2	.	.	PUNCT
ejpam-3341	147	1	=	=	NOUN
ejpam-3341	147	2	⇒.	⇒.	NOUN
ejpam-3341	147	3	since	since	SCONJ
ejpam-3341	147	4	i	i	PRON
ejpam-3341	147	5	is	be	AUX
ejpam-3341	147	6	a	a	DET
ejpam-3341	147	7	right	right	ADJ
ejpam-3341	147	8	ideal	ideal	NOUN
ejpam-3341	147	9	of	of	ADP
ejpam-3341	147	10	s	s	PRON
ejpam-3341	147	11	and	and	CCONJ
ejpam-3341	147	12	i	i	PRON
ejpam-3341	147	13	⊆	⊆	NUM
ejpam-3341	147	14	ha(s	ha(	NOUN
ejpam-3341	147	15	)	)	PUNCT
ejpam-3341	147	16	,	,	PUNCT
ejpam-3341	147	17	we	we	PRON
ejpam-3341	147	18	have	have	VERB
ejpam-3341	147	19	ha(s	ha(	NOUN
ejpam-3341	147	20	)	)	PUNCT
ejpam-3341	147	21	6=	6=	ADP
ejpam-3341	147	22	∅.	∅.	VERB
ejpam-3341	147	23	since	since	SCONJ
ejpam-3341	147	24	a	a	PRON
ejpam-3341	147	25	is	be	AUX
ejpam-3341	147	26	a	a	DET
ejpam-3341	147	27	right	right	ADJ
ejpam-3341	147	28	ideal	ideal	NOUN
ejpam-3341	147	29	of	of	ADP
ejpam-3341	147	30	s	s	PROPN
ejpam-3341	147	31	,	,	PUNCT
ejpam-3341	147	32	ha(s	ha(s	X
ejpam-3341	147	33	)	)	PUNCT
ejpam-3341	147	34	6=	6=	ADP
ejpam-3341	147	35	∅	∅	NOUN
ejpam-3341	148	1	and	and	CCONJ
ejpam-3341	148	2	i	i	PRON
ejpam-3341	148	3	is	be	AUX
ejpam-3341	148	4	a	a	DET
ejpam-3341	148	5	subset	subset	NOUN
ejpam-3341	148	6	of	of	ADP
ejpam-3341	148	7	s	s	PRON
ejpam-3341	148	8	such	such	ADJ
ejpam-3341	148	9	that	that	SCONJ
ejpam-3341	148	10	i	i	PRON
ejpam-3341	148	11	⊆	⊆	NUM
ejpam-3341	148	12	ha(s	ha(	NOUN
ejpam-3341	148	13	)	)	PUNCT
ejpam-3341	148	14	,	,	PUNCT
ejpam-3341	148	15	by	by	ADP
ejpam-3341	148	16	corollary	corollary	NOUN
ejpam-3341	148	17	2.11	2.11	NUM
ejpam-3341	148	18	,	,	PUNCT
ejpam-3341	148	19	s	s	PART
ejpam-3341	148	20	/∈	/∈	PUNCT
ejpam-3341	148	21	(	(	PUNCT
ejpam-3341	148	22	si	si	X
ejpam-3341	148	23	]	]	X
ejpam-3341	148	24	for	for	ADP
ejpam-3341	148	25	every	every	DET
ejpam-3341	148	26	s	s	PROPN
ejpam-3341	148	27	∈	∈	PROPN
ejpam-3341	148	28	s\a	s\a	NOUN
ejpam-3341	148	29	.	.	PUNCT
ejpam-3341	149	1	⇐	⇐	PROPN
ejpam-3341	149	2	=	=	PROPN
ejpam-3341	149	3	.	.	PUNCT
ejpam-3341	150	1	since	since	SCONJ
ejpam-3341	150	2	i	i	PRON
ejpam-3341	150	3	is	be	AUX
ejpam-3341	150	4	a	a	DET
ejpam-3341	150	5	right	right	ADJ
ejpam-3341	150	6	ideal	ideal	NOUN
ejpam-3341	150	7	of	of	ADP
ejpam-3341	150	8	the	the	DET
ejpam-3341	150	9	ordered	order	VERB
ejpam-3341	150	10	semigroup	semigroup	NOUN
ejpam-3341	150	11	(	(	PUNCT
ejpam-3341	150	12	s	s	PROPN
ejpam-3341	150	13	,	,	PUNCT
ejpam-3341	150	14	·	·	PUNCT
ejpam-3341	150	15	,	,	PUNCT
ejpam-3341	150	16	≤	≤	NUM
ejpam-3341	150	17	)	)	PUNCT
ejpam-3341	150	18	,	,	PUNCT
ejpam-3341	150	19	it	it	PRON
ejpam-3341	150	20	is	be	AUX
ejpam-3341	150	21	a	a	DET
ejpam-3341	150	22	right	right	ADJ
ejpam-3341	150	23	ideal	ideal	NOUN
ejpam-3341	150	24	of	of	ADP
ejpam-3341	150	25	the	the	DET
ejpam-3341	150	26	semigroup	semigroup	NOUN
ejpam-3341	150	27	(	(	PUNCT
ejpam-3341	150	28	s	s	PROPN
ejpam-3341	150	29	,	,	PUNCT
ejpam-3341	150	30	·	·	PUNCT
ejpam-3341	150	31	)	)	PUNCT
ejpam-3341	150	32	as	as	ADV
ejpam-3341	150	33	well	well	ADV
ejpam-3341	150	34	.	.	PUNCT
ejpam-3341	151	1	since	since	SCONJ
ejpam-3341	151	2	i	i	PRON
ejpam-3341	151	3	is	be	AUX
ejpam-3341	151	4	a	a	DET
ejpam-3341	151	5	right	right	ADJ
ejpam-3341	151	6	ideal	ideal	NOUN
ejpam-3341	151	7	of	of	ADP
ejpam-3341	151	8	(	(	PUNCT
ejpam-3341	151	9	s	s	PROPN
ejpam-3341	151	10	,	,	PUNCT
ejpam-3341	151	11	·	·	PUNCT
ejpam-3341	151	12	)	)	PUNCT
ejpam-3341	151	13	and	and	CCONJ
ejpam-3341	151	14	s	s	AUX
ejpam-3341	151	15	/∈	/∈	INTJ
ejpam-3341	151	16	(	(	PUNCT
ejpam-3341	151	17	si	si	X
ejpam-3341	151	18	]	]	X
ejpam-3341	151	19	for	for	ADP
ejpam-3341	151	20	every	every	DET
ejpam-3341	151	21	s	s	PROPN
ejpam-3341	151	22	∈	∈	NOUN
ejpam-3341	151	23	s\a	s\a	NOUN
ejpam-3341	151	24	,	,	PUNCT
ejpam-3341	151	25	by	by	ADP
ejpam-3341	151	26	proposition	proposition	NOUN
ejpam-3341	151	27	2.9	2.9	NUM
ejpam-3341	151	28	,	,	PUNCT
ejpam-3341	151	29	we	we	PRON
ejpam-3341	151	30	have	have	VERB
ejpam-3341	151	31	i	i	PRON
ejpam-3341	151	32	⊆	⊆	NUM
ejpam-3341	151	33	ha(s	ha(	NOUN
ejpam-3341	151	34	)	)	PUNCT
ejpam-3341	151	35	.	.	PUNCT
ejpam-3341	152	1	�	�	PROPN
ejpam-3341	152	2	summarizing	summarizing	PROPN
ejpam-3341	152	3	,	,	PUNCT
ejpam-3341	152	4	from	from	ADP
ejpam-3341	152	5	proposition	proposition	NOUN
ejpam-3341	152	6	2.3	2.3	NUM
ejpam-3341	152	7	,	,	PUNCT
ejpam-3341	152	8	corollary	corollary	ADJ
ejpam-3341	152	9	2.8	2.8	NUM
ejpam-3341	152	10	and	and	CCONJ
ejpam-3341	152	11	corollary	corollary	ADJ
ejpam-3341	152	12	2.12	2.12	NUM
ejpam-3341	152	13	we	we	PRON
ejpam-3341	152	14	have	have	VERB
ejpam-3341	152	15	the	the	DET
ejpam-3341	152	16	following	follow	VERB
ejpam-3341	152	17	theorem	theorem	NOUN
ejpam-3341	152	18	theorem	theorem	NOUN
ejpam-3341	152	19	2.13	2.13	NUM
ejpam-3341	152	20	.	.	PUNCT
ejpam-3341	153	1	let	let	VERB
ejpam-3341	153	2	(	(	PUNCT
ejpam-3341	153	3	s	s	X
ejpam-3341	153	4	,	,	PUNCT
ejpam-3341	153	5	·	·	PUNCT
ejpam-3341	153	6	,	,	PUNCT
ejpam-3341	153	7	≤	≤	NUM
ejpam-3341	153	8	)	)	PUNCT
ejpam-3341	153	9	be	be	AUX
ejpam-3341	153	10	an	an	DET
ejpam-3341	153	11	ordered	order	VERB
ejpam-3341	153	12	semigroup	semigroup	NOUN
ejpam-3341	153	13	.	.	PUNCT
ejpam-3341	154	1	then	then	ADV
ejpam-3341	154	2	we	we	PRON
ejpam-3341	154	3	have	have	VERB
ejpam-3341	154	4	the	the	DET
ejpam-3341	154	5	following	following	NOUN
ejpam-3341	154	6	:	:	PUNCT
ejpam-3341	154	7	(	(	PUNCT
ejpam-3341	154	8	1	1	X
ejpam-3341	154	9	)	)	PUNCT
ejpam-3341	154	10	if	if	SCONJ
ejpam-3341	154	11	a	a	PRON
ejpam-3341	154	12	is	be	AUX
ejpam-3341	154	13	a	a	DET
ejpam-3341	154	14	(	(	PUNCT
ejpam-3341	154	15	proper	proper	ADJ
ejpam-3341	154	16	)	)	PUNCT
ejpam-3341	154	17	ideal	ideal	NOUN
ejpam-3341	154	18	of	of	ADP
ejpam-3341	154	19	s	s	PROPN
ejpam-3341	154	20	,	,	PUNCT
ejpam-3341	154	21	then	then	ADV
ejpam-3341	154	22	a	a	DET
ejpam-3341	154	23	⊆	⊆	NUM
ejpam-3341	154	24	ha(s	ha(	NOUN
ejpam-3341	154	25	)	)	PUNCT
ejpam-3341	154	26	.	.	PUNCT
ejpam-3341	155	1	(	(	PUNCT
ejpam-3341	155	2	2	2	X
ejpam-3341	155	3	)	)	PUNCT
ejpam-3341	155	4	if	if	SCONJ
ejpam-3341	155	5	a	a	DET
ejpam-3341	155	6	a	a	DET
ejpam-3341	155	7	right	right	ADJ
ejpam-3341	155	8	ideal	ideal	NOUN
ejpam-3341	155	9	of	of	ADP
ejpam-3341	155	10	s	s	PRON
ejpam-3341	155	11	and	and	CCONJ
ejpam-3341	155	12	ha(s	ha(	NOUN
ejpam-3341	155	13	)	)	PUNCT
ejpam-3341	155	14	6=	6=	ADP
ejpam-3341	155	15	∅	∅	NOUN
ejpam-3341	155	16	,	,	PUNCT
ejpam-3341	155	17	then	then	ADV
ejpam-3341	155	18	ha(s	ha(	NOUN
ejpam-3341	155	19	)	)	PUNCT
ejpam-3341	155	20	is	be	AUX
ejpam-3341	155	21	a	a	DET
ejpam-3341	155	22	semiprime	semiprime	NOUN
ejpam-3341	155	23	ideal	ideal	NOUN
ejpam-3341	155	24	of	of	ADP
ejpam-3341	155	25	s.	s.	PROPN
ejpam-3341	155	26	n.	n.	PROPN
ejpam-3341	155	27	kehayopulu	kehayopulu	PROPN
ejpam-3341	155	28	/	/	SYM
ejpam-3341	155	29	eur	eur	PROPN
ejpam-3341	155	30	.	.	PUNCT
ejpam-3341	156	1	j.	j.	PROPN
ejpam-3341	156	2	pure	pure	PROPN
ejpam-3341	156	3	appl	appl	PROPN
ejpam-3341	156	4	.	.	PROPN
ejpam-3341	156	5	math	math	PROPN
ejpam-3341	156	6	,	,	PUNCT
ejpam-3341	156	7	11	11	NUM
ejpam-3341	156	8	(	(	PUNCT
ejpam-3341	156	9	4	4	NUM
ejpam-3341	156	10	)	)	PUNCT
ejpam-3341	156	11	(	(	PUNCT
ejpam-3341	156	12	2018	2018	NUM
ejpam-3341	156	13	)	)	PUNCT
ejpam-3341	156	14	,	,	PUNCT
ejpam-3341	156	15	911	911	NUM
ejpam-3341	156	16	-	-	SYM
ejpam-3341	156	17	921	921	NUM
ejpam-3341	156	18	916	916	NUM
ejpam-3341	156	19	(	(	PUNCT
ejpam-3341	156	20	3	3	NUM
ejpam-3341	156	21	)	)	PUNCT
ejpam-3341	156	22	if	if	SCONJ
ejpam-3341	156	23	a	a	PRON
ejpam-3341	156	24	and	and	CCONJ
ejpam-3341	156	25	i	i	PRON
ejpam-3341	156	26	are	be	AUX
ejpam-3341	156	27	right	right	ADJ
ejpam-3341	156	28	ideals	ideal	NOUN
ejpam-3341	156	29	of	of	ADP
ejpam-3341	156	30	s	s	NOUN
ejpam-3341	156	31	,	,	PUNCT
ejpam-3341	156	32	then	then	ADV
ejpam-3341	156	33	i	i	PRON
ejpam-3341	156	34	⊆	⊆	NUM
ejpam-3341	156	35	ha(s	ha(	NOUN
ejpam-3341	156	36	)	)	PUNCT
ejpam-3341	156	37	if	if	SCONJ
ejpam-3341	157	1	and	and	CCONJ
ejpam-3341	157	2	only	only	ADV
ejpam-3341	157	3	if	if	SCONJ
ejpam-3341	157	4	s	s	X
ejpam-3341	157	5	/∈	/∈	INTJ
ejpam-3341	157	6	(	(	PUNCT
ejpam-3341	157	7	si	si	X
ejpam-3341	157	8	]	]	X
ejpam-3341	157	9	for	for	ADP
ejpam-3341	157	10	every	every	DET
ejpam-3341	157	11	s	s	PROPN
ejpam-3341	157	12	∈	∈	PROPN
ejpam-3341	157	13	s\a	s\a	NOUN
ejpam-3341	157	14	.	.	PUNCT
ejpam-3341	158	1	again	again	ADV
ejpam-3341	158	2	in	in	ADP
ejpam-3341	158	3	property	property	NOUN
ejpam-3341	158	4	(	(	PUNCT
ejpam-3341	158	5	1	1	X
ejpam-3341	158	6	)	)	PUNCT
ejpam-3341	158	7	the	the	DET
ejpam-3341	158	8	assumption	assumption	NOUN
ejpam-3341	158	9	“	"	PUNCT
ejpam-3341	158	10	proper	proper	ADJ
ejpam-3341	158	11	”	"	PUNCT
ejpam-3341	158	12	can	can	AUX
ejpam-3341	158	13	be	be	AUX
ejpam-3341	158	14	omitted	omit	VERB
ejpam-3341	158	15	.	.	PUNCT
ejpam-3341	159	1	theorem	theorem	NOUN
ejpam-3341	159	2	2.13	2.13	NUM
ejpam-3341	159	3	generalizes	generalize	VERB
ejpam-3341	159	4	the	the	DET
ejpam-3341	159	5	theorem	theorem	NOUN
ejpam-3341	159	6	2.4	2.4	NUM
ejpam-3341	159	7	in	in	ADP
ejpam-3341	159	8	[	[	X
ejpam-3341	159	9	2	2	NUM
ejpam-3341	159	10	]	]	PUNCT
ejpam-3341	159	11	.	.	PUNCT
ejpam-3341	160	1	it	it	PRON
ejpam-3341	160	2	is	be	AUX
ejpam-3341	160	3	enough	enough	ADJ
ejpam-3341	160	4	to	to	PART
ejpam-3341	160	5	observe	observe	VERB
ejpam-3341	160	6	that	that	SCONJ
ejpam-3341	160	7	if	if	SCONJ
ejpam-3341	160	8	s	s	PROPN
ejpam-3341	160	9	has	have	AUX
ejpam-3341	160	10	a	a	DET
ejpam-3341	160	11	zero	zero	NUM
ejpam-3341	160	12	and	and	CCONJ
ejpam-3341	160	13	a	a	PRON
ejpam-3341	160	14	is	be	AUX
ejpam-3341	160	15	a	a	DET
ejpam-3341	160	16	proper	proper	ADJ
ejpam-3341	160	17	right	right	ADJ
ejpam-3341	160	18	ideal	ideal	NOUN
ejpam-3341	160	19	of	of	ADP
ejpam-3341	160	20	s	s	PROPN
ejpam-3341	160	21	,	,	PUNCT
ejpam-3341	160	22	then	then	ADV
ejpam-3341	160	23	0	0	NUM
ejpam-3341	160	24	∈	∈	NOUN
ejpam-3341	160	25	ha(s	ha(	NOUN
ejpam-3341	160	26	)	)	PUNCT
ejpam-3341	160	27	and	and	CCONJ
ejpam-3341	160	28	so	so	ADV
ejpam-3341	160	29	ha(s	ha(	NOUN
ejpam-3341	160	30	)	)	PUNCT
ejpam-3341	160	31	6=	6=	ADP
ejpam-3341	160	32	∅.	∅.	ADV
ejpam-3341	160	33	we	we	PRON
ejpam-3341	160	34	apply	apply	VERB
ejpam-3341	160	35	the	the	DET
ejpam-3341	160	36	above	above	ADJ
ejpam-3341	160	37	results	result	NOUN
ejpam-3341	160	38	to	to	ADP
ejpam-3341	160	39	the	the	DET
ejpam-3341	160	40	following	follow	VERB
ejpam-3341	160	41	examples	example	NOUN
ejpam-3341	160	42	.	.	PUNCT
ejpam-3341	161	1	the	the	DET
ejpam-3341	161	2	first	first	ADJ
ejpam-3341	161	3	two	two	NUM
ejpam-3341	161	4	examples	example	NOUN
ejpam-3341	161	5	are	be	AUX
ejpam-3341	161	6	on	on	ADP
ejpam-3341	161	7	ordered	order	VERB
ejpam-3341	161	8	semigroups	semigroup	NOUN
ejpam-3341	161	9	in	in	ADP
ejpam-3341	161	10	general	general	ADJ
ejpam-3341	161	11	;	;	PUNCT
ejpam-3341	161	12	the	the	DET
ejpam-3341	161	13	third	third	ADJ
ejpam-3341	161	14	one	one	NOUN
ejpam-3341	161	15	is	be	AUX
ejpam-3341	161	16	an	an	DET
ejpam-3341	161	17	example	example	NOUN
ejpam-3341	161	18	of	of	ADP
ejpam-3341	161	19	an	an	DET
ejpam-3341	161	20	ordered	order	VERB
ejpam-3341	161	21	semigroup	semigroup	NOUN
ejpam-3341	161	22	(	(	PUNCT
ejpam-3341	161	23	s	s	PROPN
ejpam-3341	161	24	,	,	PUNCT
ejpam-3341	161	25	·	·	PUNCT
ejpam-3341	161	26	,	,	PUNCT
ejpam-3341	161	27	≤	≤	NUM
ejpam-3341	161	28	)	)	PUNCT
ejpam-3341	161	29	that	that	PRON
ejpam-3341	161	30	contains	contain	VERB
ejpam-3341	161	31	a	a	DET
ejpam-3341	161	32	zero	zero	NUM
ejpam-3341	161	33	.	.	PUNCT
ejpam-3341	161	34	example	example	NOUN
ejpam-3341	161	35	2.14	2.14	NUM
ejpam-3341	161	36	.	.	PUNCT
ejpam-3341	162	1	we	we	PRON
ejpam-3341	162	2	consider	consider	VERB
ejpam-3341	162	3	the	the	DET
ejpam-3341	162	4	ordered	order	VERB
ejpam-3341	162	5	semigroup	semigroup	NOUN
ejpam-3341	162	6	s	s	PART
ejpam-3341	162	7	=	=	PUNCT
ejpam-3341	162	8	{	{	PUNCT
ejpam-3341	162	9	a	a	PRON
ejpam-3341	162	10	,	,	PUNCT
ejpam-3341	162	11	b	b	NOUN
ejpam-3341	162	12	,	,	PUNCT
ejpam-3341	162	13	c	c	NOUN
ejpam-3341	162	14	,	,	PUNCT
ejpam-3341	162	15	d	d	NOUN
ejpam-3341	162	16	,	,	PUNCT
ejpam-3341	162	17	e	e	NOUN
ejpam-3341	162	18	,	,	PUNCT
ejpam-3341	162	19	f	f	X
ejpam-3341	162	20	}	}	PUNCT
ejpam-3341	162	21	defined	define	VERB
ejpam-3341	162	22	by	by	ADP
ejpam-3341	162	23	table	table	NOUN
ejpam-3341	162	24	3	3	NUM
ejpam-3341	162	25	and	and	CCONJ
ejpam-3341	162	26	figure	figure	VERB
ejpam-3341	162	27	3	3	NUM
ejpam-3341	162	28	.	.	PUNCT
ejpam-3341	162	29	·	·	PUNCT
ejpam-3341	163	1	a	a	DET
ejpam-3341	163	2	b	b	X
ejpam-3341	163	3	c	c	NOUN
ejpam-3341	163	4	d	d	X
ejpam-3341	163	5	e	e	X
ejpam-3341	163	6	f	f	PROPN
ejpam-3341	163	7	a	a	PRON
ejpam-3341	163	8	a	a	DET
ejpam-3341	163	9	b	b	PROPN
ejpam-3341	163	10	b	b	PROPN
ejpam-3341	163	11	b	b	PROPN
ejpam-3341	163	12	e	e	X
ejpam-3341	163	13	f	f	PROPN
ejpam-3341	163	14	b	b	PROPN
ejpam-3341	163	15	a	a	DET
ejpam-3341	163	16	b	b	PROPN
ejpam-3341	163	17	b	b	PROPN
ejpam-3341	163	18	b	b	PROPN
ejpam-3341	163	19	e	e	X
ejpam-3341	163	20	f	f	PROPN
ejpam-3341	163	21	c	c	PROPN
ejpam-3341	163	22	a	a	DET
ejpam-3341	163	23	b	b	PROPN
ejpam-3341	163	24	b	b	PROPN
ejpam-3341	163	25	c	c	NOUN
ejpam-3341	163	26	e	e	NOUN
ejpam-3341	163	27	f	f	PROPN
ejpam-3341	163	28	d	d	PROPN
ejpam-3341	163	29	a	a	PRON
ejpam-3341	163	30	b	b	PROPN
ejpam-3341	163	31	b	b	PROPN
ejpam-3341	163	32	d	d	X
ejpam-3341	163	33	e	e	X
ejpam-3341	163	34	f	f	PROPN
ejpam-3341	163	35	e	e	X
ejpam-3341	163	36	e	e	X
ejpam-3341	163	37	e	e	X
ejpam-3341	163	38	e	e	X
ejpam-3341	163	39	e	e	X
ejpam-3341	163	40	e	e	X
ejpam-3341	163	41	f	f	PROPN
ejpam-3341	163	42	f	f	PROPN
ejpam-3341	164	1	f	f	PROPN
ejpam-3341	164	2	f	f	PROPN
ejpam-3341	164	3	f	f	PROPN
ejpam-3341	164	4	f	f	PROPN
ejpam-3341	164	5	f	f	PROPN
ejpam-3341	164	6	f	f	PROPN
ejpam-3341	164	7	table	table	NOUN
ejpam-3341	164	8	3	3	NUM
ejpam-3341	164	9	.	.	PUNCT
ejpam-3341	165	1	a	a	DET
ejpam-3341	165	2	b	b	NOUN
ejpam-3341	165	3	e	e	NOUN
ejpam-3341	165	4	c	c	NOUN
ejpam-3341	165	5	d	d	X
ejpam-3341	165	6	f	f	PROPN
ejpam-3341	165	7	figure	figure	NOUN
ejpam-3341	165	8	3	3	NUM
ejpam-3341	165	9	.	.	PUNCT
ejpam-3341	166	1	for	for	ADP
ejpam-3341	166	2	the	the	DET
ejpam-3341	166	3	subset	subset	NOUN
ejpam-3341	166	4	a	a	X
ejpam-3341	166	5	=	=	X
ejpam-3341	166	6	{	{	PUNCT
ejpam-3341	166	7	c	c	NOUN
ejpam-3341	166	8	,	,	PUNCT
ejpam-3341	166	9	d	d	NOUN
ejpam-3341	166	10	,	,	PUNCT
ejpam-3341	166	11	e	e	NOUN
ejpam-3341	166	12	}	}	PUNCT
ejpam-3341	166	13	of	of	ADP
ejpam-3341	166	14	s	s	PROPN
ejpam-3341	166	15	,	,	PUNCT
ejpam-3341	166	16	we	we	PRON
ejpam-3341	166	17	have	have	VERB
ejpam-3341	166	18	ha(s	ha(	NOUN
ejpam-3341	166	19	)	)	PUNCT
ejpam-3341	167	1	=	=	PUNCT
ejpam-3341	167	2	∅.	∅.	ADP
ejpam-3341	167	3	the	the	DET
ejpam-3341	167	4	sets	set	NOUN
ejpam-3341	167	5	{	{	PUNCT
ejpam-3341	167	6	f	f	NOUN
ejpam-3341	167	7	}	}	PUNCT
ejpam-3341	167	8	and	and	CCONJ
ejpam-3341	167	9	{	{	PUNCT
ejpam-3341	167	10	e	e	NOUN
ejpam-3341	167	11	,	,	PUNCT
ejpam-3341	167	12	f	f	X
ejpam-3341	167	13	}	}	PUNCT
ejpam-3341	167	14	are	be	AUX
ejpam-3341	167	15	proper	proper	ADJ
ejpam-3341	167	16	subsets	subset	NOUN
ejpam-3341	167	17	of	of	ADP
ejpam-3341	167	18	s	s	PROPN
ejpam-3341	167	19	,	,	PUNCT
ejpam-3341	167	20	so	so	SCONJ
ejpam-3341	167	21	the	the	DET
ejpam-3341	167	22	sets	set	NOUN
ejpam-3341	167	23	h{f}(s	h{f}(s	PRON
ejpam-3341	167	24	)	)	PUNCT
ejpam-3341	167	25	and	and	CCONJ
ejpam-3341	167	26	h{e	h{e	NOUN
ejpam-3341	167	27	,	,	PUNCT
ejpam-3341	167	28	f}(s	f}(s	PROPN
ejpam-3341	167	29	)	)	PUNCT
ejpam-3341	167	30	are	be	AUX
ejpam-3341	167	31	defined	define	VERB
ejpam-3341	167	32	and	and	CCONJ
ejpam-3341	167	33	,	,	PUNCT
ejpam-3341	167	34	by	by	ADP
ejpam-3341	167	35	proposition	proposition	NOUN
ejpam-3341	167	36	2.2	2.2	NUM
ejpam-3341	167	37	,	,	PUNCT
ejpam-3341	167	38	they	they	PRON
ejpam-3341	167	39	are	be	AUX
ejpam-3341	167	40	semiprime	semiprime	NOUN
ejpam-3341	167	41	subsets	subset	NOUN
ejpam-3341	167	42	of	of	ADP
ejpam-3341	167	43	s.	s.	PROPN
ejpam-3341	167	44	independently	independently	ADV
ejpam-3341	167	45	,	,	PUNCT
ejpam-3341	167	46	let	let	VERB
ejpam-3341	167	47	us	we	PRON
ejpam-3341	167	48	prove	prove	VERB
ejpam-3341	167	49	that	that	SCONJ
ejpam-3341	167	50	h{e	h{e	NOUN
ejpam-3341	167	51	,	,	PUNCT
ejpam-3341	167	52	f}(s	f}(s	PROPN
ejpam-3341	167	53	)	)	PUNCT
ejpam-3341	167	54	is	be	AUX
ejpam-3341	167	55	semiprime	semiprime	NOUN
ejpam-3341	167	56	.	.	PUNCT
ejpam-3341	168	1	we	we	PRON
ejpam-3341	168	2	first	first	ADV
ejpam-3341	168	3	prove	prove	VERB
ejpam-3341	168	4	that	that	SCONJ
ejpam-3341	168	5	h{e	h{e	NOUN
ejpam-3341	168	6	,	,	PUNCT
ejpam-3341	168	7	f}(s	f}(s	PROPN
ejpam-3341	168	8	)	)	PUNCT
ejpam-3341	168	9	=	=	PRON
ejpam-3341	168	10	{	{	PUNCT
ejpam-3341	168	11	e	e	NOUN
ejpam-3341	168	12	,	,	PUNCT
ejpam-3341	168	13	f	f	NOUN
ejpam-3341	168	14	}	}	PUNCT
ejpam-3341	168	15	.	.	PUNCT
ejpam-3341	169	1	let	let	VERB
ejpam-3341	169	2	now	now	ADV
ejpam-3341	169	3	i	i	PRON
ejpam-3341	169	4	be	be	VERB
ejpam-3341	169	5	an	an	DET
ejpam-3341	169	6	ideal	ideal	NOUN
ejpam-3341	169	7	of	of	ADP
ejpam-3341	169	8	s	s	PRON
ejpam-3341	169	9	such	such	ADJ
ejpam-3341	169	10	that	that	SCONJ
ejpam-3341	169	11	i2	i2	PROPN
ejpam-3341	169	12	⊆	⊆	NUM
ejpam-3341	169	13	{	{	PUNCT
ejpam-3341	169	14	e	e	NOUN
ejpam-3341	169	15	,	,	PUNCT
ejpam-3341	169	16	f	f	NOUN
ejpam-3341	169	17	}	}	PUNCT
ejpam-3341	169	18	.	.	PUNCT
ejpam-3341	170	1	then	then	ADV
ejpam-3341	170	2	i	i	PRON
ejpam-3341	170	3	⊆	⊆	NUM
ejpam-3341	170	4	{	{	PUNCT
ejpam-3341	170	5	e	e	NOUN
ejpam-3341	170	6	,	,	PUNCT
ejpam-3341	170	7	f	f	NOUN
ejpam-3341	170	8	}	}	PUNCT
ejpam-3341	170	9	.	.	PUNCT
ejpam-3341	171	1	indeed	indeed	ADV
ejpam-3341	171	2	:	:	PUNCT
ejpam-3341	172	1	if	if	SCONJ
ejpam-3341	172	2	x	x	SYM
ejpam-3341	172	3	∈	∈	PROPN
ejpam-3341	172	4	i	i	PRON
ejpam-3341	172	5	,	,	PUNCT
ejpam-3341	172	6	then	then	ADV
ejpam-3341	172	7	x2	x2	PROPN
ejpam-3341	172	8	∈	∈	PROPN
ejpam-3341	172	9	i2	i2	PROPN
ejpam-3341	172	10	⊆	⊆	NUM
ejpam-3341	172	11	{	{	PUNCT
ejpam-3341	172	12	e	e	NOUN
ejpam-3341	172	13	,	,	PUNCT
ejpam-3341	172	14	f	f	PROPN
ejpam-3341	172	15	}	}	PUNCT
ejpam-3341	172	16	,	,	PUNCT
ejpam-3341	172	17	so	so	CCONJ
ejpam-3341	172	18	x2	x2	NOUN
ejpam-3341	172	19	=	=	PUNCT
ejpam-3341	172	20	e	e	PROPN
ejpam-3341	172	21	or	or	CCONJ
ejpam-3341	172	22	x2	x2	NOUN
ejpam-3341	172	23	=	=	SYM
ejpam-3341	172	24	f	f	PROPN
ejpam-3341	172	25	.	.	PUNCT
ejpam-3341	173	1	if	if	SCONJ
ejpam-3341	173	2	x2	x2	PRON
ejpam-3341	173	3	=	=	SYM
ejpam-3341	173	4	e	e	X
ejpam-3341	173	5	then	then	ADV
ejpam-3341	173	6	,	,	PUNCT
ejpam-3341	173	7	by	by	ADP
ejpam-3341	173	8	table	table	NOUN
ejpam-3341	173	9	3	3	NUM
ejpam-3341	173	10	,	,	PUNCT
ejpam-3341	173	11	we	we	PRON
ejpam-3341	173	12	have	have	VERB
ejpam-3341	173	13	x	x	X
ejpam-3341	173	14	=	=	SYM
ejpam-3341	173	15	e	e	NOUN
ejpam-3341	173	16	and	and	CCONJ
ejpam-3341	173	17	so	so	ADV
ejpam-3341	173	18	x	x	SYM
ejpam-3341	173	19	∈	∈	PROPN
ejpam-3341	173	20	{	{	PUNCT
ejpam-3341	173	21	e	e	NOUN
ejpam-3341	173	22	,	,	PUNCT
ejpam-3341	173	23	f	f	NOUN
ejpam-3341	173	24	}	}	PUNCT
ejpam-3341	173	25	.	.	PUNCT
ejpam-3341	174	1	n.	n.	PROPN
ejpam-3341	174	2	kehayopulu	kehayopulu	PROPN
ejpam-3341	174	3	/	/	SYM
ejpam-3341	174	4	eur	eur	PROPN
ejpam-3341	174	5	.	.	PUNCT
ejpam-3341	175	1	j.	j.	PROPN
ejpam-3341	175	2	pure	pure	PROPN
ejpam-3341	175	3	appl	appl	PROPN
ejpam-3341	175	4	.	.	PROPN
ejpam-3341	175	5	math	math	PROPN
ejpam-3341	175	6	,	,	PUNCT
ejpam-3341	175	7	11	11	NUM
ejpam-3341	175	8	(	(	PUNCT
ejpam-3341	175	9	4	4	NUM
ejpam-3341	175	10	)	)	PUNCT
ejpam-3341	175	11	(	(	PUNCT
ejpam-3341	175	12	2018	2018	NUM
ejpam-3341	175	13	)	)	PUNCT
ejpam-3341	175	14	,	,	PUNCT
ejpam-3341	175	15	911	911	NUM
ejpam-3341	175	16	-	-	SYM
ejpam-3341	175	17	921	921	NUM
ejpam-3341	175	18	917	917	NUM
ejpam-3341	176	1	if	if	SCONJ
ejpam-3341	176	2	x2	x2	PROPN
ejpam-3341	176	3	=	=	SYM
ejpam-3341	176	4	f	f	PROPN
ejpam-3341	176	5	,	,	PUNCT
ejpam-3341	176	6	then	then	ADV
ejpam-3341	176	7	x	x	X
ejpam-3341	176	8	=	=	SYM
ejpam-3341	176	9	f	f	PROPN
ejpam-3341	176	10	and	and	CCONJ
ejpam-3341	176	11	again	again	ADV
ejpam-3341	176	12	x	x	X
ejpam-3341	176	13	∈	∈	NOUN
ejpam-3341	176	14	{	{	PUNCT
ejpam-3341	176	15	e	e	NOUN
ejpam-3341	176	16	,	,	PUNCT
ejpam-3341	176	17	f	f	NOUN
ejpam-3341	176	18	}	}	PUNCT
ejpam-3341	176	19	.	.	PUNCT
ejpam-3341	177	1	independently	independently	ADV
ejpam-3341	177	2	,	,	PUNCT
ejpam-3341	177	3	the	the	DET
ejpam-3341	177	4	set	set	NOUN
ejpam-3341	177	5	h{f}(s	h{f}(s	NOUN
ejpam-3341	177	6	)	)	PUNCT
ejpam-3341	177	7	is	be	AUX
ejpam-3341	177	8	also	also	ADV
ejpam-3341	177	9	a	a	DET
ejpam-3341	177	10	semiprime	semiprime	NOUN
ejpam-3341	177	11	subset	subset	NOUN
ejpam-3341	177	12	of	of	ADP
ejpam-3341	177	13	s.	s.	PROPN
ejpam-3341	177	14	indeed	indeed	ADV
ejpam-3341	177	15	,	,	PUNCT
ejpam-3341	177	16	we	we	PRON
ejpam-3341	177	17	have	have	VERB
ejpam-3341	177	18	h{f}(s	h{f}(s	PRON
ejpam-3341	177	19	)	)	PUNCT
ejpam-3341	177	20	=	=	PRON
ejpam-3341	178	1	{	{	PUNCT
ejpam-3341	178	2	f	f	NOUN
ejpam-3341	178	3	}	}	PUNCT
ejpam-3341	178	4	;	;	PUNCT
ejpam-3341	178	5	and	and	CCONJ
ejpam-3341	178	6	if	if	SCONJ
ejpam-3341	178	7	i	i	PRON
ejpam-3341	178	8	is	be	AUX
ejpam-3341	178	9	an	an	DET
ejpam-3341	178	10	ideal	ideal	NOUN
ejpam-3341	178	11	of	of	ADP
ejpam-3341	178	12	s	s	PRON
ejpam-3341	178	13	such	such	ADJ
ejpam-3341	178	14	that	that	SCONJ
ejpam-3341	178	15	i2	i2	PROPN
ejpam-3341	178	16	⊆	⊆	NUM
ejpam-3341	178	17	{	{	PUNCT
ejpam-3341	178	18	f	f	NOUN
ejpam-3341	178	19	}	}	PUNCT
ejpam-3341	178	20	and	and	CCONJ
ejpam-3341	178	21	x	x	PUNCT
ejpam-3341	178	22	∈	∈	PROPN
ejpam-3341	179	1	i	i	PRON
ejpam-3341	179	2	,	,	PUNCT
ejpam-3341	179	3	then	then	ADV
ejpam-3341	179	4	x2	x2	PROPN
ejpam-3341	179	5	=	=	SYM
ejpam-3341	179	6	f	f	PROPN
ejpam-3341	179	7	and	and	CCONJ
ejpam-3341	179	8	,	,	PUNCT
ejpam-3341	179	9	by	by	ADP
ejpam-3341	179	10	table	table	NOUN
ejpam-3341	179	11	3	3	NUM
ejpam-3341	179	12	,	,	PUNCT
ejpam-3341	179	13	x	x	PUNCT
ejpam-3341	179	14	=	=	SYM
ejpam-3341	179	15	f	f	X
ejpam-3341	179	16	;	;	PUNCT
ejpam-3341	179	17	so	so	CCONJ
ejpam-3341	179	18	i	i	PRON
ejpam-3341	179	19	⊆	⊆	NUM
ejpam-3341	179	20	{	{	PUNCT
ejpam-3341	179	21	f	f	NOUN
ejpam-3341	179	22	}	}	PUNCT
ejpam-3341	179	23	.	.	PUNCT
ejpam-3341	180	1	the	the	DET
ejpam-3341	180	2	sets	set	NOUN
ejpam-3341	180	3	{	{	PUNCT
ejpam-3341	180	4	f	f	NOUN
ejpam-3341	180	5	}	}	PUNCT
ejpam-3341	180	6	and	and	CCONJ
ejpam-3341	180	7	{	{	PUNCT
ejpam-3341	180	8	e	e	NOUN
ejpam-3341	180	9	,	,	PUNCT
ejpam-3341	180	10	f	f	X
ejpam-3341	180	11	}	}	PUNCT
ejpam-3341	180	12	are	be	AUX
ejpam-3341	180	13	ideals	ideal	NOUN
ejpam-3341	180	14	of	of	ADP
ejpam-3341	180	15	s.	s.	PROPN
ejpam-3341	180	16	we	we	PRON
ejpam-3341	180	17	have	have	AUX
ejpam-3341	180	18	already	already	ADV
ejpam-3341	180	19	seen	see	VERB
ejpam-3341	180	20	that	that	SCONJ
ejpam-3341	180	21	{	{	PUNCT
ejpam-3341	180	22	f	f	X
ejpam-3341	180	23	}	}	PUNCT
ejpam-3341	180	24	⊆	⊆	NUM
ejpam-3341	180	25	h{f}(s	h{f}(s	NOUN
ejpam-3341	180	26	)	)	PUNCT
ejpam-3341	180	27	and	and	CCONJ
ejpam-3341	180	28	{	{	PUNCT
ejpam-3341	180	29	e	e	NOUN
ejpam-3341	180	30	,	,	PUNCT
ejpam-3341	180	31	f	f	NOUN
ejpam-3341	180	32	}	}	PUNCT
ejpam-3341	180	33	⊆	⊆	NUM
ejpam-3341	180	34	h{e	h{e	NOUN
ejpam-3341	180	35	,	,	PUNCT
ejpam-3341	180	36	f	f	PROPN
ejpam-3341	180	37	}	}	PUNCT
ejpam-3341	180	38	;	;	PUNCT
ejpam-3341	180	39	that	that	PRON
ejpam-3341	180	40	is	be	AUX
ejpam-3341	180	41	a	a	DET
ejpam-3341	180	42	consequence	consequence	NOUN
ejpam-3341	180	43	of	of	ADP
ejpam-3341	180	44	proposition	proposition	NOUN
ejpam-3341	180	45	2.3	2.3	NUM
ejpam-3341	180	46	as	as	ADV
ejpam-3341	180	47	well	well	ADV
ejpam-3341	180	48	.	.	PUNCT
ejpam-3341	181	1	since	since	SCONJ
ejpam-3341	181	2	h{f}(s	h{f}(s	PRON
ejpam-3341	181	3	)	)	PUNCT
ejpam-3341	181	4	6=	6=	ADP
ejpam-3341	181	5	∅	∅	NOUN
ejpam-3341	181	6	,	,	PUNCT
ejpam-3341	181	7	by	by	ADP
ejpam-3341	181	8	proposition	proposition	NOUN
ejpam-3341	181	9	2.5	2.5	NUM
ejpam-3341	181	10	,	,	PUNCT
ejpam-3341	181	11	h{f}(s	h{f}(s	PROPN
ejpam-3341	181	12	)	)	PUNCT
ejpam-3341	181	13	is	be	AUX
ejpam-3341	181	14	a	a	DET
ejpam-3341	181	15	right	right	ADJ
ejpam-3341	181	16	ideal	ideal	NOUN
ejpam-3341	181	17	of	of	ADP
ejpam-3341	181	18	s	s	PROPN
ejpam-3341	181	19	;	;	PUNCT
ejpam-3341	181	20	which	which	PRON
ejpam-3341	181	21	is	be	AUX
ejpam-3341	181	22	true	true	ADJ
ejpam-3341	181	23	.	.	PUNCT
ejpam-3341	182	1	in	in	ADP
ejpam-3341	182	2	a	a	DET
ejpam-3341	182	3	similar	similar	ADJ
ejpam-3341	182	4	way	way	NOUN
ejpam-3341	182	5	all	all	PRON
ejpam-3341	182	6	of	of	ADP
ejpam-3341	182	7	the	the	DET
ejpam-3341	182	8	above	above	ADJ
ejpam-3341	182	9	results	result	NOUN
ejpam-3341	182	10	can	can	AUX
ejpam-3341	182	11	be	be	AUX
ejpam-3341	182	12	applied	apply	VERB
ejpam-3341	182	13	to	to	ADP
ejpam-3341	182	14	this	this	DET
ejpam-3341	182	15	example	example	NOUN
ejpam-3341	182	16	.	.	PUNCT
ejpam-3341	183	1	example	example	NOUN
ejpam-3341	183	2	2.15	2.15	NUM
ejpam-3341	183	3	.	.	PUNCT
ejpam-3341	184	1	we	we	PRON
ejpam-3341	184	2	consider	consider	VERB
ejpam-3341	184	3	the	the	DET
ejpam-3341	184	4	ordered	order	VERB
ejpam-3341	184	5	semigroup	semigroup	NOUN
ejpam-3341	184	6	s	s	PART
ejpam-3341	184	7	=	=	PUNCT
ejpam-3341	184	8	{	{	PUNCT
ejpam-3341	184	9	a	a	PRON
ejpam-3341	184	10	,	,	PUNCT
ejpam-3341	184	11	b	b	NOUN
ejpam-3341	184	12	,	,	PUNCT
ejpam-3341	184	13	c	c	NOUN
ejpam-3341	184	14	,	,	PUNCT
ejpam-3341	184	15	d	d	NOUN
ejpam-3341	184	16	,	,	PUNCT
ejpam-3341	184	17	e	e	NOUN
ejpam-3341	184	18	,	,	PUNCT
ejpam-3341	184	19	f	f	X
ejpam-3341	184	20	}	}	PUNCT
ejpam-3341	184	21	defined	define	VERB
ejpam-3341	184	22	by	by	ADP
ejpam-3341	184	23	table	table	NOUN
ejpam-3341	184	24	4	4	NUM
ejpam-3341	184	25	and	and	CCONJ
ejpam-3341	184	26	figure	figure	VERB
ejpam-3341	184	27	4	4	NUM
ejpam-3341	184	28	.	.	PUNCT
ejpam-3341	184	29	·	·	PUNCT
ejpam-3341	185	1	a	a	DET
ejpam-3341	185	2	b	b	X
ejpam-3341	185	3	c	c	NOUN
ejpam-3341	185	4	d	d	X
ejpam-3341	185	5	e	e	X
ejpam-3341	185	6	f	f	PROPN
ejpam-3341	185	7	a	a	PRON
ejpam-3341	185	8	a	a	PRON
ejpam-3341	185	9	a	a	DET
ejpam-3341	185	10	a	a	PROPN
ejpam-3341	185	11	d	d	NOUN
ejpam-3341	185	12	a	a	DET
ejpam-3341	185	13	a	a	DET
ejpam-3341	185	14	b	b	NOUN
ejpam-3341	185	15	a	a	DET
ejpam-3341	185	16	b	b	PROPN
ejpam-3341	185	17	b	b	PROPN
ejpam-3341	185	18	d	d	PROPN
ejpam-3341	185	19	b	b	PROPN
ejpam-3341	185	20	b	b	PROPN
ejpam-3341	185	21	c	c	PROPN
ejpam-3341	185	22	a	a	DET
ejpam-3341	185	23	b	b	NOUN
ejpam-3341	185	24	c	c	NOUN
ejpam-3341	185	25	d	d	X
ejpam-3341	185	26	e	e	X
ejpam-3341	185	27	e	e	X
ejpam-3341	185	28	d	d	X
ejpam-3341	185	29	a	a	PRON
ejpam-3341	185	30	a	a	PROPN
ejpam-3341	185	31	d	d	X
ejpam-3341	185	32	d	d	PROPN
ejpam-3341	185	33	d	d	PROPN
ejpam-3341	185	34	d	d	X
ejpam-3341	185	35	e	e	PROPN
ejpam-3341	185	36	a	a	DET
ejpam-3341	185	37	b	b	NOUN
ejpam-3341	185	38	c	c	NOUN
ejpam-3341	185	39	d	d	X
ejpam-3341	185	40	e	e	X
ejpam-3341	185	41	e	e	X
ejpam-3341	185	42	f	f	PROPN
ejpam-3341	185	43	a	a	DET
ejpam-3341	185	44	b	b	X
ejpam-3341	185	45	c	c	NOUN
ejpam-3341	185	46	d	d	X
ejpam-3341	185	47	e	e	X
ejpam-3341	185	48	f	f	PROPN
ejpam-3341	185	49	table	table	NOUN
ejpam-3341	185	50	4	4	NUM
ejpam-3341	185	51	.	.	PUNCT
ejpam-3341	186	1	e	e	X
ejpam-3341	186	2	a	a	X
ejpam-3341	186	3	d	d	X
ejpam-3341	186	4	b	b	PROPN
ejpam-3341	186	5	c	c	X
ejpam-3341	186	6	f	f	PROPN
ejpam-3341	186	7	figure	figure	NOUN
ejpam-3341	186	8	4	4	NUM
ejpam-3341	186	9	.	.	PUNCT
ejpam-3341	187	1	the	the	DET
ejpam-3341	187	2	proper	proper	ADJ
ejpam-3341	187	3	ideals	ideal	NOUN
ejpam-3341	187	4	of	of	ADP
ejpam-3341	187	5	s	s	NOUN
ejpam-3341	187	6	are	be	AUX
ejpam-3341	187	7	the	the	DET
ejpam-3341	187	8	sets	set	NOUN
ejpam-3341	187	9	{	{	PUNCT
ejpam-3341	187	10	a	a	PRON
ejpam-3341	187	11	,	,	PUNCT
ejpam-3341	187	12	d	d	NOUN
ejpam-3341	187	13	}	}	PUNCT
ejpam-3341	187	14	and	and	CCONJ
ejpam-3341	187	15	{	{	PUNCT
ejpam-3341	187	16	a	a	PRON
ejpam-3341	187	17	,	,	PUNCT
ejpam-3341	187	18	b	b	NOUN
ejpam-3341	187	19	,	,	PUNCT
ejpam-3341	187	20	d	d	NOUN
ejpam-3341	187	21	}	}	PUNCT
ejpam-3341	187	22	.	.	PUNCT
ejpam-3341	188	1	moreover	moreover	ADV
ejpam-3341	188	2	we	we	PRON
ejpam-3341	188	3	have	have	VERB
ejpam-3341	188	4	h{a	h{a	NOUN
ejpam-3341	188	5	,	,	PUNCT
ejpam-3341	188	6	d}(s	d}(s	NOUN
ejpam-3341	188	7	)	)	PUNCT
ejpam-3341	188	8	=	=	PRON
ejpam-3341	188	9	{	{	PUNCT
ejpam-3341	188	10	a	a	X
ejpam-3341	188	11	,	,	PUNCT
ejpam-3341	188	12	d	d	NOUN
ejpam-3341	188	13	}	}	PUNCT
ejpam-3341	188	14	and	and	CCONJ
ejpam-3341	188	15	h{a	h{a	NOUN
ejpam-3341	188	16	,	,	PUNCT
ejpam-3341	188	17	b	b	NOUN
ejpam-3341	188	18	,	,	PUNCT
ejpam-3341	188	19	d}(s	d}(s	NOUN
ejpam-3341	188	20	)	)	PUNCT
ejpam-3341	189	1	=	=	PRON
ejpam-3341	189	2	{	{	PUNCT
ejpam-3341	189	3	a	a	PRON
ejpam-3341	189	4	,	,	PUNCT
ejpam-3341	189	5	b	b	NOUN
ejpam-3341	189	6	,	,	PUNCT
ejpam-3341	189	7	d	d	NOUN
ejpam-3341	189	8	}	}	PUNCT
ejpam-3341	189	9	.	.	PUNCT
ejpam-3341	190	1	since	since	SCONJ
ejpam-3341	190	2	{	{	PUNCT
ejpam-3341	190	3	a	a	PRON
ejpam-3341	190	4	,	,	PUNCT
ejpam-3341	190	5	d	d	NOUN
ejpam-3341	190	6	}	}	PUNCT
ejpam-3341	190	7	(	(	PUNCT
ejpam-3341	190	8	resp	resp	NOUN
ejpam-3341	190	9	.	.	PUNCT
ejpam-3341	191	1	{	{	PUNCT
ejpam-3341	191	2	a	a	DET
ejpam-3341	191	3	,	,	PUNCT
ejpam-3341	191	4	b	b	NOUN
ejpam-3341	191	5	,	,	PUNCT
ejpam-3341	191	6	d	d	NOUN
ejpam-3341	191	7	}	}	PUNCT
ejpam-3341	191	8	)	)	PUNCT
ejpam-3341	192	1	is	be	AUX
ejpam-3341	192	2	a	a	DET
ejpam-3341	192	3	right	right	ADJ
ejpam-3341	192	4	ideal	ideal	NOUN
ejpam-3341	192	5	of	of	ADP
ejpam-3341	192	6	s	s	NOUN
ejpam-3341	192	7	and	and	CCONJ
ejpam-3341	192	8	h{a	h{a	NOUN
ejpam-3341	192	9	,	,	PUNCT
ejpam-3341	192	10	d}(s	d}(s	NOUN
ejpam-3341	192	11	)	)	PUNCT
ejpam-3341	192	12	6=	6=	ADP
ejpam-3341	192	13	∅	∅	NOUN
ejpam-3341	192	14	(	(	PUNCT
ejpam-3341	192	15	resp	resp	NOUN
ejpam-3341	192	16	.	.	PUNCT
ejpam-3341	193	1	h{a	h{a	NOUN
ejpam-3341	193	2	,	,	PUNCT
ejpam-3341	193	3	b	b	NOUN
ejpam-3341	193	4	,	,	PUNCT
ejpam-3341	193	5	d}(s	d}(s	PROPN
ejpam-3341	193	6	)	)	PUNCT
ejpam-3341	193	7	6=	6=	ADP
ejpam-3341	193	8	∅	∅	NOUN
ejpam-3341	193	9	)	)	PUNCT
ejpam-3341	193	10	,	,	PUNCT
ejpam-3341	193	11	by	by	ADP
ejpam-3341	193	12	corollary	corollary	ADJ
ejpam-3341	193	13	2.8	2.8	NUM
ejpam-3341	193	14	,	,	PUNCT
ejpam-3341	193	15	the	the	DET
ejpam-3341	193	16	sets	set	NOUN
ejpam-3341	193	17	h{a	h{a	NOUN
ejpam-3341	193	18	,	,	PUNCT
ejpam-3341	193	19	d}(s	d}(s	NOUN
ejpam-3341	193	20	)	)	PUNCT
ejpam-3341	193	21	and	and	CCONJ
ejpam-3341	193	22	h{a	h{a	NOUN
ejpam-3341	193	23	,	,	PUNCT
ejpam-3341	193	24	b	b	NOUN
ejpam-3341	193	25	,	,	PUNCT
ejpam-3341	193	26	d}(s	d}(s	NOUN
ejpam-3341	193	27	)	)	PUNCT
ejpam-3341	193	28	are	be	AUX
ejpam-3341	193	29	semiprime	semiprime	NOUN
ejpam-3341	193	30	ideals	ideal	NOUN
ejpam-3341	193	31	of	of	ADP
ejpam-3341	193	32	s.	s.	PROPN
ejpam-3341	193	33	independently	independently	ADV
ejpam-3341	193	34	we	we	PRON
ejpam-3341	193	35	can	can	AUX
ejpam-3341	193	36	prove	prove	VERB
ejpam-3341	193	37	that	that	SCONJ
ejpam-3341	193	38	the	the	DET
ejpam-3341	193	39	set	set	NOUN
ejpam-3341	193	40	h{a	h{a	NOUN
ejpam-3341	193	41	,	,	PUNCT
ejpam-3341	193	42	d}(s	d}(s	NOUN
ejpam-3341	193	43	)	)	PUNCT
ejpam-3341	193	44	is	be	AUX
ejpam-3341	193	45	a	a	DET
ejpam-3341	193	46	semiprime	semiprime	NOUN
ejpam-3341	193	47	subset	subset	NOUN
ejpam-3341	193	48	(	(	PUNCT
ejpam-3341	193	49	and	and	CCONJ
ejpam-3341	193	50	thus	thus	ADV
ejpam-3341	193	51	a	a	DET
ejpam-3341	193	52	semiprime	semiprime	NOUN
ejpam-3341	193	53	ideal	ideal	NOUN
ejpam-3341	193	54	)	)	PUNCT
ejpam-3341	193	55	of	of	ADP
ejpam-3341	193	56	s	s	PROPN
ejpam-3341	193	57	,	,	PUNCT
ejpam-3341	193	58	by	by	ADP
ejpam-3341	193	59	showing	show	VERB
ejpam-3341	193	60	that	that	SCONJ
ejpam-3341	193	61	the	the	DET
ejpam-3341	193	62	set	set	NOUN
ejpam-3341	193	63	i	i	PRON
ejpam-3341	193	64	=	=	PUNCT
ejpam-3341	193	65	{	{	PUNCT
ejpam-3341	193	66	a	a	PRON
ejpam-3341	193	67	,	,	PUNCT
ejpam-3341	193	68	d	d	X
ejpam-3341	193	69	}	}	PUNCT
ejpam-3341	193	70	is	be	AUX
ejpam-3341	193	71	the	the	DET
ejpam-3341	193	72	only	only	ADJ
ejpam-3341	193	73	ideal	ideal	NOUN
ejpam-3341	193	74	of	of	ADP
ejpam-3341	193	75	s	s	PRON
ejpam-3341	193	76	such	such	ADJ
ejpam-3341	193	77	that	that	DET
ejpam-3341	193	78	i2	i2	PROPN
ejpam-3341	193	79	⊆	⊆	NUM
ejpam-3341	193	80	{	{	PUNCT
ejpam-3341	193	81	a	a	DET
ejpam-3341	193	82	,	,	PUNCT
ejpam-3341	193	83	d	d	NOUN
ejpam-3341	193	84	}	}	PUNCT
ejpam-3341	193	85	or	or	CCONJ
ejpam-3341	193	86	in	in	ADP
ejpam-3341	193	87	the	the	DET
ejpam-3341	193	88	way	way	NOUN
ejpam-3341	193	89	indicated	indicate	VERB
ejpam-3341	193	90	in	in	ADP
ejpam-3341	193	91	example	example	NOUN
ejpam-3341	193	92	2.14	2.14	NUM
ejpam-3341	193	93	.	.	PUNCT
ejpam-3341	194	1	the	the	DET
ejpam-3341	194	2	sets	set	NOUN
ejpam-3341	194	3	{	{	PUNCT
ejpam-3341	194	4	a	a	DET
ejpam-3341	194	5	,	,	PUNCT
ejpam-3341	194	6	b	b	NOUN
ejpam-3341	194	7	,	,	PUNCT
ejpam-3341	194	8	d	d	NOUN
ejpam-3341	194	9	}	}	PUNCT
ejpam-3341	194	10	and	and	CCONJ
ejpam-3341	194	11	{	{	PUNCT
ejpam-3341	194	12	a	a	PRON
ejpam-3341	194	13	,	,	PUNCT
ejpam-3341	194	14	d	d	NOUN
ejpam-3341	194	15	}	}	PUNCT
ejpam-3341	194	16	are	be	AUX
ejpam-3341	194	17	right	right	ADJ
ejpam-3341	194	18	ideals	ideal	NOUN
ejpam-3341	194	19	of	of	ADP
ejpam-3341	194	20	s	s	PRON
ejpam-3341	194	21	and	and	CCONJ
ejpam-3341	194	22	{	{	PUNCT
ejpam-3341	194	23	a	a	PRON
ejpam-3341	194	24	,	,	PUNCT
ejpam-3341	194	25	d	d	NOUN
ejpam-3341	194	26	}	}	PUNCT
ejpam-3341	194	27	⊆	⊆	NUM
ejpam-3341	194	28	h{a	h{a	NOUN
ejpam-3341	194	29	,	,	PUNCT
ejpam-3341	194	30	b	b	NOUN
ejpam-3341	194	31	,	,	PUNCT
ejpam-3341	194	32	d}(s	d}(s	NOUN
ejpam-3341	194	33	)	)	PUNCT
ejpam-3341	194	34	.	.	PUNCT
ejpam-3341	195	1	so	so	ADV
ejpam-3341	195	2	,	,	PUNCT
ejpam-3341	195	3	by	by	ADP
ejpam-3341	195	4	the	the	DET
ejpam-3341	195	5	⇒-part	⇒-part	PROPN
ejpam-3341	195	6	of	of	ADP
ejpam-3341	195	7	corollary	corollary	ADJ
ejpam-3341	195	8	2.12	2.12	NUM
ejpam-3341	195	9	,	,	PUNCT
ejpam-3341	195	10	we	we	PRON
ejpam-3341	195	11	have	have	VERB
ejpam-3341	195	12	s	s	PRON
ejpam-3341	195	13	/∈	/∈	PUNCT
ejpam-3341	195	14	(	(	PUNCT
ejpam-3341	195	15	s{a	s{a	PROPN
ejpam-3341	195	16	,	,	PUNCT
ejpam-3341	195	17	d	d	PROPN
ejpam-3341	195	18	}	}	PUNCT
ejpam-3341	195	19	]	]	PUNCT
ejpam-3341	195	20	for	for	ADP
ejpam-3341	195	21	every	every	DET
ejpam-3341	195	22	s	s	PART
ejpam-3341	195	23	∈	∈	NOUN
ejpam-3341	195	24	s\{a	s\{a	NOUN
ejpam-3341	195	25	,	,	PUNCT
ejpam-3341	195	26	b	b	NOUN
ejpam-3341	195	27	,	,	PUNCT
ejpam-3341	195	28	d	d	NOUN
ejpam-3341	195	29	}	}	PUNCT
ejpam-3341	195	30	.	.	PUNCT
ejpam-3341	196	1	independently	independently	ADV
ejpam-3341	196	2	,	,	PUNCT
ejpam-3341	196	3	if	if	SCONJ
ejpam-3341	196	4	s	s	VERB
ejpam-3341	196	5	∈	∈	NOUN
ejpam-3341	196	6	s\{a	s\{a	NOUN
ejpam-3341	196	7	,	,	PUNCT
ejpam-3341	196	8	b	b	NOUN
ejpam-3341	196	9	,	,	PUNCT
ejpam-3341	196	10	d	d	NOUN
ejpam-3341	196	11	}	}	PUNCT
ejpam-3341	196	12	,	,	PUNCT
ejpam-3341	196	13	then	then	ADV
ejpam-3341	196	14	s	s	VERB
ejpam-3341	196	15	=	=	SYM
ejpam-3341	196	16	c	c	PROPN
ejpam-3341	196	17	or	or	CCONJ
ejpam-3341	196	18	s	s	NOUN
ejpam-3341	196	19	=	=	SYM
ejpam-3341	196	20	e	e	PROPN
ejpam-3341	196	21	or	or	CCONJ
ejpam-3341	196	22	s	s	PROPN
ejpam-3341	196	23	=	=	SYM
ejpam-3341	196	24	f	f	PROPN
ejpam-3341	196	25	;	;	PUNCT
ejpam-3341	196	26	c	c	X
ejpam-3341	196	27	/∈	/∈	PUNCT
ejpam-3341	197	1	(	(	PUNCT
ejpam-3341	197	2	a	a	DET
ejpam-3341	197	3	,	,	PUNCT
ejpam-3341	197	4	d	d	X
ejpam-3341	197	5	]	]	X
ejpam-3341	197	6	=	=	SYM
ejpam-3341	197	7	(	(	PUNCT
ejpam-3341	197	8	c{a	c{a	PROPN
ejpam-3341	197	9	,	,	PUNCT
ejpam-3341	197	10	d	d	NOUN
ejpam-3341	197	11	}	}	PUNCT
ejpam-3341	197	12	]	]	PUNCT
ejpam-3341	197	13	,	,	PUNCT
ejpam-3341	197	14	e	e	X
ejpam-3341	197	15	/∈	/∈	PUNCT
ejpam-3341	198	1	(	(	PUNCT
ejpam-3341	198	2	a	a	DET
ejpam-3341	198	3	,	,	PUNCT
ejpam-3341	198	4	d	d	X
ejpam-3341	198	5	]	]	X
ejpam-3341	198	6	=	=	SYM
ejpam-3341	198	7	(	(	PUNCT
ejpam-3341	198	8	e{a	e{a	NOUN
ejpam-3341	198	9	,	,	PUNCT
ejpam-3341	198	10	d	d	NOUN
ejpam-3341	198	11	}	}	PUNCT
ejpam-3341	198	12	]	]	PUNCT
ejpam-3341	198	13	and	and	CCONJ
ejpam-3341	198	14	f	f	PROPN
ejpam-3341	198	15	/∈	/∈	PUNCT
ejpam-3341	199	1	(	(	PUNCT
ejpam-3341	199	2	a	a	DET
ejpam-3341	199	3	,	,	PUNCT
ejpam-3341	199	4	d	d	X
ejpam-3341	199	5	]	]	X
ejpam-3341	199	6	=	=	X
ejpam-3341	199	7	(	(	PUNCT
ejpam-3341	199	8	f{a	f{a	ADJ
ejpam-3341	199	9	,	,	PUNCT
ejpam-3341	199	10	d	d	NOUN
ejpam-3341	199	11	}	}	PUNCT
ejpam-3341	199	12	]	]	PUNCT
ejpam-3341	199	13	.	.	PUNCT
ejpam-3341	200	1	n.	n.	PROPN
ejpam-3341	200	2	kehayopulu	kehayopulu	PROPN
ejpam-3341	200	3	/	/	SYM
ejpam-3341	200	4	eur	eur	PROPN
ejpam-3341	200	5	.	.	PUNCT
ejpam-3341	201	1	j.	j.	PROPN
ejpam-3341	201	2	pure	pure	PROPN
ejpam-3341	201	3	appl	appl	PROPN
ejpam-3341	201	4	.	.	PROPN
ejpam-3341	201	5	math	math	PROPN
ejpam-3341	201	6	,	,	PUNCT
ejpam-3341	201	7	11	11	NUM
ejpam-3341	201	8	(	(	PUNCT
ejpam-3341	201	9	4	4	NUM
ejpam-3341	201	10	)	)	PUNCT
ejpam-3341	201	11	(	(	PUNCT
ejpam-3341	201	12	2018	2018	NUM
ejpam-3341	201	13	)	)	PUNCT
ejpam-3341	201	14	,	,	PUNCT
ejpam-3341	201	15	911	911	NUM
ejpam-3341	201	16	-	-	SYM
ejpam-3341	201	17	921	921	NUM
ejpam-3341	201	18	918	918	NUM
ejpam-3341	201	19	in	in	ADP
ejpam-3341	201	20	addition	addition	NOUN
ejpam-3341	201	21	,	,	PUNCT
ejpam-3341	201	22	since	since	SCONJ
ejpam-3341	201	23	{	{	PUNCT
ejpam-3341	201	24	a	a	PRON
ejpam-3341	201	25	,	,	PUNCT
ejpam-3341	201	26	b	b	NOUN
ejpam-3341	201	27	,	,	PUNCT
ejpam-3341	201	28	d	d	NOUN
ejpam-3341	201	29	}	}	PUNCT
ejpam-3341	201	30	and	and	CCONJ
ejpam-3341	201	31	{	{	PUNCT
ejpam-3341	201	32	a	a	PRON
ejpam-3341	201	33	,	,	PUNCT
ejpam-3341	201	34	d	d	NOUN
ejpam-3341	201	35	}	}	PUNCT
ejpam-3341	201	36	are	be	AUX
ejpam-3341	201	37	right	right	ADJ
ejpam-3341	201	38	ideals	ideal	NOUN
ejpam-3341	201	39	of	of	ADP
ejpam-3341	201	40	s	s	PRON
ejpam-3341	201	41	and	and	CCONJ
ejpam-3341	201	42	s	s	PART
ejpam-3341	201	43	/∈	/∈	PUNCT
ejpam-3341	201	44	(	(	PUNCT
ejpam-3341	201	45	sa	sa	PROPN
ejpam-3341	201	46	,	,	PUNCT
ejpam-3341	201	47	sd	sd	X
ejpam-3341	201	48	]	]	PUNCT
ejpam-3341	201	49	=	=	SYM
ejpam-3341	201	50	(	(	PUNCT
ejpam-3341	201	51	s{a	s{a	PROPN
ejpam-3341	201	52	,	,	PUNCT
ejpam-3341	201	53	d	d	PROPN
ejpam-3341	201	54	}	}	PUNCT
ejpam-3341	201	55	]	]	PUNCT
ejpam-3341	201	56	for	for	ADP
ejpam-3341	201	57	every	every	DET
ejpam-3341	201	58	s	s	PART
ejpam-3341	201	59	∈	∈	NOUN
ejpam-3341	201	60	s\{a	s\{a	NOUN
ejpam-3341	201	61	,	,	PUNCT
ejpam-3341	201	62	b	b	NOUN
ejpam-3341	201	63	,	,	PUNCT
ejpam-3341	201	64	d	d	NOUN
ejpam-3341	201	65	}	}	PUNCT
ejpam-3341	201	66	,	,	PUNCT
ejpam-3341	201	67	by	by	ADP
ejpam-3341	201	68	the	the	DET
ejpam-3341	201	69	⇐	⇐	ADJ
ejpam-3341	201	70	-part	-part	NOUN
ejpam-3341	201	71	of	of	ADP
ejpam-3341	201	72	corollary	corollary	ADJ
ejpam-3341	201	73	2.12	2.12	NUM
ejpam-3341	201	74	,	,	PUNCT
ejpam-3341	201	75	we	we	PRON
ejpam-3341	201	76	have	have	VERB
ejpam-3341	201	77	{	{	PUNCT
ejpam-3341	201	78	a	a	DET
ejpam-3341	201	79	,	,	PUNCT
ejpam-3341	201	80	d	d	NOUN
ejpam-3341	201	81	}	}	PUNCT
ejpam-3341	201	82	⊆	⊆	NUM
ejpam-3341	201	83	h{a	h{a	NOUN
ejpam-3341	201	84	,	,	PUNCT
ejpam-3341	201	85	b	b	NOUN
ejpam-3341	201	86	,	,	PUNCT
ejpam-3341	201	87	d}(s	d}(s	PROPN
ejpam-3341	201	88	)	)	PUNCT
ejpam-3341	201	89	;	;	PUNCT
ejpam-3341	201	90	independently	independently	ADV
ejpam-3341	201	91	,	,	PUNCT
ejpam-3341	201	92	we	we	PRON
ejpam-3341	201	93	can	can	AUX
ejpam-3341	201	94	check	check	VERB
ejpam-3341	201	95	that	that	SCONJ
ejpam-3341	201	96	this	this	PRON
ejpam-3341	201	97	is	be	AUX
ejpam-3341	201	98	true	true	ADJ
ejpam-3341	201	99	.	.	PUNCT
ejpam-3341	202	1	all	all	PRON
ejpam-3341	202	2	of	of	ADP
ejpam-3341	202	3	the	the	DET
ejpam-3341	202	4	results	result	NOUN
ejpam-3341	202	5	given	give	VERB
ejpam-3341	202	6	above	above	ADV
ejpam-3341	202	7	in	in	ADP
ejpam-3341	202	8	a	a	DET
ejpam-3341	202	9	similar	similar	ADJ
ejpam-3341	202	10	way	way	NOUN
ejpam-3341	202	11	can	can	AUX
ejpam-3341	202	12	be	be	AUX
ejpam-3341	202	13	applied	apply	VERB
ejpam-3341	202	14	.	.	PUNCT
ejpam-3341	203	1	example	example	NOUN
ejpam-3341	203	2	2.16	2.16	NUM
ejpam-3341	203	3	.	.	PUNCT
ejpam-3341	204	1	we	we	PRON
ejpam-3341	204	2	consider	consider	VERB
ejpam-3341	204	3	the	the	DET
ejpam-3341	204	4	ordered	order	VERB
ejpam-3341	204	5	semigroup	semigroup	NOUN
ejpam-3341	204	6	s	s	PART
ejpam-3341	204	7	=	=	PUNCT
ejpam-3341	204	8	{	{	PUNCT
ejpam-3341	204	9	a	a	PRON
ejpam-3341	204	10	,	,	PUNCT
ejpam-3341	204	11	b	b	NOUN
ejpam-3341	204	12	,	,	PUNCT
ejpam-3341	204	13	c	c	NOUN
ejpam-3341	204	14	,	,	PUNCT
ejpam-3341	204	15	d	d	NOUN
ejpam-3341	204	16	,	,	PUNCT
ejpam-3341	204	17	e	e	NOUN
ejpam-3341	204	18	}	}	PUNCT
ejpam-3341	204	19	defined	define	VERB
ejpam-3341	204	20	by	by	ADP
ejpam-3341	204	21	table	table	NOUN
ejpam-3341	204	22	5	5	NUM
ejpam-3341	204	23	and	and	CCONJ
ejpam-3341	204	24	figure	figure	VERB
ejpam-3341	204	25	5	5	NUM
ejpam-3341	204	26	.	.	PUNCT
ejpam-3341	205	1	this	this	PRON
ejpam-3341	205	2	is	be	AUX
ejpam-3341	205	3	an	an	DET
ejpam-3341	205	4	ordered	order	VERB
ejpam-3341	205	5	semigroup	semigroup	NOUN
ejpam-3341	205	6	with	with	ADP
ejpam-3341	205	7	zero	zero	NUM
ejpam-3341	205	8	;	;	PUNCT
ejpam-3341	205	9	the	the	DET
ejpam-3341	205	10	element	element	NOUN
ejpam-3341	205	11	a	a	PRON
ejpam-3341	205	12	is	be	AUX
ejpam-3341	205	13	the	the	DET
ejpam-3341	205	14	zero	zero	NUM
ejpam-3341	205	15	element	element	NOUN
ejpam-3341	205	16	of	of	ADP
ejpam-3341	205	17	s	s	PRON
ejpam-3341	205	18	;	;	PUNCT
ejpam-3341	205	19	that	that	PRON
ejpam-3341	205	20	is	be	AUX
ejpam-3341	205	21	ax	ax	ADJ
ejpam-3341	205	22	=	=	PUNCT
ejpam-3341	205	23	xa	xa	PROPN
ejpam-3341	205	24	=	=	PUNCT
ejpam-3341	205	25	a	a	PROPN
ejpam-3341	205	26	and	and	CCONJ
ejpam-3341	205	27	a	a	DET
ejpam-3341	205	28	≤	≤	NOUN
ejpam-3341	205	29	x	x	PUNCT
ejpam-3341	205	30	for	for	ADP
ejpam-3341	205	31	every	every	DET
ejpam-3341	205	32	x	x	PROPN
ejpam-3341	205	33	∈	∈	PROPN
ejpam-3341	205	34	s.	s.	PROPN
ejpam-3341	205	35	·	·	PUNCT
ejpam-3341	206	1	a	a	DET
ejpam-3341	206	2	b	b	X
ejpam-3341	206	3	c	c	NOUN
ejpam-3341	206	4	d	d	PROPN
ejpam-3341	206	5	e	e	X
ejpam-3341	206	6	a	a	PRON
ejpam-3341	206	7	a	a	DET
ejpam-3341	206	8	a	a	DET
ejpam-3341	206	9	a	a	DET
ejpam-3341	206	10	a	a	DET
ejpam-3341	206	11	a	a	DET
ejpam-3341	206	12	b	b	NOUN
ejpam-3341	206	13	a	a	DET
ejpam-3341	206	14	a	a	DET
ejpam-3341	206	15	a	a	NOUN
ejpam-3341	206	16	a	a	DET
ejpam-3341	206	17	a	a	PRON
ejpam-3341	206	18	c	c	NOUN
ejpam-3341	206	19	a	a	DET
ejpam-3341	206	20	a	a	DET
ejpam-3341	206	21	c	c	NOUN
ejpam-3341	206	22	c	c	NOUN
ejpam-3341	206	23	a	a	PRON
ejpam-3341	206	24	d	d	NOUN
ejpam-3341	206	25	a	a	DET
ejpam-3341	206	26	a	a	DET
ejpam-3341	206	27	c	c	NOUN
ejpam-3341	206	28	c	c	NOUN
ejpam-3341	206	29	a	a	DET
ejpam-3341	206	30	e	e	NOUN
ejpam-3341	206	31	a	a	PRON
ejpam-3341	206	32	a	a	DET
ejpam-3341	206	33	e	e	NOUN
ejpam-3341	206	34	e	e	X
ejpam-3341	206	35	a	a	DET
ejpam-3341	206	36	table	table	NOUN
ejpam-3341	206	37	5	5	NUM
ejpam-3341	206	38	.	.	PUNCT
ejpam-3341	206	39	a	a	DET
ejpam-3341	206	40	b	b	NOUN
ejpam-3341	206	41	c	c	NOUN
ejpam-3341	206	42	e	e	NOUN
ejpam-3341	206	43	d	d	NOUN
ejpam-3341	206	44	figure	figure	NOUN
ejpam-3341	206	45	5	5	NUM
ejpam-3341	206	46	.	.	PUNCT
ejpam-3341	207	1	the	the	DET
ejpam-3341	207	2	set	set	NOUN
ejpam-3341	207	3	a	a	X
ejpam-3341	207	4	=	=	X
ejpam-3341	207	5	{	{	PUNCT
ejpam-3341	207	6	a	a	PROPN
ejpam-3341	207	7	,	,	PUNCT
ejpam-3341	207	8	b	b	NOUN
ejpam-3341	207	9	,	,	PUNCT
ejpam-3341	207	10	c	c	NOUN
ejpam-3341	207	11	,	,	PUNCT
ejpam-3341	207	12	d	d	X
ejpam-3341	207	13	}	}	PUNCT
ejpam-3341	207	14	is	be	AUX
ejpam-3341	207	15	a	a	DET
ejpam-3341	207	16	right	right	ADJ
ejpam-3341	207	17	ideal	ideal	NOUN
ejpam-3341	207	18	of	of	ADP
ejpam-3341	207	19	s	s	PROPN
ejpam-3341	207	20	,	,	PUNCT
ejpam-3341	207	21	s\a	s\a	PROPN
ejpam-3341	207	22	=	=	SYM
ejpam-3341	207	23	{	{	PUNCT
ejpam-3341	207	24	e	e	NOUN
ejpam-3341	207	25	}	}	PUNCT
ejpam-3341	207	26	and	and	CCONJ
ejpam-3341	207	27	ha(s	ha(	NOUN
ejpam-3341	207	28	)	)	PUNCT
ejpam-3341	208	1	=	=	PRON
ejpam-3341	208	2	{	{	PUNCT
ejpam-3341	208	3	a	a	PRON
ejpam-3341	208	4	,	,	PUNCT
ejpam-3341	208	5	b	b	NOUN
ejpam-3341	208	6	,	,	PUNCT
ejpam-3341	208	7	e	e	NOUN
ejpam-3341	208	8	}	}	PUNCT
ejpam-3341	208	9	.	.	PUNCT
ejpam-3341	209	1	since	since	SCONJ
ejpam-3341	209	2	ha(s	ha(	NOUN
ejpam-3341	209	3	)	)	PUNCT
ejpam-3341	209	4	6=	6=	ADP
ejpam-3341	209	5	∅	∅	NOUN
ejpam-3341	209	6	,	,	PUNCT
ejpam-3341	209	7	by	by	ADP
ejpam-3341	209	8	corollary	corollary	ADJ
ejpam-3341	209	9	2.8	2.8	NUM
ejpam-3341	209	10	,	,	PUNCT
ejpam-3341	209	11	ha(s	ha(s	NUM
ejpam-3341	209	12	)	)	PUNCT
ejpam-3341	209	13	is	be	AUX
ejpam-3341	209	14	a	a	DET
ejpam-3341	209	15	semiprime	semiprime	NOUN
ejpam-3341	209	16	ideal	ideal	NOUN
ejpam-3341	209	17	of	of	ADP
ejpam-3341	209	18	s.	s.	PROPN
ejpam-3341	209	19	independently	independently	ADV
ejpam-3341	209	20	,	,	PUNCT
ejpam-3341	209	21	by	by	ADP
ejpam-3341	209	22	looking	look	VERB
ejpam-3341	209	23	at	at	ADP
ejpam-3341	209	24	table	table	NOUN
ejpam-3341	209	25	5	5	NUM
ejpam-3341	209	26	and	and	CCONJ
ejpam-3341	209	27	figure	figure	VERB
ejpam-3341	209	28	5	5	NUM
ejpam-3341	209	29	we	we	PRON
ejpam-3341	209	30	can	can	AUX
ejpam-3341	209	31	see	see	VERB
ejpam-3341	209	32	that	that	SCONJ
ejpam-3341	209	33	this	this	PRON
ejpam-3341	209	34	is	be	AUX
ejpam-3341	209	35	indeed	indeed	ADV
ejpam-3341	209	36	an	an	DET
ejpam-3341	209	37	ideal	ideal	NOUN
ejpam-3341	209	38	of	of	ADP
ejpam-3341	209	39	s.	s.	PROPN
ejpam-3341	209	40	moreover	moreover	ADV
ejpam-3341	209	41	,	,	PUNCT
ejpam-3341	209	42	it	it	PRON
ejpam-3341	209	43	is	be	AUX
ejpam-3341	209	44	a	a	DET
ejpam-3341	209	45	semiprime	semiprime	NOUN
ejpam-3341	209	46	subset	subset	NOUN
ejpam-3341	209	47	of	of	ADP
ejpam-3341	209	48	s	s	PROPN
ejpam-3341	209	49	(	(	PUNCT
ejpam-3341	209	50	and	and	CCONJ
ejpam-3341	209	51	so	so	ADV
ejpam-3341	209	52	a	a	DET
ejpam-3341	209	53	semiprime	semiprime	NOUN
ejpam-3341	209	54	ideal	ideal	NOUN
ejpam-3341	209	55	of	of	ADP
ejpam-3341	209	56	s	s	PRON
ejpam-3341	209	57	as	as	ADP
ejpam-3341	209	58	corollary	corollary	ADJ
ejpam-3341	209	59	2.8	2.8	NUM
ejpam-3341	209	60	shows	show	NOUN
ejpam-3341	209	61	)	)	PUNCT
ejpam-3341	209	62	.	.	PUNCT
ejpam-3341	210	1	indeed	indeed	ADV
ejpam-3341	210	2	,	,	PUNCT
ejpam-3341	210	3	if	if	SCONJ
ejpam-3341	210	4	i	i	PRON
ejpam-3341	210	5	is	be	AUX
ejpam-3341	210	6	an	an	DET
ejpam-3341	210	7	ideal	ideal	NOUN
ejpam-3341	210	8	of	of	ADP
ejpam-3341	210	9	s	s	PRON
ejpam-3341	210	10	such	such	ADJ
ejpam-3341	210	11	that	that	DET
ejpam-3341	210	12	i2	i2	PROPN
ejpam-3341	210	13	⊆	⊆	NUM
ejpam-3341	210	14	{	{	PUNCT
ejpam-3341	210	15	a	a	PRON
ejpam-3341	210	16	,	,	PUNCT
ejpam-3341	210	17	b	b	NOUN
ejpam-3341	210	18	,	,	PUNCT
ejpam-3341	210	19	e	e	NOUN
ejpam-3341	210	20	}	}	PUNCT
ejpam-3341	210	21	and	and	CCONJ
ejpam-3341	210	22	x	x	PUNCT
ejpam-3341	210	23	∈	∈	PROPN
ejpam-3341	211	1	i	i	PRON
ejpam-3341	211	2	,	,	PUNCT
ejpam-3341	211	3	then	then	ADV
ejpam-3341	211	4	x2	x2	INTJ
ejpam-3341	211	5	=	=	PUNCT
ejpam-3341	211	6	a	a	PRON
ejpam-3341	211	7	or	or	CCONJ
ejpam-3341	211	8	x2	x2	NOUN
ejpam-3341	211	9	=	=	SYM
ejpam-3341	211	10	b	b	PROPN
ejpam-3341	211	11	or	or	CCONJ
ejpam-3341	211	12	x2	x2	PROPN
ejpam-3341	211	13	=	=	PROPN
ejpam-3341	211	14	e.	e.	PROPN
ejpam-3341	211	15	as	as	SCONJ
ejpam-3341	211	16	there	there	PRON
ejpam-3341	211	17	is	be	VERB
ejpam-3341	211	18	no	no	DET
ejpam-3341	211	19	element	element	NOUN
ejpam-3341	211	20	x	x	PUNCT
ejpam-3341	211	21	of	of	ADP
ejpam-3341	211	22	s	s	PRON
ejpam-3341	211	23	such	such	ADJ
ejpam-3341	211	24	that	that	SCONJ
ejpam-3341	211	25	x2	x2	PROPN
ejpam-3341	211	26	=	=	SYM
ejpam-3341	211	27	b	b	PROPN
ejpam-3341	211	28	or	or	CCONJ
ejpam-3341	211	29	x2	x2	NOUN
ejpam-3341	211	30	=	=	SYM
ejpam-3341	211	31	e	e	X
ejpam-3341	211	32	,	,	PUNCT
ejpam-3341	211	33	we	we	PRON
ejpam-3341	211	34	have	have	VERB
ejpam-3341	211	35	x2	x2	NOUN
ejpam-3341	211	36	=	=	PUNCT
ejpam-3341	211	37	a	a	PROPN
ejpam-3341	211	38	and	and	CCONJ
ejpam-3341	211	39	so	so	ADV
ejpam-3341	211	40	x	x	X
ejpam-3341	211	41	=	=	PUNCT
ejpam-3341	211	42	a	a	PRON
ejpam-3341	211	43	or	or	CCONJ
ejpam-3341	211	44	x	x	SYM
ejpam-3341	211	45	=	=	SYM
ejpam-3341	211	46	b	b	PROPN
ejpam-3341	211	47	or	or	CCONJ
ejpam-3341	211	48	x	x	X
ejpam-3341	211	49	=	=	SYM
ejpam-3341	211	50	e	e	NOUN
ejpam-3341	211	51	;	;	PUNCT
ejpam-3341	211	52	that	that	PRON
ejpam-3341	211	53	is	is	ADV
ejpam-3341	211	54	x	x	PART
ejpam-3341	211	55	∈	∈	PROPN
ejpam-3341	211	56	{	{	PUNCT
ejpam-3341	211	57	a	a	PROPN
ejpam-3341	211	58	,	,	PUNCT
ejpam-3341	211	59	b	b	NOUN
ejpam-3341	211	60	,	,	PUNCT
ejpam-3341	211	61	e	e	NOUN
ejpam-3341	211	62	}	}	PUNCT
ejpam-3341	211	63	.	.	PUNCT
ejpam-3341	212	1	thus	thus	ADV
ejpam-3341	212	2	we	we	PRON
ejpam-3341	212	3	have	have	VERB
ejpam-3341	212	4	i	i	PRON
ejpam-3341	212	5	⊆	⊆	NUM
ejpam-3341	212	6	{	{	PUNCT
ejpam-3341	212	7	a	a	PRON
ejpam-3341	212	8	,	,	PUNCT
ejpam-3341	212	9	b	b	NOUN
ejpam-3341	212	10	,	,	PUNCT
ejpam-3341	212	11	e	e	NOUN
ejpam-3341	212	12	}	}	PUNCT
ejpam-3341	212	13	and	and	CCONJ
ejpam-3341	212	14	{	{	PUNCT
ejpam-3341	212	15	a	a	PRON
ejpam-3341	212	16	,	,	PUNCT
ejpam-3341	212	17	b	b	NOUN
ejpam-3341	212	18	,	,	PUNCT
ejpam-3341	212	19	e	e	NOUN
ejpam-3341	212	20	}	}	PUNCT
ejpam-3341	212	21	is	be	AUX
ejpam-3341	212	22	semiprime	semiprime	NOUN
ejpam-3341	212	23	.	.	PUNCT
ejpam-3341	213	1	as	as	SCONJ
ejpam-3341	213	2	one	one	PRON
ejpam-3341	213	3	can	can	AUX
ejpam-3341	213	4	see	see	VERB
ejpam-3341	213	5	,	,	PUNCT
ejpam-3341	213	6	a	a	DET
ejpam-3341	213	7	=	=	X
ejpam-3341	213	8	{	{	PUNCT
ejpam-3341	213	9	a	a	PROPN
ejpam-3341	213	10	,	,	PUNCT
ejpam-3341	213	11	b	b	NOUN
ejpam-3341	213	12	,	,	PUNCT
ejpam-3341	213	13	c	c	X
ejpam-3341	213	14	,	,	PUNCT
ejpam-3341	213	15	e	e	NOUN
ejpam-3341	213	16	}	}	PUNCT
ejpam-3341	213	17	is	be	AUX
ejpam-3341	213	18	an	an	DET
ejpam-3341	213	19	ideal	ideal	NOUN
ejpam-3341	213	20	of	of	ADP
ejpam-3341	213	21	s	s	PRON
ejpam-3341	213	22	and	and	CCONJ
ejpam-3341	213	23	ha(s	ha(	NOUN
ejpam-3341	213	24	)	)	PUNCT
ejpam-3341	214	1	=	=	VERB
ejpam-3341	214	2	s.	s.	PROPN
ejpam-3341	214	3	we	we	PRON
ejpam-3341	214	4	can	can	AUX
ejpam-3341	214	5	check	check	VERB
ejpam-3341	214	6	that	that	DET
ejpam-3341	214	7	h{a	h{a	NOUN
ejpam-3341	214	8	,	,	PUNCT
ejpam-3341	214	9	b	b	NOUN
ejpam-3341	214	10	,	,	PUNCT
ejpam-3341	214	11	e}(s	e}(s	PROPN
ejpam-3341	214	12	)	)	PUNCT
ejpam-3341	214	13	=	=	PRON
ejpam-3341	214	14	{	{	PUNCT
ejpam-3341	214	15	a	a	PRON
ejpam-3341	214	16	,	,	PUNCT
ejpam-3341	214	17	b	b	NOUN
ejpam-3341	214	18	,	,	PUNCT
ejpam-3341	214	19	e	e	NOUN
ejpam-3341	214	20	}	}	PUNCT
ejpam-3341	214	21	.	.	PUNCT
ejpam-3341	215	1	since	since	SCONJ
ejpam-3341	215	2	h{a	h{a	NOUN
ejpam-3341	215	3	,	,	PUNCT
ejpam-3341	215	4	b	b	NOUN
ejpam-3341	215	5	,	,	PUNCT
ejpam-3341	215	6	e}(s	e}(s	PROPN
ejpam-3341	215	7	)	)	PUNCT
ejpam-3341	215	8	is	be	AUX
ejpam-3341	215	9	a	a	DET
ejpam-3341	215	10	left	left	ADJ
ejpam-3341	215	11	ideal	ideal	NOUN
ejpam-3341	215	12	of	of	ADP
ejpam-3341	215	13	s	s	PRON
ejpam-3341	215	14	and	and	CCONJ
ejpam-3341	215	15	{	{	PUNCT
ejpam-3341	215	16	a	a	DET
ejpam-3341	215	17	,	,	PUNCT
ejpam-3341	215	18	b	b	NOUN
ejpam-3341	215	19	}	}	PUNCT
ejpam-3341	215	20	is	be	AUX
ejpam-3341	215	21	a	a	DET
ejpam-3341	215	22	subset	subset	NOUN
ejpam-3341	215	23	of	of	ADP
ejpam-3341	215	24	s	s	PRON
ejpam-3341	215	25	such	such	ADJ
ejpam-3341	215	26	that	that	SCONJ
ejpam-3341	215	27	{	{	PUNCT
ejpam-3341	215	28	a	a	PRON
ejpam-3341	215	29	,	,	PUNCT
ejpam-3341	215	30	b	b	NOUN
ejpam-3341	215	31	}	}	PUNCT
ejpam-3341	215	32	⊆	⊆	NUM
ejpam-3341	215	33	h{a	h{a	NOUN
ejpam-3341	215	34	,	,	PUNCT
ejpam-3341	215	35	b	b	NOUN
ejpam-3341	215	36	,	,	PUNCT
ejpam-3341	215	37	e}(s	e}(s	PROPN
ejpam-3341	215	38	)	)	PUNCT
ejpam-3341	215	39	,	,	PUNCT
ejpam-3341	215	40	by	by	ADP
ejpam-3341	215	41	proposition	proposition	NOUN
ejpam-3341	215	42	2.10	2.10	NUM
ejpam-3341	215	43	,	,	PUNCT
ejpam-3341	215	44	for	for	ADP
ejpam-3341	215	45	every	every	DET
ejpam-3341	215	46	s	s	X
ejpam-3341	215	47	∈	∈	X
ejpam-3341	215	48	s\{a	s\{a	NOUN
ejpam-3341	215	49	,	,	PUNCT
ejpam-3341	215	50	b	b	NOUN
ejpam-3341	215	51	,	,	PUNCT
ejpam-3341	215	52	e	e	NOUN
ejpam-3341	215	53	}	}	PUNCT
ejpam-3341	215	54	,	,	PUNCT
ejpam-3341	215	55	we	we	PRON
ejpam-3341	215	56	have	have	VERB
ejpam-3341	215	57	s	s	PRON
ejpam-3341	215	58	/∈	/∈	PUNCT
ejpam-3341	215	59	(	(	PUNCT
ejpam-3341	215	60	s{a	s{a	PROPN
ejpam-3341	215	61	,	,	PUNCT
ejpam-3341	215	62	b	b	NOUN
ejpam-3341	215	63	}	}	PUNCT
ejpam-3341	215	64	)	)	PUNCT
ejpam-3341	216	1	=	=	SYM
ejpam-3341	216	2	(	(	PUNCT
ejpam-3341	216	3	sa	sa	PROPN
ejpam-3341	216	4	,	,	PUNCT
ejpam-3341	216	5	sb	sb	PROPN
ejpam-3341	216	6	]	]	X
ejpam-3341	216	7	,	,	PUNCT
ejpam-3341	216	8	that	that	PRON
ejpam-3341	216	9	is	be	AUX
ejpam-3341	216	10	c	c	NOUN
ejpam-3341	216	11	/∈	/∈	PUNCT
ejpam-3341	217	1	(	(	PUNCT
ejpam-3341	217	2	ca	ca	NOUN
ejpam-3341	217	3	,	,	PUNCT
ejpam-3341	217	4	cb	cb	PROPN
ejpam-3341	217	5	]	]	X
ejpam-3341	217	6	=	=	X
ejpam-3341	217	7	(	(	PUNCT
ejpam-3341	217	8	a	a	X
ejpam-3341	217	9	]	]	X
ejpam-3341	217	10	and	and	CCONJ
ejpam-3341	217	11	d	d	NOUN
ejpam-3341	217	12	/∈	/∈	PUNCT
ejpam-3341	218	1	(	(	PUNCT
ejpam-3341	218	2	da	da	ADJ
ejpam-3341	218	3	,	,	PUNCT
ejpam-3341	218	4	db	db	X
ejpam-3341	218	5	]	]	X
ejpam-3341	218	6	=	=	X
ejpam-3341	218	7	(	(	PUNCT
ejpam-3341	218	8	a	a	X
ejpam-3341	218	9	]	]	X
ejpam-3341	218	10	;	;	PUNCT
ejpam-3341	218	11	independently	independently	ADV
ejpam-3341	218	12	we	we	PRON
ejpam-3341	218	13	can	can	AUX
ejpam-3341	218	14	check	check	VERB
ejpam-3341	218	15	that	that	SCONJ
ejpam-3341	218	16	this	this	PRON
ejpam-3341	218	17	is	be	AUX
ejpam-3341	218	18	indeed	indeed	ADV
ejpam-3341	218	19	so	so	ADV
ejpam-3341	218	20	as	as	ADP
ejpam-3341	218	21	c	c	PROPN
ejpam-3341	218	22	�	�	PROPN
ejpam-3341	218	23	a	a	PROPN
ejpam-3341	218	24	and	and	CCONJ
ejpam-3341	219	1	d	d	PROPN
ejpam-3341	219	2	�	�	PROPN
ejpam-3341	219	3	b.	b.	PROPN
ejpam-3341	219	4	all	all	DET
ejpam-3341	219	5	the	the	DET
ejpam-3341	219	6	above	above	ADJ
ejpam-3341	219	7	results	result	NOUN
ejpam-3341	219	8	can	can	AUX
ejpam-3341	219	9	be	be	AUX
ejpam-3341	219	10	applied	apply	VERB
ejpam-3341	219	11	to	to	ADP
ejpam-3341	219	12	this	this	DET
ejpam-3341	219	13	example	example	NOUN
ejpam-3341	219	14	.	.	PUNCT
ejpam-3341	220	1	n.	n.	PROPN
ejpam-3341	220	2	kehayopulu	kehayopulu	PROPN
ejpam-3341	220	3	/	/	SYM
ejpam-3341	220	4	eur	eur	PROPN
ejpam-3341	220	5	.	.	PUNCT
ejpam-3341	221	1	j.	j.	PROPN
ejpam-3341	221	2	pure	pure	PROPN
ejpam-3341	221	3	appl	appl	PROPN
ejpam-3341	221	4	.	.	PROPN
ejpam-3341	221	5	math	math	PROPN
ejpam-3341	221	6	,	,	PUNCT
ejpam-3341	221	7	11	11	NUM
ejpam-3341	221	8	(	(	PUNCT
ejpam-3341	221	9	4	4	NUM
ejpam-3341	221	10	)	)	PUNCT
ejpam-3341	221	11	(	(	PUNCT
ejpam-3341	221	12	2018	2018	NUM
ejpam-3341	221	13	)	)	PUNCT
ejpam-3341	221	14	,	,	PUNCT
ejpam-3341	221	15	911	911	NUM
ejpam-3341	221	16	-	-	SYM
ejpam-3341	221	17	921	921	NUM
ejpam-3341	221	18	919	919	NUM
ejpam-3341	221	19	for	for	ADP
ejpam-3341	221	20	a	a	DET
ejpam-3341	221	21	subset	subset	NOUN
ejpam-3341	221	22	a	a	PRON
ejpam-3341	221	23	of	of	ADP
ejpam-3341	221	24	an	an	DET
ejpam-3341	221	25	ordered	order	VERB
ejpam-3341	221	26	semigroup	semigroup	NOUN
ejpam-3341	221	27	(	(	PUNCT
ejpam-3341	221	28	s	s	PROPN
ejpam-3341	221	29	,	,	PUNCT
ejpam-3341	221	30	·	·	PUNCT
ejpam-3341	221	31	,	,	PUNCT
ejpam-3341	221	32	≤	≤	NUM
ejpam-3341	221	33	)	)	PUNCT
ejpam-3341	221	34	,	,	PUNCT
ejpam-3341	221	35	we	we	PRON
ejpam-3341	221	36	denote	denote	VERB
ejpam-3341	221	37	by	by	ADP
ejpam-3341	221	38	pr(a	pr(a	NOUN
ejpam-3341	221	39	)	)	PUNCT
ejpam-3341	221	40	the	the	DET
ejpam-3341	221	41	subset	subset	NOUN
ejpam-3341	221	42	of	of	ADP
ejpam-3341	221	43	s	s	PRON
ejpam-3341	221	44	defined	define	VERB
ejpam-3341	221	45	by	by	ADP
ejpam-3341	221	46	pr(a	pr(a	NOUN
ejpam-3341	221	47	)	)	PUNCT
ejpam-3341	221	48	:	:	PUNCT
ejpam-3341	222	1	=	=	PUNCT
ejpam-3341	222	2	{	{	PUNCT
ejpam-3341	222	3	p	p	X
ejpam-3341	222	4	∈	∈	PROPN
ejpam-3341	222	5	s	s	VERB
ejpam-3341	222	6	|	|	ADV
ejpam-3341	222	7	∃	∃	PROPN
ejpam-3341	222	8	s	s	PART
ejpam-3341	222	9	∈	∈	PROPN
ejpam-3341	222	10	s\a	s\a	NOUN
ejpam-3341	222	11	such	such	ADJ
ejpam-3341	222	12	that	that	PRON
ejpam-3341	222	13	sp	sp	ADP
ejpam-3341	222	14	∈	∈	PROPN
ejpam-3341	222	15	a	a	PRON
ejpam-3341	222	16	}	}	PUNCT
ejpam-3341	222	17	(	(	PUNCT
ejpam-3341	222	18	cf	cf	NOUN
ejpam-3341	222	19	.	.	PUNCT
ejpam-3341	223	1	also	also	ADV
ejpam-3341	223	2	[	[	X
ejpam-3341	223	3	2	2	NUM
ejpam-3341	223	4	]	]	PUNCT
ejpam-3341	223	5	)	)	PUNCT
ejpam-3341	223	6	.	.	PUNCT
ejpam-3341	224	1	clearly	clearly	ADV
ejpam-3341	224	2	pr(a	pr(a	PUNCT
ejpam-3341	224	3	)	)	PUNCT
ejpam-3341	224	4	=	=	SYM
ejpam-3341	224	5	∅	∅	NOUN
ejpam-3341	224	6	or	or	CCONJ
ejpam-3341	224	7	pr(a	pr(a	NUM
ejpam-3341	224	8	)	)	PUNCT
ejpam-3341	225	1	6=	6=	ADP
ejpam-3341	225	2	∅.	∅.	VERB
ejpam-3341	225	3	for	for	ADP
ejpam-3341	225	4	the	the	DET
ejpam-3341	225	5	ordered	order	VERB
ejpam-3341	225	6	semigroup	semigroup	NOUN
ejpam-3341	225	7	s	s	AUX
ejpam-3341	225	8	defined	define	VERB
ejpam-3341	225	9	in	in	ADP
ejpam-3341	225	10	example	example	NOUN
ejpam-3341	225	11	2.1	2.1	NUM
ejpam-3341	225	12	and	and	CCONJ
ejpam-3341	225	13	the	the	DET
ejpam-3341	225	14	subset	subset	NOUN
ejpam-3341	225	15	a	a	X
ejpam-3341	225	16	=	=	X
ejpam-3341	225	17	{	{	PUNCT
ejpam-3341	225	18	c	c	NOUN
ejpam-3341	225	19	}	}	PUNCT
ejpam-3341	225	20	of	of	ADP
ejpam-3341	225	21	s	s	PROPN
ejpam-3341	225	22	,	,	PUNCT
ejpam-3341	225	23	we	we	PRON
ejpam-3341	225	24	have	have	AUX
ejpam-3341	225	25	pr(a	pr(a	VERB
ejpam-3341	225	26	)	)	PUNCT
ejpam-3341	225	27	=	=	PUNCT
ejpam-3341	226	1	∅.	∅.	NOUN
ejpam-3341	226	2	if	if	SCONJ
ejpam-3341	226	3	a	a	PRON
ejpam-3341	226	4	is	be	AUX
ejpam-3341	226	5	a	a	DET
ejpam-3341	226	6	proper	proper	ADJ
ejpam-3341	226	7	left	left	ADJ
ejpam-3341	226	8	ideal	ideal	NOUN
ejpam-3341	226	9	of	of	ADP
ejpam-3341	226	10	(	(	PUNCT
ejpam-3341	226	11	s	s	PROPN
ejpam-3341	226	12	,	,	PUNCT
ejpam-3341	226	13	·	·	PUNCT
ejpam-3341	226	14	)	)	PUNCT
ejpam-3341	226	15	,	,	PUNCT
ejpam-3341	226	16	then	then	ADV
ejpam-3341	226	17	a	a	DET
ejpam-3341	226	18	⊆	⊆	NUM
ejpam-3341	226	19	pr(a	pr(a	NOUN
ejpam-3341	226	20	)	)	PUNCT
ejpam-3341	226	21	,	,	PUNCT
ejpam-3341	226	22	and	and	CCONJ
ejpam-3341	226	23	thus	thus	ADV
ejpam-3341	226	24	pr(a	pr(a	PUNCT
ejpam-3341	226	25	)	)	PUNCT
ejpam-3341	226	26	6=	6=	ADP
ejpam-3341	226	27	∅.	∅.	ADP
ejpam-3341	226	28	indeed	indeed	ADV
ejpam-3341	226	29	:	:	PUNCT
ejpam-3341	226	30	let	let	VERB
ejpam-3341	226	31	p	p	PRON
ejpam-3341	226	32	∈	∈	PROPN
ejpam-3341	226	33	a.	a.	NOUN
ejpam-3341	226	34	take	take	VERB
ejpam-3341	226	35	an	an	DET
ejpam-3341	226	36	element	element	NOUN
ejpam-3341	226	37	s	s	PART
ejpam-3341	226	38	∈	∈	NOUN
ejpam-3341	226	39	s\a	s\a	NOUN
ejpam-3341	226	40	(	(	PUNCT
ejpam-3341	226	41	a	a	PRON
ejpam-3341	226	42	is	be	AUX
ejpam-3341	226	43	proper	proper	ADJ
ejpam-3341	226	44	)	)	PUNCT
ejpam-3341	226	45	.	.	PUNCT
ejpam-3341	227	1	we	we	PRON
ejpam-3341	227	2	have	have	VERB
ejpam-3341	227	3	sp	sp	ADP
ejpam-3341	227	4	∈	∈	PROPN
ejpam-3341	227	5	(	(	PUNCT
ejpam-3341	227	6	s\a)a	s\a)a	NOUN
ejpam-3341	227	7	⊆	⊆	NUM
ejpam-3341	227	8	sa	sa	NOUN
ejpam-3341	227	9	⊆	⊆	NUM
ejpam-3341	227	10	a	a	PRON
ejpam-3341	228	1	and	and	CCONJ
ejpam-3341	228	2	so	so	ADV
ejpam-3341	228	3	sp	sp	ADP
ejpam-3341	228	4	∈	∈	NOUN
ejpam-3341	228	5	a.	a.	NOUN
ejpam-3341	228	6	since	since	SCONJ
ejpam-3341	228	7	p	p	PROPN
ejpam-3341	228	8	∈	∈	PROPN
ejpam-3341	228	9	s	s	NOUN
ejpam-3341	228	10	,	,	PUNCT
ejpam-3341	228	11	s	s	PART
ejpam-3341	228	12	∈	∈	X
ejpam-3341	228	13	s\a	s\a	PROPN
ejpam-3341	228	14	and	and	CCONJ
ejpam-3341	228	15	sp	sp	ADP
ejpam-3341	228	16	∈	∈	PROPN
ejpam-3341	228	17	a	a	X
ejpam-3341	228	18	,	,	PUNCT
ejpam-3341	228	19	we	we	PRON
ejpam-3341	228	20	have	have	VERB
ejpam-3341	228	21	p	p	NOUN
ejpam-3341	228	22	∈	∈	PROPN
ejpam-3341	228	23	pr(a	pr(a	NOUN
ejpam-3341	228	24	)	)	PUNCT
ejpam-3341	228	25	.	.	PUNCT
ejpam-3341	229	1	example	example	NOUN
ejpam-3341	230	1	2.17	2.17	NUM
ejpam-3341	230	2	.	.	PUNCT
ejpam-3341	231	1	let	let	VERB
ejpam-3341	231	2	us	we	PRON
ejpam-3341	231	3	consider	consider	VERB
ejpam-3341	231	4	the	the	DET
ejpam-3341	231	5	ordered	order	VERB
ejpam-3341	231	6	semigroup	semigroup	NOUN
ejpam-3341	231	7	of	of	ADP
ejpam-3341	231	8	the	the	DET
ejpam-3341	231	9	example	example	NOUN
ejpam-3341	231	10	2.14	2.14	NUM
ejpam-3341	231	11	.	.	PUNCT
ejpam-3341	232	1	for	for	ADP
ejpam-3341	232	2	the	the	DET
ejpam-3341	232	3	subset	subset	NOUN
ejpam-3341	232	4	{	{	PUNCT
ejpam-3341	232	5	c	c	NOUN
ejpam-3341	232	6	,	,	PUNCT
ejpam-3341	232	7	e	e	NOUN
ejpam-3341	232	8	}	}	PUNCT
ejpam-3341	232	9	of	of	ADP
ejpam-3341	232	10	s	s	PROPN
ejpam-3341	232	11	,	,	PUNCT
ejpam-3341	232	12	we	we	PRON
ejpam-3341	232	13	have	have	AUX
ejpam-3341	232	14	pr({c	pr({c	NOUN
ejpam-3341	232	15	,	,	PUNCT
ejpam-3341	232	16	e	e	NOUN
ejpam-3341	232	17	}	}	PUNCT
ejpam-3341	232	18	)	)	PUNCT
ejpam-3341	233	1	=	=	PRON
ejpam-3341	233	2	{	{	PUNCT
ejpam-3341	233	3	e	e	NOUN
ejpam-3341	233	4	}	}	PUNCT
ejpam-3341	233	5	.	.	PUNCT
ejpam-3341	234	1	for	for	ADP
ejpam-3341	234	2	the	the	DET
ejpam-3341	234	3	subset	subset	NOUN
ejpam-3341	234	4	{	{	PUNCT
ejpam-3341	234	5	c	c	X
ejpam-3341	234	6	,	,	PUNCT
ejpam-3341	234	7	d	d	NOUN
ejpam-3341	234	8	,	,	PUNCT
ejpam-3341	234	9	e	e	NOUN
ejpam-3341	234	10	}	}	PUNCT
ejpam-3341	234	11	of	of	ADP
ejpam-3341	234	12	s	s	PROPN
ejpam-3341	234	13	,	,	PUNCT
ejpam-3341	234	14	we	we	PRON
ejpam-3341	234	15	also	also	ADV
ejpam-3341	234	16	have	have	AUX
ejpam-3341	234	17	pr({c	pr({c	NOUN
ejpam-3341	234	18	,	,	PUNCT
ejpam-3341	234	19	d	d	NOUN
ejpam-3341	234	20	,	,	PUNCT
ejpam-3341	234	21	e	e	NOUN
ejpam-3341	234	22	}	}	PUNCT
ejpam-3341	234	23	)	)	PUNCT
ejpam-3341	235	1	=	=	PRON
ejpam-3341	235	2	{	{	PUNCT
ejpam-3341	235	3	e	e	NOUN
ejpam-3341	235	4	}	}	PUNCT
ejpam-3341	235	5	.	.	PUNCT
ejpam-3341	236	1	on	on	ADP
ejpam-3341	236	2	the	the	DET
ejpam-3341	236	3	other	other	ADJ
ejpam-3341	236	4	hand	hand	NOUN
ejpam-3341	236	5	,	,	PUNCT
ejpam-3341	236	6	the	the	DET
ejpam-3341	236	7	sets	set	NOUN
ejpam-3341	236	8	{	{	PUNCT
ejpam-3341	236	9	f	f	NOUN
ejpam-3341	236	10	}	}	PUNCT
ejpam-3341	236	11	and	and	CCONJ
ejpam-3341	236	12	{	{	PUNCT
ejpam-3341	236	13	e	e	NOUN
ejpam-3341	236	14	,	,	PUNCT
ejpam-3341	236	15	f	f	X
ejpam-3341	236	16	}	}	PUNCT
ejpam-3341	236	17	are	be	AUX
ejpam-3341	236	18	proper	proper	ADJ
ejpam-3341	236	19	left	left	ADJ
ejpam-3341	236	20	ideals	ideal	NOUN
ejpam-3341	236	21	of	of	ADP
ejpam-3341	236	22	s	s	PROPN
ejpam-3341	236	23	,	,	PUNCT
ejpam-3341	236	24	and	and	CCONJ
ejpam-3341	236	25	we	we	PRON
ejpam-3341	236	26	have	have	VERB
ejpam-3341	236	27	{	{	PUNCT
ejpam-3341	236	28	f	f	X
ejpam-3341	236	29	}	}	PUNCT
ejpam-3341	236	30	=	=	SYM
ejpam-3341	236	31	pr({f	pr({f	NOUN
ejpam-3341	236	32	}	}	PUNCT
ejpam-3341	236	33	)	)	PUNCT
ejpam-3341	236	34	⊆	⊆	NUM
ejpam-3341	236	35	pr({f	pr({f	NOUN
ejpam-3341	236	36	}	}	PUNCT
ejpam-3341	236	37	)	)	PUNCT
ejpam-3341	236	38	and	and	CCONJ
ejpam-3341	236	39	{	{	PUNCT
ejpam-3341	236	40	e	e	NOUN
ejpam-3341	236	41	,	,	PUNCT
ejpam-3341	236	42	f	f	NOUN
ejpam-3341	236	43	}	}	PUNCT
ejpam-3341	236	44	=	=	NOUN
ejpam-3341	236	45	pr({e	pr({e	NOUN
ejpam-3341	236	46	,	,	PUNCT
ejpam-3341	236	47	f	f	NOUN
ejpam-3341	236	48	}	}	PUNCT
ejpam-3341	236	49	)	)	PUNCT
ejpam-3341	236	50	⊆	⊆	NUM
ejpam-3341	236	51	pr({e	pr({e	NOUN
ejpam-3341	236	52	,	,	PUNCT
ejpam-3341	236	53	f	f	NOUN
ejpam-3341	236	54	}	}	PUNCT
ejpam-3341	236	55	)	)	PUNCT
ejpam-3341	236	56	.	.	PUNCT
ejpam-3341	237	1	in	in	ADP
ejpam-3341	237	2	a	a	DET
ejpam-3341	237	3	semigroup	semigroup	NOUN
ejpam-3341	237	4	(	(	PUNCT
ejpam-3341	237	5	s	s	PROPN
ejpam-3341	237	6	,	,	PUNCT
ejpam-3341	237	7	·	·	PUNCT
ejpam-3341	237	8	)	)	PUNCT
ejpam-3341	237	9	containing	contain	VERB
ejpam-3341	237	10	an	an	DET
ejpam-3341	237	11	identity	identity	NOUN
ejpam-3341	237	12	e	e	NOUN
ejpam-3341	237	13	,	,	PUNCT
ejpam-3341	237	14	if	if	SCONJ
ejpam-3341	237	15	a	a	PRON
ejpam-3341	237	16	is	be	AUX
ejpam-3341	237	17	a	a	DET
ejpam-3341	237	18	proper	proper	ADJ
ejpam-3341	237	19	right	right	ADJ
ejpam-3341	237	20	ideal	ideal	NOUN
ejpam-3341	237	21	of	of	ADP
ejpam-3341	237	22	s	s	PROPN
ejpam-3341	237	23	,	,	PUNCT
ejpam-3341	237	24	then	then	ADV
ejpam-3341	237	25	a	a	DET
ejpam-3341	237	26	⊆	⊆	NUM
ejpam-3341	237	27	pr(a	pr(a	NOUN
ejpam-3341	237	28	)	)	PUNCT
ejpam-3341	237	29	.	.	PUNCT
ejpam-3341	238	1	indeed	indeed	ADV
ejpam-3341	238	2	,	,	PUNCT
ejpam-3341	238	3	as	as	SCONJ
ejpam-3341	238	4	a	a	PRON
ejpam-3341	238	5	is	be	AUX
ejpam-3341	238	6	proper	proper	ADJ
ejpam-3341	238	7	,	,	PUNCT
ejpam-3341	238	8	we	we	PRON
ejpam-3341	238	9	have	have	VERB
ejpam-3341	238	10	e	e	NOUN
ejpam-3341	238	11	∈	∈	NOUN
ejpam-3341	238	12	s\a	s\a	NOUN
ejpam-3341	238	13	;	;	PUNCT
ejpam-3341	238	14	and	and	CCONJ
ejpam-3341	238	15	if	if	SCONJ
ejpam-3341	238	16	p	p	PROPN
ejpam-3341	238	17	∈	∈	PROPN
ejpam-3341	238	18	a	a	PRON
ejpam-3341	238	19	,	,	PUNCT
ejpam-3341	238	20	then	then	ADV
ejpam-3341	238	21	ep	ep	PROPN
ejpam-3341	238	22	=	=	PUNCT
ejpam-3341	238	23	p	p	X
ejpam-3341	238	24	∈	∈	PROPN
ejpam-3341	238	25	a	a	PRON
ejpam-3341	238	26	,	,	PUNCT
ejpam-3341	238	27	thus	thus	ADV
ejpam-3341	238	28	p	p	PROPN
ejpam-3341	238	29	∈	∈	PROPN
ejpam-3341	238	30	pr(a	pr(a	PUNCT
ejpam-3341	238	31	)	)	PUNCT
ejpam-3341	238	32	(	(	PUNCT
ejpam-3341	238	33	see	see	VERB
ejpam-3341	238	34	also	also	ADV
ejpam-3341	238	35	[	[	X
ejpam-3341	238	36	2	2	NUM
ejpam-3341	238	37	]	]	PUNCT
ejpam-3341	238	38	)	)	PUNCT
ejpam-3341	238	39	.	.	PUNCT
ejpam-3341	239	1	according	accord	VERB
ejpam-3341	239	2	to	to	ADP
ejpam-3341	239	3	[	[	X
ejpam-3341	239	4	2	2	NUM
ejpam-3341	239	5	;	;	PUNCT
ejpam-3341	239	6	proposition	proposition	NOUN
ejpam-3341	239	7	2.5	2.5	NUM
ejpam-3341	239	8	]	]	PUNCT
ejpam-3341	239	9	,	,	PUNCT
ejpam-3341	239	10	if	if	SCONJ
ejpam-3341	239	11	(	(	PUNCT
ejpam-3341	239	12	s	s	X
ejpam-3341	239	13	,	,	PUNCT
ejpam-3341	239	14	·	·	PUNCT
ejpam-3341	239	15	,	,	PUNCT
ejpam-3341	239	16	≤	≤	NUM
ejpam-3341	239	17	)	)	PUNCT
ejpam-3341	239	18	is	be	AUX
ejpam-3341	239	19	an	an	DET
ejpam-3341	239	20	ordered	order	VERB
ejpam-3341	239	21	semigroup	semigroup	NOUN
ejpam-3341	239	22	,	,	PUNCT
ejpam-3341	239	23	e	e	X
ejpam-3341	239	24	an	an	DET
ejpam-3341	239	25	identity	identity	NOUN
ejpam-3341	239	26	of	of	ADP
ejpam-3341	239	27	(	(	PUNCT
ejpam-3341	239	28	s	s	X
ejpam-3341	239	29	,	,	PUNCT
ejpam-3341	239	30	·	·	PUNCT
ejpam-3341	239	31	)	)	PUNCT
ejpam-3341	239	32	and	and	CCONJ
ejpam-3341	239	33	a	a	DET
ejpam-3341	239	34	a	a	DET
ejpam-3341	239	35	proper	proper	ADJ
ejpam-3341	239	36	right	right	ADJ
ejpam-3341	239	37	ideal	ideal	NOUN
ejpam-3341	239	38	of	of	ADP
ejpam-3341	239	39	(	(	PUNCT
ejpam-3341	239	40	s	s	PROPN
ejpam-3341	239	41	,	,	PUNCT
ejpam-3341	239	42	·	·	PUNCT
ejpam-3341	239	43	,	,	PUNCT
ejpam-3341	239	44	≤	≤	NUM
ejpam-3341	239	45	)	)	PUNCT
ejpam-3341	239	46	,	,	PUNCT
ejpam-3341	239	47	then	then	ADV
ejpam-3341	239	48	the	the	DET
ejpam-3341	239	49	set	set	NOUN
ejpam-3341	239	50	pr(a	pr(a	PUNCT
ejpam-3341	239	51	)	)	PUNCT
ejpam-3341	239	52	is	be	AUX
ejpam-3341	239	53	a	a	DET
ejpam-3341	239	54	completely	completely	ADV
ejpam-3341	239	55	prime	prime	ADJ
ejpam-3341	239	56	right	right	ADJ
ejpam-3341	239	57	ideal	ideal	NOUN
ejpam-3341	239	58	of	of	ADP
ejpam-3341	239	59	s	s	PRON
ejpam-3341	239	60	and	and	CCONJ
ejpam-3341	239	61	a	a	DET
ejpam-3341	239	62	⊆	⊆	NUM
ejpam-3341	239	63	pr(a	pr(a	NOUN
ejpam-3341	239	64	)	)	PUNCT
ejpam-3341	239	65	.	.	PUNCT
ejpam-3341	240	1	the	the	DET
ejpam-3341	240	2	first	first	ADJ
ejpam-3341	240	3	part	part	NOUN
ejpam-3341	240	4	of	of	ADP
ejpam-3341	240	5	this	this	DET
ejpam-3341	240	6	proposition	proposition	NOUN
ejpam-3341	240	7	can	can	AUX
ejpam-3341	240	8	be	be	AUX
ejpam-3341	240	9	also	also	ADV
ejpam-3341	240	10	obtained	obtain	VERB
ejpam-3341	240	11	as	as	ADP
ejpam-3341	240	12	a	a	DET
ejpam-3341	240	13	corollary	corollary	NOUN
ejpam-3341	240	14	to	to	ADP
ejpam-3341	240	15	the	the	DET
ejpam-3341	240	16	following	follow	VERB
ejpam-3341	240	17	proposition	proposition	NOUN
ejpam-3341	240	18	.	.	PUNCT
ejpam-3341	241	1	proposition	proposition	NOUN
ejpam-3341	241	2	2.18	2.18	NUM
ejpam-3341	241	3	.	.	PUNCT
ejpam-3341	242	1	let	let	VERB
ejpam-3341	242	2	a	a	DET
ejpam-3341	242	3	be	be	AUX
ejpam-3341	242	4	a	a	DET
ejpam-3341	242	5	proper	proper	ADJ
ejpam-3341	242	6	right	right	NOUN
ejpam-3341	242	7	of	of	ADP
ejpam-3341	242	8	an	an	DET
ejpam-3341	242	9	ordered	order	VERB
ejpam-3341	242	10	semigroup	semigroup	PROPN
ejpam-3341	242	11	s.	s.	PROPN
ejpam-3341	242	12	if	if	SCONJ
ejpam-3341	242	13	pr(a	pr(a	VERB
ejpam-3341	242	14	)	)	PUNCT
ejpam-3341	242	15	is	be	AUX
ejpam-3341	242	16	nonempty	nonempty	ADJ
ejpam-3341	242	17	,	,	PUNCT
ejpam-3341	242	18	then	then	ADV
ejpam-3341	242	19	it	it	PRON
ejpam-3341	242	20	is	be	AUX
ejpam-3341	242	21	a	a	DET
ejpam-3341	242	22	completely	completely	ADV
ejpam-3341	242	23	prime	prime	ADJ
ejpam-3341	242	24	right	right	ADJ
ejpam-3341	242	25	ideal	ideal	NOUN
ejpam-3341	242	26	of	of	ADP
ejpam-3341	242	27	s.	s.	PROPN
ejpam-3341	242	28	in	in	ADP
ejpam-3341	242	29	contrast	contrast	NOUN
ejpam-3341	242	30	to	to	ADP
ejpam-3341	242	31	semigroups	semigroups	X
ejpam-3341	242	32	containing	contain	VERB
ejpam-3341	242	33	identity	identity	NOUN
ejpam-3341	242	34	,	,	PUNCT
ejpam-3341	242	35	if	if	SCONJ
ejpam-3341	242	36	s	s	NOUN
ejpam-3341	242	37	is	be	AUX
ejpam-3341	242	38	an	an	DET
ejpam-3341	242	39	ordered	order	VERB
ejpam-3341	242	40	semigroup	semigroup	NOUN
ejpam-3341	242	41	and	and	CCONJ
ejpam-3341	242	42	a	a	PRON
ejpam-3341	242	43	is	be	AUX
ejpam-3341	242	44	a	a	DET
ejpam-3341	242	45	proper	proper	ADJ
ejpam-3341	242	46	right	right	ADJ
ejpam-3341	242	47	ideal	ideal	NOUN
ejpam-3341	242	48	of	of	ADP
ejpam-3341	242	49	s	s	PROPN
ejpam-3341	242	50	,	,	PUNCT
ejpam-3341	242	51	then	then	ADV
ejpam-3341	242	52	the	the	DET
ejpam-3341	242	53	property	property	NOUN
ejpam-3341	242	54	a	a	DET
ejpam-3341	242	55	⊆	⊆	NUM
ejpam-3341	242	56	pr(a	pr(a	NOUN
ejpam-3341	242	57	)	)	PUNCT
ejpam-3341	242	58	does	do	AUX
ejpam-3341	242	59	not	not	PART
ejpam-3341	242	60	hold	hold	VERB
ejpam-3341	242	61	in	in	ADP
ejpam-3341	242	62	general	general	ADJ
ejpam-3341	242	63	.	.	PUNCT
ejpam-3341	243	1	let	let	VERB
ejpam-3341	243	2	us	we	PRON
ejpam-3341	243	3	show	show	VERB
ejpam-3341	243	4	it	it	PRON
ejpam-3341	243	5	by	by	ADP
ejpam-3341	243	6	the	the	DET
ejpam-3341	243	7	following	following	ADJ
ejpam-3341	243	8	example	example	NOUN
ejpam-3341	243	9	2.19	2.19	NUM
ejpam-3341	243	10	.	.	PUNCT
ejpam-3341	244	1	consider	consider	VERB
ejpam-3341	244	2	the	the	DET
ejpam-3341	244	3	ordered	order	VERB
ejpam-3341	244	4	semigroup	semigroup	NOUN
ejpam-3341	244	5	of	of	ADP
ejpam-3341	244	6	the	the	DET
ejpam-3341	244	7	example	example	NOUN
ejpam-3341	244	8	2.14	2.14	NUM
ejpam-3341	244	9	.	.	PUNCT
ejpam-3341	245	1	as	as	SCONJ
ejpam-3341	245	2	we	we	PRON
ejpam-3341	245	3	have	have	AUX
ejpam-3341	245	4	already	already	ADV
ejpam-3341	245	5	seen	see	VERB
ejpam-3341	245	6	in	in	ADP
ejpam-3341	245	7	example	example	NOUN
ejpam-3341	245	8	2.17	2.17	NUM
ejpam-3341	245	9	,	,	PUNCT
ejpam-3341	245	10	for	for	ADP
ejpam-3341	245	11	the	the	DET
ejpam-3341	245	12	subset	subset	NOUN
ejpam-3341	246	1	a	a	X
ejpam-3341	246	2	=	=	X
ejpam-3341	246	3	{	{	PUNCT
ejpam-3341	246	4	c	c	NOUN
ejpam-3341	246	5	,	,	PUNCT
ejpam-3341	246	6	d	d	NOUN
ejpam-3341	246	7	,	,	PUNCT
ejpam-3341	246	8	e	e	NOUN
ejpam-3341	246	9	}	}	PUNCT
ejpam-3341	246	10	of	of	ADP
ejpam-3341	246	11	s	s	PROPN
ejpam-3341	246	12	,	,	PUNCT
ejpam-3341	246	13	we	we	PRON
ejpam-3341	246	14	have	have	AUX
ejpam-3341	246	15	pr(a	pr(a	VERB
ejpam-3341	246	16	)	)	PUNCT
ejpam-3341	246	17	=	=	SYM
ejpam-3341	246	18	{	{	PUNCT
ejpam-3341	246	19	e	e	NOUN
ejpam-3341	246	20	}	}	PUNCT
ejpam-3341	246	21	and	and	CCONJ
ejpam-3341	246	22	so	so	ADV
ejpam-3341	246	23	a	a	DET
ejpam-3341	246	24	*	*	PUNCT
ejpam-3341	246	25	pr(a	pr(a	NOUN
ejpam-3341	246	26	)	)	PUNCT
ejpam-3341	246	27	.	.	PUNCT
ejpam-3341	247	1	we	we	PRON
ejpam-3341	247	2	observe	observe	VERB
ejpam-3341	247	3	here	here	ADV
ejpam-3341	247	4	that	that	SCONJ
ejpam-3341	247	5	the	the	DET
ejpam-3341	247	6	set	set	NOUN
ejpam-3341	247	7	{	{	PUNCT
ejpam-3341	247	8	c	c	NOUN
ejpam-3341	247	9	,	,	PUNCT
ejpam-3341	247	10	d	d	NOUN
ejpam-3341	247	11	,	,	PUNCT
ejpam-3341	247	12	e	e	NOUN
ejpam-3341	247	13	}	}	PUNCT
ejpam-3341	247	14	is	be	AUX
ejpam-3341	247	15	not	not	PART
ejpam-3341	247	16	an	an	DET
ejpam-3341	247	17	ideal	ideal	NOUN
ejpam-3341	247	18	of	of	ADP
ejpam-3341	247	19	s.	s.	PROPN
ejpam-3341	247	20	in	in	ADP
ejpam-3341	247	21	this	this	DET
ejpam-3341	247	22	respect	respect	NOUN
ejpam-3341	247	23	,	,	PUNCT
ejpam-3341	247	24	we	we	PRON
ejpam-3341	247	25	have	have	VERB
ejpam-3341	247	26	the	the	DET
ejpam-3341	247	27	following	follow	VERB
ejpam-3341	247	28	proposition	proposition	NOUN
ejpam-3341	247	29	2.20	2.20	NUM
ejpam-3341	247	30	.	.	PUNCT
ejpam-3341	248	1	let	let	VERB
ejpam-3341	248	2	a	a	PRON
ejpam-3341	248	3	be	be	AUX
ejpam-3341	248	4	a	a	DET
ejpam-3341	248	5	proper	proper	ADJ
ejpam-3341	248	6	ideal	ideal	NOUN
ejpam-3341	248	7	of	of	ADP
ejpam-3341	248	8	an	an	DET
ejpam-3341	248	9	ordered	order	VERB
ejpam-3341	248	10	semigroup	semigroup	NOUN
ejpam-3341	248	11	(	(	PUNCT
ejpam-3341	248	12	s	s	PROPN
ejpam-3341	248	13	,	,	PUNCT
ejpam-3341	248	14	·	·	PUNCT
ejpam-3341	248	15	,	,	PUNCT
ejpam-3341	248	16	≤	≤	NUM
ejpam-3341	248	17	)	)	PUNCT
ejpam-3341	248	18	.	.	PUNCT
ejpam-3341	249	1	then	then	ADV
ejpam-3341	249	2	pr(a	pr(a	PUNCT
ejpam-3341	249	3	)	)	PUNCT
ejpam-3341	249	4	is	be	AUX
ejpam-3341	249	5	a	a	DET
ejpam-3341	249	6	completely	completely	ADV
ejpam-3341	249	7	prime	prime	ADJ
ejpam-3341	249	8	right	right	ADJ
ejpam-3341	249	9	ideal	ideal	NOUN
ejpam-3341	249	10	of	of	ADP
ejpam-3341	249	11	s	s	AUX
ejpam-3341	249	12	containing	contain	VERB
ejpam-3341	249	13	a.	a.	NOUN
ejpam-3341	249	14	proof	proof	NOUN
ejpam-3341	249	15	.	.	PUNCT
ejpam-3341	250	1	since	since	SCONJ
ejpam-3341	250	2	a	a	PRON
ejpam-3341	250	3	is	be	AUX
ejpam-3341	250	4	a	a	DET
ejpam-3341	250	5	proper	proper	ADJ
ejpam-3341	250	6	left	left	ADJ
ejpam-3341	250	7	ideal	ideal	NOUN
ejpam-3341	250	8	of	of	ADP
ejpam-3341	250	9	(	(	PUNCT
ejpam-3341	250	10	s	s	PROPN
ejpam-3341	250	11	,	,	PUNCT
ejpam-3341	250	12	·	·	PUNCT
ejpam-3341	250	13	)	)	PUNCT
ejpam-3341	250	14	,	,	PUNCT
ejpam-3341	250	15	we	we	PRON
ejpam-3341	250	16	have	have	VERB
ejpam-3341	250	17	a	a	DET
ejpam-3341	250	18	⊆	⊆	NUM
ejpam-3341	250	19	pr(a	pr(a	NOUN
ejpam-3341	250	20	)	)	PUNCT
ejpam-3341	250	21	and	and	CCONJ
ejpam-3341	250	22	so	so	ADV
ejpam-3341	250	23	pr(a	pr(a	PUNCT
ejpam-3341	250	24	)	)	PUNCT
ejpam-3341	250	25	6=	6=	ADP
ejpam-3341	250	26	∅.	∅.	PRON
ejpam-3341	250	27	since	since	SCONJ
ejpam-3341	250	28	a	a	PRON
ejpam-3341	250	29	is	be	AUX
ejpam-3341	250	30	a	a	DET
ejpam-3341	250	31	proper	proper	ADJ
ejpam-3341	250	32	right	right	ADJ
ejpam-3341	250	33	ideal	ideal	NOUN
ejpam-3341	250	34	of	of	ADP
ejpam-3341	250	35	(	(	PUNCT
ejpam-3341	250	36	s	s	PROPN
ejpam-3341	250	37	,	,	PUNCT
ejpam-3341	250	38	·	·	PUNCT
ejpam-3341	250	39	,	,	PUNCT
ejpam-3341	250	40	≤	≤	NUM
ejpam-3341	250	41	)	)	PUNCT
ejpam-3341	250	42	and	and	CCONJ
ejpam-3341	250	43	pr(a	pr(a	NOUN
ejpam-3341	250	44	)	)	PUNCT
ejpam-3341	250	45	6=	6=	ADP
ejpam-3341	250	46	∅	∅	NOUN
ejpam-3341	250	47	,	,	PUNCT
ejpam-3341	250	48	by	by	ADP
ejpam-3341	250	49	proposition	proposition	NOUN
ejpam-3341	250	50	2.18	2.18	NUM
ejpam-3341	250	51	,	,	PUNCT
ejpam-3341	250	52	pr(a	pr(a	PROPN
ejpam-3341	250	53	)	)	PUNCT
ejpam-3341	250	54	is	be	AUX
ejpam-3341	250	55	a	a	DET
ejpam-3341	250	56	completely	completely	ADV
ejpam-3341	250	57	prime	prime	ADJ
ejpam-3341	250	58	right	right	ADJ
ejpam-3341	250	59	ideal	ideal	NOUN
ejpam-3341	250	60	of	of	ADP
ejpam-3341	250	61	s	s	AUX
ejpam-3341	250	62	containing	contain	VERB
ejpam-3341	250	63	a.	a.	NOUN
ejpam-3341	250	64	�	�	PROPN
ejpam-3341	250	65	we	we	PRON
ejpam-3341	250	66	apply	apply	VERB
ejpam-3341	250	67	proposition	proposition	NOUN
ejpam-3341	250	68	2.20	2.20	NUM
ejpam-3341	250	69	to	to	ADP
ejpam-3341	250	70	the	the	DET
ejpam-3341	250	71	following	follow	VERB
ejpam-3341	250	72	example	example	NOUN
ejpam-3341	250	73	example	example	NOUN
ejpam-3341	250	74	2.21	2.21	NUM
ejpam-3341	250	75	.	.	PUNCT
ejpam-3341	251	1	consider	consider	VERB
ejpam-3341	251	2	the	the	DET
ejpam-3341	251	3	ordered	order	VERB
ejpam-3341	251	4	semigroup	semigroup	PROPN
ejpam-3341	251	5	s	s	PROPN
ejpam-3341	251	6	of	of	ADP
ejpam-3341	251	7	the	the	DET
ejpam-3341	251	8	example	example	NOUN
ejpam-3341	251	9	2.14	2.14	NUM
ejpam-3341	251	10	.	.	PUNCT
ejpam-3341	252	1	the	the	DET
ejpam-3341	252	2	sets	set	NOUN
ejpam-3341	252	3	{	{	PUNCT
ejpam-3341	252	4	f	f	NOUN
ejpam-3341	252	5	}	}	PUNCT
ejpam-3341	252	6	and	and	CCONJ
ejpam-3341	252	7	{	{	PUNCT
ejpam-3341	252	8	e	e	NOUN
ejpam-3341	252	9	,	,	PUNCT
ejpam-3341	252	10	f	f	X
ejpam-3341	252	11	}	}	PUNCT
ejpam-3341	252	12	are	be	AUX
ejpam-3341	252	13	the	the	DET
ejpam-3341	252	14	only	only	ADJ
ejpam-3341	252	15	proper	proper	ADJ
ejpam-3341	252	16	ideals	ideal	NOUN
ejpam-3341	252	17	of	of	ADP
ejpam-3341	252	18	s	s	NOUN
ejpam-3341	252	19	;	;	PUNCT
ejpam-3341	252	20	and	and	CCONJ
ejpam-3341	252	21	as	as	SCONJ
ejpam-3341	252	22	we	we	PRON
ejpam-3341	252	23	have	have	AUX
ejpam-3341	252	24	seen	see	VERB
ejpam-3341	252	25	in	in	ADP
ejpam-3341	252	26	example	example	NOUN
ejpam-3341	252	27	2.17	2.17	NUM
ejpam-3341	252	28	,	,	PUNCT
ejpam-3341	252	29	for	for	ADP
ejpam-3341	252	30	the	the	DET
ejpam-3341	252	31	set	set	NOUN
ejpam-3341	252	32	a	a	X
ejpam-3341	252	33	=	=	SYM
ejpam-3341	252	34	{	{	PUNCT
ejpam-3341	252	35	e	e	NOUN
ejpam-3341	252	36	,	,	PUNCT
ejpam-3341	252	37	f	f	PROPN
ejpam-3341	252	38	}	}	PUNCT
ejpam-3341	252	39	,	,	PUNCT
ejpam-3341	252	40	we	we	PRON
ejpam-3341	252	41	have	have	AUX
ejpam-3341	252	42	pr(a	pr(a	VERB
ejpam-3341	252	43	)	)	PUNCT
ejpam-3341	252	44	=	=	SYM
ejpam-3341	252	45	{	{	PUNCT
ejpam-3341	252	46	e	e	NOUN
ejpam-3341	252	47	,	,	PUNCT
ejpam-3341	252	48	f	f	NOUN
ejpam-3341	252	49	}	}	PUNCT
ejpam-3341	252	50	.	.	PUNCT
ejpam-3341	253	1	by	by	ADP
ejpam-3341	253	2	proposition	proposition	NOUN
ejpam-3341	253	3	2.20	2.20	NUM
ejpam-3341	253	4	,	,	PUNCT
ejpam-3341	253	5	pr(a	pr(a	NOUN
ejpam-3341	253	6	)	)	PUNCT
ejpam-3341	253	7	is	be	AUX
ejpam-3341	253	8	a	a	DET
ejpam-3341	253	9	completely	completely	ADV
ejpam-3341	253	10	prime	prime	ADJ
ejpam-3341	253	11	ideal	ideal	NOUN
ejpam-3341	253	12	of	of	ADP
ejpam-3341	253	13	s.	s.	PROPN
ejpam-3341	253	14	independently	independently	ADV
ejpam-3341	253	15	,	,	PUNCT
ejpam-3341	253	16	we	we	PRON
ejpam-3341	253	17	can	can	AUX
ejpam-3341	253	18	check	check	VERB
ejpam-3341	253	19	that	that	SCONJ
ejpam-3341	253	20	if	if	SCONJ
ejpam-3341	253	21	c	c	NOUN
ejpam-3341	253	22	,	,	PUNCT
ejpam-3341	253	23	d	d	X
ejpam-3341	253	24	are	be	AUX
ejpam-3341	253	25	subsets	subset	NOUN
ejpam-3341	253	26	of	of	ADP
ejpam-3341	253	27	s	s	PRON
ejpam-3341	253	28	such	such	ADJ
ejpam-3341	253	29	that	that	DET
ejpam-3341	253	30	cd	cd	PROPN
ejpam-3341	253	31	⊆	⊆	NUM
ejpam-3341	253	32	{	{	PUNCT
ejpam-3341	253	33	e	e	NOUN
ejpam-3341	253	34	,	,	PUNCT
ejpam-3341	253	35	f	f	PROPN
ejpam-3341	253	36	}	}	PUNCT
ejpam-3341	253	37	,	,	PUNCT
ejpam-3341	253	38	then	then	ADV
ejpam-3341	253	39	c	c	PROPN
ejpam-3341	253	40	⊆	⊆	NUM
ejpam-3341	253	41	{	{	PUNCT
ejpam-3341	253	42	e	e	NOUN
ejpam-3341	253	43	,	,	PUNCT
ejpam-3341	253	44	f	f	NOUN
ejpam-3341	253	45	}	}	PUNCT
ejpam-3341	253	46	or	or	CCONJ
ejpam-3341	253	47	d	d	ADP
ejpam-3341	253	48	⊆	⊆	NUM
ejpam-3341	253	49	{	{	PUNCT
ejpam-3341	253	50	e	e	NOUN
ejpam-3341	253	51	,	,	PUNCT
ejpam-3341	253	52	f	f	NOUN
ejpam-3341	253	53	}	}	PUNCT
ejpam-3341	253	54	(	(	PUNCT
ejpam-3341	253	55	or	or	CCONJ
ejpam-3341	253	56	we	we	PRON
ejpam-3341	253	57	can	can	AUX
ejpam-3341	253	58	check	check	VERB
ejpam-3341	253	59	that	that	SCONJ
ejpam-3341	253	60	if	if	SCONJ
ejpam-3341	253	61	x	x	X
ejpam-3341	253	62	,	,	PUNCT
ejpam-3341	253	63	y	y	PROPN
ejpam-3341	253	64	∈	∈	PROPN
ejpam-3341	253	65	s	s	VERB
ejpam-3341	253	66	such	such	ADJ
ejpam-3341	253	67	that	that	SCONJ
ejpam-3341	253	68	xy	xy	PROPN
ejpam-3341	253	69	∈	∈	PROPN
ejpam-3341	253	70	{	{	PUNCT
ejpam-3341	253	71	e	e	NOUN
ejpam-3341	253	72	,	,	PUNCT
ejpam-3341	253	73	f	f	PROPN
ejpam-3341	253	74	}	}	PUNCT
ejpam-3341	253	75	,	,	PUNCT
ejpam-3341	253	76	then	then	ADV
ejpam-3341	253	77	x	x	X
ejpam-3341	253	78	∈	∈	PROPN
ejpam-3341	253	79	{	{	PUNCT
ejpam-3341	253	80	e	e	NOUN
ejpam-3341	253	81	,	,	PUNCT
ejpam-3341	253	82	f	f	NOUN
ejpam-3341	253	83	}	}	PUNCT
ejpam-3341	253	84	or	or	CCONJ
ejpam-3341	253	85	y	y	PROPN
ejpam-3341	253	86	∈	∈	PROPN
ejpam-3341	253	87	{	{	PUNCT
ejpam-3341	253	88	e	e	NOUN
ejpam-3341	253	89	,	,	PUNCT
ejpam-3341	253	90	f	f	NOUN
ejpam-3341	253	91	}	}	PUNCT
ejpam-3341	253	92	)	)	PUNCT
ejpam-3341	253	93	which	which	PRON
ejpam-3341	253	94	means	mean	VERB
ejpam-3341	253	95	that	that	SCONJ
ejpam-3341	253	96	{	{	PUNCT
ejpam-3341	253	97	e	e	NOUN
ejpam-3341	253	98	,	,	PUNCT
ejpam-3341	253	99	f	f	X
ejpam-3341	253	100	}	}	PUNCT
ejpam-3341	253	101	is	be	AUX
ejpam-3341	253	102	a	a	DET
ejpam-3341	253	103	completely	completely	ADV
ejpam-3341	253	104	references	reference	NOUN
ejpam-3341	253	105	920	920	NUM
ejpam-3341	253	106	prime	prime	ADJ
ejpam-3341	253	107	ideal	ideal	NOUN
ejpam-3341	253	108	of	of	ADP
ejpam-3341	253	109	s.	s.	PROPN
ejpam-3341	253	110	similarly	similarly	ADV
ejpam-3341	253	111	,	,	PUNCT
ejpam-3341	253	112	the	the	DET
ejpam-3341	253	113	set	set	NOUN
ejpam-3341	253	114	pr({f	pr({f	NOUN
ejpam-3341	253	115	}	}	PUNCT
ejpam-3341	253	116	(=	(=	NOUN
ejpam-3341	253	117	{	{	PUNCT
ejpam-3341	253	118	f	f	X
ejpam-3341	253	119	}	}	PUNCT
ejpam-3341	253	120	)	)	PUNCT
ejpam-3341	253	121	is	be	AUX
ejpam-3341	253	122	a	a	DET
ejpam-3341	253	123	completely	completely	ADV
ejpam-3341	253	124	prime	prime	ADJ
ejpam-3341	253	125	ideal	ideal	NOUN
ejpam-3341	253	126	of	of	ADP
ejpam-3341	253	127	s.	s.	PROPN
ejpam-3341	253	128	this	this	PRON
ejpam-3341	253	129	being	be	AUX
ejpam-3341	253	130	so	so	ADV
ejpam-3341	253	131	,	,	PUNCT
ejpam-3341	253	132	we	we	PRON
ejpam-3341	253	133	add	add	VERB
ejpam-3341	253	134	to	to	PART
ejpam-3341	253	135	example	example	VERB
ejpam-3341	253	136	2.14	2.14	NUM
ejpam-3341	253	137	a	a	DET
ejpam-3341	253	138	second	second	ADJ
ejpam-3341	253	139	proof	proof	NOUN
ejpam-3341	253	140	that	that	SCONJ
ejpam-3341	253	141	the	the	DET
ejpam-3341	253	142	sets	set	NOUN
ejpam-3341	253	143	{	{	PUNCT
ejpam-3341	253	144	e	e	NOUN
ejpam-3341	253	145	,	,	PUNCT
ejpam-3341	253	146	f	f	X
ejpam-3341	253	147	}	}	PUNCT
ejpam-3341	253	148	and	and	CCONJ
ejpam-3341	253	149	{	{	PUNCT
ejpam-3341	253	150	f	f	X
ejpam-3341	253	151	}	}	PUNCT
ejpam-3341	253	152	are	be	AUX
ejpam-3341	253	153	indeed	indeed	ADV
ejpam-3341	253	154	semiprime	semiprime	ADJ
ejpam-3341	253	155	ideals	ideal	NOUN
ejpam-3341	253	156	of	of	ADP
ejpam-3341	253	157	s	s	NOUN
ejpam-3341	253	158	;	;	PUNCT
ejpam-3341	253	159	as	as	SCONJ
ejpam-3341	253	160	every	every	DET
ejpam-3341	253	161	completely	completely	ADV
ejpam-3341	253	162	prime	prime	ADJ
ejpam-3341	253	163	ideal	ideal	NOUN
ejpam-3341	253	164	is	be	AUX
ejpam-3341	253	165	a	a	DET
ejpam-3341	253	166	prime	prime	ADJ
ejpam-3341	253	167	ideal	ideal	NOUN
ejpam-3341	253	168	and	and	CCONJ
ejpam-3341	253	169	every	every	DET
ejpam-3341	253	170	prime	prime	ADJ
ejpam-3341	253	171	ideal	ideal	NOUN
ejpam-3341	253	172	is	be	AUX
ejpam-3341	253	173	a	a	DET
ejpam-3341	253	174	semiprime	semiprime	NOUN
ejpam-3341	253	175	ideal	ideal	NOUN
ejpam-3341	253	176	.	.	PUNCT
ejpam-3341	254	1	according	accord	VERB
ejpam-3341	254	2	[	[	X
ejpam-3341	254	3	2	2	NUM
ejpam-3341	254	4	;	;	PUNCT
ejpam-3341	254	5	p.	p.	NOUN
ejpam-3341	254	6	526	526	NUM
ejpam-3341	254	7	,	,	PUNCT
ejpam-3341	254	8	l.	l.	PROPN
ejpam-3341	254	9	–	–	PUNCT
ejpam-3341	254	10	9	9	NUM
ejpam-3341	254	11	to	to	PART
ejpam-3341	254	12	–	–	PUNCT
ejpam-3341	254	13	7	7	NUM
ejpam-3341	254	14	]	]	PUNCT
ejpam-3341	254	15	,	,	PUNCT
ejpam-3341	254	16	if	if	SCONJ
ejpam-3341	254	17	i	i	PRON
ejpam-3341	254	18	and	and	CCONJ
ejpam-3341	254	19	j	j	PROPN
ejpam-3341	254	20	are	be	AUX
ejpam-3341	254	21	right	right	ADJ
ejpam-3341	254	22	ideals	ideal	NOUN
ejpam-3341	254	23	of	of	ADP
ejpam-3341	254	24	an	an	DET
ejpam-3341	254	25	ordered	order	VERB
ejpam-3341	254	26	semigroup	semigroup	NOUN
ejpam-3341	254	27	s	s	PROPN
ejpam-3341	254	28	,	,	PUNCT
ejpam-3341	254	29	then	then	ADV
ejpam-3341	254	30	(	(	PUNCT
ejpam-3341	254	31	ij	ij	INTJ
ejpam-3341	254	32	]	]	PUNCT
ejpam-3341	254	33	is	be	AUX
ejpam-3341	254	34	a	a	DET
ejpam-3341	254	35	right	right	ADJ
ejpam-3341	254	36	ideal	ideal	NOUN
ejpam-3341	254	37	of	of	ADP
ejpam-3341	254	38	s.	s.	PROPN
ejpam-3341	254	39	the	the	DET
ejpam-3341	254	40	authors	author	NOUN
ejpam-3341	254	41	assume	assume	VERB
ejpam-3341	254	42	that	that	SCONJ
ejpam-3341	254	43	each	each	DET
ejpam-3341	254	44	ordered	order	VERB
ejpam-3341	254	45	semigroup	semigroup	NOUN
ejpam-3341	254	46	has	have	VERB
ejpam-3341	254	47	an	an	DET
ejpam-3341	254	48	identity	identity	NOUN
ejpam-3341	254	49	and	and	CCONJ
ejpam-3341	254	50	a	a	DET
ejpam-3341	254	51	zero	zero	NUM
ejpam-3341	254	52	[	[	X
ejpam-3341	254	53	see	see	INTJ
ejpam-3341	254	54	p.	p.	NOUN
ejpam-3341	254	55	525	525	NUM
ejpam-3341	254	56	,	,	PUNCT
ejpam-3341	254	57	l.	l.	NOUN
ejpam-3341	254	58	22–23	22–23	NUM
ejpam-3341	254	59	]	]	PUNCT
ejpam-3341	254	60	.	.	PUNCT
ejpam-3341	255	1	it	it	PRON
ejpam-3341	255	2	might	might	AUX
ejpam-3341	255	3	be	be	AUX
ejpam-3341	255	4	noted	note	VERB
ejpam-3341	255	5	that	that	SCONJ
ejpam-3341	255	6	,	,	PUNCT
ejpam-3341	255	7	more	more	ADV
ejpam-3341	255	8	generally	generally	ADV
ejpam-3341	255	9	,	,	PUNCT
ejpam-3341	255	10	if	if	SCONJ
ejpam-3341	255	11	i	i	PRON
ejpam-3341	255	12	is	be	AUX
ejpam-3341	255	13	a	a	DET
ejpam-3341	255	14	nonempty	nonempty	ADJ
ejpam-3341	255	15	subset	subset	NOUN
ejpam-3341	255	16	of	of	ADP
ejpam-3341	255	17	an	an	DET
ejpam-3341	255	18	ordered	order	VERB
ejpam-3341	255	19	semigroup	semigroup	PROPN
ejpam-3341	255	20	s	s	PROPN
ejpam-3341	255	21	and	and	CCONJ
ejpam-3341	255	22	j	j	PROPN
ejpam-3341	255	23	a	a	DET
ejpam-3341	255	24	right	right	ADJ
ejpam-3341	255	25	ideal	ideal	NOUN
ejpam-3341	255	26	of	of	ADP
ejpam-3341	255	27	s	s	PROPN
ejpam-3341	255	28	,	,	PUNCT
ejpam-3341	255	29	then	then	ADV
ejpam-3341	255	30	(	(	PUNCT
ejpam-3341	255	31	ij	ij	INTJ
ejpam-3341	255	32	]	]	PUNCT
ejpam-3341	255	33	is	be	AUX
ejpam-3341	255	34	a	a	DET
ejpam-3341	255	35	right	right	ADJ
ejpam-3341	255	36	ideal	ideal	NOUN
ejpam-3341	255	37	of	of	ADP
ejpam-3341	255	38	s.	s.	PROPN
ejpam-3341	255	39	if	if	SCONJ
ejpam-3341	255	40	i	i	PRON
ejpam-3341	255	41	is	be	AUX
ejpam-3341	255	42	a	a	DET
ejpam-3341	255	43	left	left	ADJ
ejpam-3341	255	44	ideal	ideal	NOUN
ejpam-3341	255	45	of	of	ADP
ejpam-3341	255	46	s	s	PRON
ejpam-3341	255	47	and	and	CCONJ
ejpam-3341	255	48	j	j	PROPN
ejpam-3341	255	49	a	a	DET
ejpam-3341	255	50	nonempty	nonempty	NOUN
ejpam-3341	255	51	subset	subset	NOUN
ejpam-3341	255	52	of	of	ADP
ejpam-3341	255	53	s	s	PROPN
ejpam-3341	255	54	,	,	PUNCT
ejpam-3341	255	55	then	then	ADV
ejpam-3341	255	56	(	(	PUNCT
ejpam-3341	255	57	ij	ij	INTJ
ejpam-3341	255	58	]	]	PUNCT
ejpam-3341	255	59	is	be	AUX
ejpam-3341	255	60	a	a	DET
ejpam-3341	255	61	left	left	ADJ
ejpam-3341	255	62	ideal	ideal	NOUN
ejpam-3341	255	63	of	of	ADP
ejpam-3341	255	64	s.	s.	PROPN
ejpam-3341	255	65	as	as	ADP
ejpam-3341	255	66	a	a	DET
ejpam-3341	255	67	consequence	consequence	NOUN
ejpam-3341	255	68	,	,	PUNCT
ejpam-3341	255	69	if	if	SCONJ
ejpam-3341	255	70	i	i	PRON
ejpam-3341	255	71	and	and	CCONJ
ejpam-3341	255	72	j	j	PROPN
ejpam-3341	255	73	are	be	AUX
ejpam-3341	255	74	ideals	ideal	NOUN
ejpam-3341	255	75	of	of	ADP
ejpam-3341	255	76	s	s	NOUN
ejpam-3341	255	77	,	,	PUNCT
ejpam-3341	255	78	then	then	ADV
ejpam-3341	255	79	(	(	PUNCT
ejpam-3341	255	80	ij	ij	INTJ
ejpam-3341	255	81	]	]	PUNCT
ejpam-3341	255	82	is	be	AUX
ejpam-3341	255	83	an	an	DET
ejpam-3341	255	84	ideal	ideal	NOUN
ejpam-3341	255	85	of	of	ADP
ejpam-3341	255	86	s.	s.	PROPN
ejpam-3341	255	87	the	the	DET
ejpam-3341	255	88	finite	finite	PROPN
ejpam-3341	255	89	intersection	intersection	NOUN
ejpam-3341	255	90	of	of	ADP
ejpam-3341	255	91	right	right	ADJ
ejpam-3341	255	92	(	(	PUNCT
ejpam-3341	255	93	resp	resp	NOUN
ejpam-3341	255	94	.	.	PUNCT
ejpam-3341	256	1	left	leave	VERB
ejpam-3341	256	2	,	,	PUNCT
ejpam-3341	256	3	two	two	NUM
ejpam-3341	256	4	-	-	PUNCT
ejpam-3341	256	5	sided	sided	ADJ
ejpam-3341	256	6	)	)	PUNCT
ejpam-3341	256	7	ideals	ideal	NOUN
ejpam-3341	256	8	of	of	ADP
ejpam-3341	256	9	an	an	DET
ejpam-3341	256	10	ordered	order	VERB
ejpam-3341	256	11	semigroup	semigroup	NOUN
ejpam-3341	256	12	s	s	NOUN
ejpam-3341	256	13	,	,	PUNCT
ejpam-3341	256	14	if	if	SCONJ
ejpam-3341	256	15	it	it	PRON
ejpam-3341	256	16	is	be	AUX
ejpam-3341	256	17	nonempty	nonempty	ADJ
ejpam-3341	256	18	,	,	PUNCT
ejpam-3341	256	19	is	be	AUX
ejpam-3341	256	20	a	a	DET
ejpam-3341	256	21	right	right	ADJ
ejpam-3341	256	22	(	(	PUNCT
ejpam-3341	256	23	resp	resp	NOUN
ejpam-3341	256	24	.	.	PUNCT
ejpam-3341	257	1	left	leave	VERB
ejpam-3341	257	2	,	,	PUNCT
ejpam-3341	257	3	two	two	NUM
ejpam-3341	257	4	-	-	PUNCT
ejpam-3341	257	5	sided	sided	ADJ
ejpam-3341	257	6	)	)	PUNCT
ejpam-3341	257	7	ideal	ideal	NOUN
ejpam-3341	257	8	of	of	ADP
ejpam-3341	257	9	s	s	PRON
ejpam-3341	257	10	;	;	PUNCT
ejpam-3341	257	11	this	this	PRON
ejpam-3341	257	12	generalizes	generalize	VERB
ejpam-3341	257	13	the	the	DET
ejpam-3341	257	14	corresponding	corresponding	ADJ
ejpam-3341	257	15	result	result	NOUN
ejpam-3341	257	16	in	in	ADP
ejpam-3341	257	17	[	[	X
ejpam-3341	257	18	2	2	NUM
ejpam-3341	257	19	;	;	PUNCT
ejpam-3341	257	20	corollary	corollary	ADJ
ejpam-3341	257	21	2.2	2.2	NUM
ejpam-3341	257	22	]	]	PUNCT
ejpam-3341	257	23	.	.	PUNCT
ejpam-3341	258	1	finally	finally	ADV
ejpam-3341	258	2	,	,	PUNCT
ejpam-3341	258	3	it	it	PRON
ejpam-3341	258	4	might	might	AUX
ejpam-3341	258	5	be	be	AUX
ejpam-3341	258	6	mentioned	mention	VERB
ejpam-3341	258	7	that	that	SCONJ
ejpam-3341	258	8	the	the	DET
ejpam-3341	258	9	proposition	proposition	NOUN
ejpam-3341	258	10	2.1	2.1	NUM
ejpam-3341	258	11	in	in	ADP
ejpam-3341	258	12	[	[	X
ejpam-3341	258	13	2	2	NUM
ejpam-3341	258	14	]	]	PUNCT
ejpam-3341	258	15	,	,	PUNCT
ejpam-3341	258	16	actually	actually	ADV
ejpam-3341	258	17	a	a	DET
ejpam-3341	258	18	lemma	lemma	PROPN
ejpam-3341	258	19	used	use	VERB
ejpam-3341	258	20	throughout	throughout	ADP
ejpam-3341	258	21	the	the	DET
ejpam-3341	258	22	paper	paper	NOUN
ejpam-3341	258	23	,	,	PUNCT
ejpam-3341	258	24	is	be	AUX
ejpam-3341	258	25	not	not	PART
ejpam-3341	258	26	new	new	ADJ
ejpam-3341	258	27	(	(	PUNCT
ejpam-3341	258	28	see	see	VERB
ejpam-3341	258	29	,	,	PUNCT
ejpam-3341	258	30	for	for	ADP
ejpam-3341	258	31	example	example	NOUN
ejpam-3341	258	32	[	[	X
ejpam-3341	258	33	4	4	NUM
ejpam-3341	258	34	;	;	PUNCT
ejpam-3341	258	35	the	the	DET
ejpam-3341	258	36	lemma	lemma	PROPN
ejpam-3341	258	37	]	]	PUNCT
ejpam-3341	258	38	or	or	CCONJ
ejpam-3341	258	39	[	[	X
ejpam-3341	258	40	5	5	NUM
ejpam-3341	258	41	;	;	PUNCT
ejpam-3341	258	42	lemma	lemma	PROPN
ejpam-3341	258	43	1	1	NUM
ejpam-3341	258	44	]	]	NUM
ejpam-3341	258	45	)	)	PUNCT
ejpam-3341	258	46	.	.	PUNCT
ejpam-3341	259	1	the	the	DET
ejpam-3341	259	2	proposition	proposition	NOUN
ejpam-3341	259	3	2.3	2.3	NUM
ejpam-3341	259	4	in	in	ADP
ejpam-3341	259	5	[	[	X
ejpam-3341	259	6	2	2	NUM
ejpam-3341	259	7	]	]	PUNCT
ejpam-3341	259	8	is	be	AUX
ejpam-3341	259	9	also	also	ADV
ejpam-3341	259	10	not	not	PART
ejpam-3341	259	11	new	new	ADJ
ejpam-3341	259	12	,	,	PUNCT
ejpam-3341	259	13	it	it	PRON
ejpam-3341	259	14	is	be	AUX
ejpam-3341	259	15	a	a	DET
ejpam-3341	259	16	special	special	ADJ
ejpam-3341	259	17	case	case	NOUN
ejpam-3341	259	18	of	of	ADP
ejpam-3341	259	19	the	the	DET
ejpam-3341	259	20	proposition	proposition	NOUN
ejpam-3341	259	21	in	in	ADP
ejpam-3341	259	22	[	[	X
ejpam-3341	259	23	5	5	NUM
ejpam-3341	259	24	]	]	PUNCT
ejpam-3341	259	25	,	,	PUNCT
ejpam-3341	259	26	where	where	SCONJ
ejpam-3341	259	27	has	have	AUX
ejpam-3341	259	28	been	be	AUX
ejpam-3341	259	29	shown	show	VERB
ejpam-3341	259	30	that	that	SCONJ
ejpam-3341	259	31	if	if	SCONJ
ejpam-3341	259	32	an	an	DET
ejpam-3341	259	33	ideal	ideal	NOUN
ejpam-3341	259	34	of	of	ADP
ejpam-3341	259	35	an	an	DET
ejpam-3341	259	36	ordered	order	VERB
ejpam-3341	259	37	semigroup	semigroup	NOUN
ejpam-3341	259	38	is	be	AUX
ejpam-3341	259	39	completely	completely	ADV
ejpam-3341	259	40	semiprime	semiprime	NOUN
ejpam-3341	259	41	and	and	CCONJ
ejpam-3341	259	42	prime	prime	NOUN
ejpam-3341	259	43	,	,	PUNCT
ejpam-3341	259	44	then	then	ADV
ejpam-3341	259	45	it	it	PRON
ejpam-3341	259	46	is	be	AUX
ejpam-3341	259	47	completely	completely	ADV
ejpam-3341	259	48	prime	prime	ADJ
ejpam-3341	259	49	(	(	PUNCT
ejpam-3341	259	50	without	without	ADP
ejpam-3341	259	51	using	use	VERB
ejpam-3341	259	52	the	the	DET
ejpam-3341	259	53	identity	identity	NOUN
ejpam-3341	259	54	considered	consider	VERB
ejpam-3341	259	55	in	in	ADP
ejpam-3341	259	56	[	[	X
ejpam-3341	259	57	2	2	NUM
ejpam-3341	259	58	]	]	NUM
ejpam-3341	259	59	)	)	PUNCT
ejpam-3341	259	60	.	.	PUNCT
ejpam-3341	260	1	the	the	DET
ejpam-3341	260	2	fact	fact	NOUN
ejpam-3341	260	3	that	that	SCONJ
ejpam-3341	260	4	every	every	DET
ejpam-3341	260	5	semigroup	semigroup	NOUN
ejpam-3341	260	6	endowed	endow	VERB
ejpam-3341	260	7	with	with	ADP
ejpam-3341	260	8	the	the	DET
ejpam-3341	260	9	order	order	NOUN
ejpam-3341	260	10	≤=	≤=	ADJ
ejpam-3341	260	11	{	{	PUNCT
ejpam-3341	260	12	x	x	NOUN
ejpam-3341	260	13	,	,	PUNCT
ejpam-3341	260	14	y	y	NOUN
ejpam-3341	260	15	)	)	PUNCT
ejpam-3341	260	16	|	|	ADV
ejpam-3341	260	17	x	x	X
ejpam-3341	260	18	=	=	SYM
ejpam-3341	260	19	y	y	NOUN
ejpam-3341	260	20	}	}	PUNCT
ejpam-3341	260	21	is	be	AUX
ejpam-3341	260	22	an	an	DET
ejpam-3341	260	23	ordered	order	VERB
ejpam-3341	260	24	semigroup	semigroup	NOUN
ejpam-3341	260	25	and	and	CCONJ
ejpam-3341	260	26	,	,	PUNCT
ejpam-3341	260	27	as	as	ADP
ejpam-3341	260	28	a	a	DET
ejpam-3341	260	29	consequence	consequence	NOUN
ejpam-3341	260	30	,	,	PUNCT
ejpam-3341	260	31	the	the	DET
ejpam-3341	260	32	notion	notion	NOUN
ejpam-3341	260	33	of	of	ADP
ejpam-3341	260	34	a	a	DET
ejpam-3341	260	35	right	right	ADJ
ejpam-3341	260	36	chain	chain	NOUN
ejpam-3341	260	37	ordered	order	VERB
ejpam-3341	260	38	semigroup	semigroup	PROPN
ejpam-3341	260	39	generalizes	generalize	VERB
ejpam-3341	260	40	the	the	DET
ejpam-3341	260	41	notion	notion	NOUN
ejpam-3341	260	42	of	of	ADP
ejpam-3341	260	43	a	a	DET
ejpam-3341	260	44	right	right	ADJ
ejpam-3341	260	45	chain	chain	NOUN
ejpam-3341	260	46	semigroup	semigroup	NOUN
ejpam-3341	260	47	(	(	PUNCT
ejpam-3341	260	48	p.	p.	NOUN
ejpam-3341	260	49	525	525	NUM
ejpam-3341	260	50	,	,	PUNCT
ejpam-3341	260	51	l.	l.	PROPN
ejpam-3341	260	52	11–19	11–19	PROPN
ejpam-3341	260	53	;	;	PUNCT
ejpam-3341	260	54	p.	p.	NOUN
ejpam-3341	260	55	524	524	NUM
ejpam-3341	260	56	,	,	PUNCT
ejpam-3341	260	57	l.	l.	PROPN
ejpam-3341	260	58	–	–	PUNCT
ejpam-3341	260	59	10	10	NUM
ejpam-3341	260	60	to	to	PART
ejpam-3341	260	61	–	–	PUNCT
ejpam-3341	260	62	7	7	NUM
ejpam-3341	260	63	]	]	PUNCT
ejpam-3341	260	64	in	in	ADP
ejpam-3341	260	65	[	[	X
ejpam-3341	260	66	2	2	NUM
ejpam-3341	260	67	]	]	PUNCT
ejpam-3341	260	68	)	)	PUNCT
ejpam-3341	260	69	is	be	AUX
ejpam-3341	260	70	well	well	ADV
ejpam-3341	260	71	known	know	VERB
ejpam-3341	260	72	as	as	SCONJ
ejpam-3341	260	73	it	it	PRON
ejpam-3341	260	74	is	be	AUX
ejpam-3341	260	75	known	know	VERB
ejpam-3341	260	76	for	for	ADP
ejpam-3341	260	77	any	any	DET
ejpam-3341	260	78	type	type	NOUN
ejpam-3341	260	79	of	of	ADP
ejpam-3341	260	80	ordered	order	VERB
ejpam-3341	260	81	semigroups	semigroup	NOUN
ejpam-3341	260	82	–	–	PUNCT
ejpam-3341	260	83	see	see	VERB
ejpam-3341	260	84	,	,	PUNCT
ejpam-3341	260	85	for	for	ADP
ejpam-3341	260	86	example	example	NOUN
ejpam-3341	260	87	[	[	X
ejpam-3341	260	88	4–7	4–7	X
ejpam-3341	260	89	]	]	X
ejpam-3341	260	90	.	.	PUNCT
ejpam-3341	261	1	i	i	PRON
ejpam-3341	261	2	would	would	AUX
ejpam-3341	261	3	like	like	VERB
ejpam-3341	261	4	to	to	PART
ejpam-3341	261	5	thank	thank	VERB
ejpam-3341	261	6	the	the	DET
ejpam-3341	261	7	two	two	NUM
ejpam-3341	261	8	anonymous	anonymous	ADJ
ejpam-3341	261	9	referees	referee	NOUN
ejpam-3341	261	10	for	for	ADP
ejpam-3341	261	11	their	their	PRON
ejpam-3341	261	12	time	time	NOUN
ejpam-3341	261	13	to	to	PART
ejpam-3341	261	14	read	read	VERB
ejpam-3341	261	15	the	the	DET
ejpam-3341	261	16	paper	paper	NOUN
ejpam-3341	261	17	carefully	carefully	ADV
ejpam-3341	261	18	,	,	PUNCT
ejpam-3341	261	19	their	their	PRON
ejpam-3341	261	20	interest	interest	NOUN
ejpam-3341	261	21	on	on	ADP
ejpam-3341	261	22	my	my	PRON
ejpam-3341	261	23	work	work	NOUN
ejpam-3341	261	24	and	and	CCONJ
ejpam-3341	261	25	their	their	PRON
ejpam-3341	261	26	prompt	prompt	ADJ
ejpam-3341	261	27	reply	reply	NOUN
ejpam-3341	261	28	–	–	PUNCT
ejpam-3341	261	29	something	something	PRON
ejpam-3341	261	30	lately	lately	ADV
ejpam-3341	261	31	not	not	PART
ejpam-3341	261	32	very	very	ADV
ejpam-3341	261	33	usual	usual	ADJ
ejpam-3341	261	34	.	.	PUNCT
ejpam-3341	262	1	references	reference	NOUN
ejpam-3341	262	2	[	[	X
ejpam-3341	262	3	1	1	NUM
ejpam-3341	262	4	]	]	X
ejpam-3341	262	5	g.	g.	NOUN
ejpam-3341	262	6	birkhoff	birkhoff	PROPN
ejpam-3341	262	7	,	,	PUNCT
ejpam-3341	262	8	lattice	lattice	PROPN
ejpam-3341	262	9	theory	theory	NOUN
ejpam-3341	262	10	.	.	PUNCT
ejpam-3341	263	1	corrected	correct	VERB
ejpam-3341	263	2	reprint	reprint	NOUN
ejpam-3341	263	3	of	of	ADP
ejpam-3341	263	4	the	the	DET
ejpam-3341	263	5	1967	1967	NUM
ejpam-3341	263	6	third	third	PROPN
ejpam-3341	263	7	edition	edition	NOUN
ejpam-3341	263	8	.	.	PUNCT
ejpam-3341	264	1	american	american	PROPN
ejpam-3341	264	2	mathematical	mathematical	PROPN
ejpam-3341	264	3	society	society	NOUN
ejpam-3341	264	4	colloquium	colloquium	NOUN
ejpam-3341	264	5	publications	publication	NOUN
ejpam-3341	264	6	,	,	PUNCT
ejpam-3341	264	7	25	25	NUM
ejpam-3341	264	8	.	.	PUNCT
ejpam-3341	265	1	american	american	PROPN
ejpam-3341	265	2	mathematical	mathematical	PROPN
ejpam-3341	265	3	society	society	NOUN
ejpam-3341	265	4	,	,	PUNCT
ejpam-3341	265	5	providence	providence	NOUN
ejpam-3341	265	6	,	,	PUNCT
ejpam-3341	265	7	r.i	r.i	PROPN
ejpam-3341	265	8	.	.	PROPN
ejpam-3341	265	9	,	,	PUNCT
ejpam-3341	265	10	1979	1979	NUM
ejpam-3341	265	11	vi+418	vi+418	NOUN
ejpam-3341	265	12	pp	pp	ADV
ejpam-3341	265	13	.	.	PUNCT
ejpam-3341	266	1	[	[	X
ejpam-3341	266	2	2	2	X
ejpam-3341	266	3	]	]	PUNCT
ejpam-3341	266	4	t.	t.	NOUN
ejpam-3341	266	5	changphas	changphas	PROPN
ejpam-3341	266	6	,	,	PUNCT
ejpam-3341	266	7	p.	p.	PROPN
ejpam-3341	266	8	luangchaisri	luangchaisri	PROPN
ejpam-3341	266	9	,	,	PUNCT
ejpam-3341	266	10	r.	r.	PROPN
ejpam-3341	266	11	mazurek	mazurek	PROPN
ejpam-3341	266	12	.	.	PUNCT
ejpam-3341	267	1	on	on	ADP
ejpam-3341	267	2	right	right	ADJ
ejpam-3341	267	3	chain	chain	NOUN
ejpam-3341	267	4	ordered	order	VERB
ejpam-3341	267	5	semigroups	semigroup	NOUN
ejpam-3341	267	6	.	.	PUNCT
ejpam-3341	268	1	semigroup	semigroup	PROPN
ejpam-3341	268	2	forum	forum	PROPN
ejpam-3341	268	3	96(3):523–535	96(3):523–535	PROPN
ejpam-3341	268	4	,	,	PUNCT
ejpam-3341	268	5	2018	2018	NUM
ejpam-3341	268	6	.	.	PUNCT
ejpam-3341	269	1	[	[	X
ejpam-3341	269	2	3	3	X
ejpam-3341	269	3	]	]	PUNCT
ejpam-3341	269	4	l.	l.	PROPN
ejpam-3341	269	5	fuchs	fuchs	PROPN
ejpam-3341	269	6	.	.	PUNCT
ejpam-3341	270	1	partially	partially	ADV
ejpam-3341	270	2	ordered	order	VERB
ejpam-3341	270	3	algebraic	algebraic	ADJ
ejpam-3341	270	4	systems	system	NOUN
ejpam-3341	270	5	.	.	PUNCT
ejpam-3341	271	1	pergamon	pergamon	PROPN
ejpam-3341	271	2	press	press	PROPN
ejpam-3341	271	3	,	,	PUNCT
ejpam-3341	271	4	oxford	oxford	PROPN
ejpam-3341	271	5	-	-	PUNCT
ejpam-3341	271	6	london	london	PROPN
ejpam-3341	271	7	-	-	PUNCT
ejpam-3341	271	8	new	new	PROPN
ejpam-3341	271	9	york	york	PROPN
ejpam-3341	271	10	-	-	PUNCT
ejpam-3341	271	11	paris	paris	PROPN
ejpam-3341	271	12	;	;	PUNCT
ejpam-3341	271	13	addison	addison	PROPN
ejpam-3341	271	14	-	-	PUNCT
ejpam-3341	271	15	wesley	wesley	PROPN
ejpam-3341	271	16	publishing	publishing	PROPN
ejpam-3341	271	17	co.	co.	PROPN
ejpam-3341	271	18	,	,	PUNCT
ejpam-3341	271	19	inc	inc	PROPN
ejpam-3341	271	20	.	.	PROPN
ejpam-3341	271	21	,	,	PUNCT
ejpam-3341	271	22	reading	reading	NOUN
ejpam-3341	271	23	,	,	PUNCT
ejpam-3341	271	24	mass.-palo	mass.-palo	NOUN
ejpam-3341	271	25	alto	alto	NOUN
ejpam-3341	271	26	,	,	PUNCT
ejpam-3341	271	27	calif.london	calif.london	PROPN
ejpam-3341	271	28	1963	1963	NUM
ejpam-3341	271	29	ix+229	ix+229	NUM
ejpam-3341	271	30	pp	pp	ADV
ejpam-3341	271	31	.	.	PUNCT
ejpam-3341	272	1	[	[	X
ejpam-3341	272	2	4	4	X
ejpam-3341	272	3	]	]	X
ejpam-3341	272	4	n.	n.	NOUN
ejpam-3341	272	5	kehayopulu	kehayopulu	PROPN
ejpam-3341	272	6	.	.	PUNCT
ejpam-3341	273	1	on	on	ADP
ejpam-3341	273	2	weakly	weakly	ADJ
ejpam-3341	273	3	prime	prime	ADJ
ejpam-3341	273	4	ideals	ideal	NOUN
ejpam-3341	273	5	of	of	ADP
ejpam-3341	273	6	ordered	order	VERB
ejpam-3341	273	7	semigroups	semigroup	NOUN
ejpam-3341	273	8	.	.	PUNCT
ejpam-3341	273	9	math	math	NOUN
ejpam-3341	273	10	.	.	PUNCT
ejpam-3341	274	1	japon	japon	PROPN
ejpam-3341	274	2	.	.	PUNCT
ejpam-3341	275	1	35(6):1051–1056	35(6):1051–1056	NUM
ejpam-3341	275	2	,	,	PUNCT
ejpam-3341	275	3	1990	1990	NUM
ejpam-3341	275	4	.	.	PUNCT
ejpam-3341	276	1	[	[	X
ejpam-3341	276	2	5	5	NUM
ejpam-3341	276	3	]	]	PUNCT
ejpam-3341	276	4	n.	n.	NOUN
ejpam-3341	276	5	kehayopulu	kehayopulu	PROPN
ejpam-3341	276	6	.	.	PUNCT
ejpam-3341	277	1	on	on	ADP
ejpam-3341	277	2	prime	prime	ADJ
ejpam-3341	277	3	,	,	PUNCT
ejpam-3341	277	4	weakly	weakly	ADJ
ejpam-3341	277	5	prime	prime	ADJ
ejpam-3341	277	6	ideals	ideal	NOUN
ejpam-3341	277	7	in	in	ADP
ejpam-3341	277	8	ordered	order	VERB
ejpam-3341	277	9	semigroups	semigroup	NOUN
ejpam-3341	277	10	.	.	PUNCT
ejpam-3341	278	1	semigroup	semigroup	PROPN
ejpam-3341	278	2	forum	forum	PROPN
ejpam-3341	278	3	44(3):341–346	44(3):341–346	PROPN
ejpam-3341	278	4	,	,	PUNCT
ejpam-3341	278	5	1992	1992	NUM
ejpam-3341	278	6	.	.	PUNCT
ejpam-3341	279	1	references	reference	NOUN
ejpam-3341	279	2	921	921	NUM
ejpam-3341	279	3	[	[	X
ejpam-3341	279	4	6	6	NUM
ejpam-3341	279	5	]	]	PUNCT
ejpam-3341	279	6	n.	n.	PROPN
ejpam-3341	279	7	kehayopulu	kehayopulu	PROPN
ejpam-3341	279	8	.	.	PUNCT
ejpam-3341	280	1	ordered	order	VERB
ejpam-3341	280	2	semigroups	semigroup	NOUN
ejpam-3341	280	3	whose	whose	DET
ejpam-3341	280	4	elements	element	NOUN
ejpam-3341	280	5	are	be	AUX
ejpam-3341	280	6	separated	separate	VERB
ejpam-3341	280	7	by	by	ADP
ejpam-3341	280	8	prime	prime	ADJ
ejpam-3341	280	9	ideals	ideal	NOUN
ejpam-3341	280	10	.	.	PUNCT
ejpam-3341	281	1	math	math	NOUN
ejpam-3341	281	2	.	.	PUNCT
ejpam-3341	282	1	slovaca	slovaca	PROPN
ejpam-3341	282	2	62(3):417–424	62(3):417–424	NUM
ejpam-3341	282	3	,	,	PUNCT
ejpam-3341	282	4	2012	2012	NUM
ejpam-3341	282	5	.	.	PUNCT
ejpam-3341	283	1	[	[	X
ejpam-3341	283	2	7	7	X
ejpam-3341	283	3	]	]	X
ejpam-3341	283	4	n.	n.	NOUN
ejpam-3341	283	5	kehayopulu	kehayopulu	PROPN
ejpam-3341	283	6	,	,	PUNCT
ejpam-3341	283	7	m.	m.	NOUN
ejpam-3341	283	8	tsingelis	tsingelis	PROPN
ejpam-3341	283	9	.	.	PUNCT
ejpam-3341	284	1	archimedean	archimedean	PROPN
ejpam-3341	284	2	ordered	order	VERB
ejpam-3341	284	3	semigroups	semigroup	NOUN
ejpam-3341	284	4	as	as	ADP
ejpam-3341	284	5	ideal	ideal	ADJ
ejpam-3341	284	6	extensions	extension	NOUN
ejpam-3341	284	7	.	.	PUNCT
ejpam-3341	285	1	semigroup	semigroup	PROPN
ejpam-3341	285	2	forum	forum	PROPN
ejpam-3341	285	3	78(2):343–348	78(2):343–348	PROPN
ejpam-3341	285	4	,	,	PUNCT
ejpam-3341	285	5	2009	2009	NUM
ejpam-3341	285	6	.	.	PUNCT
ejpam-3341	286	1	[	[	X
ejpam-3341	286	2	8	8	NUM
ejpam-3341	286	3	]	]	PUNCT
ejpam-3341	286	4	m.	m.	NOUN
ejpam-3341	286	5	petrich	petrich	PROPN
ejpam-3341	286	6	.	.	PUNCT
ejpam-3341	287	1	introduction	introduction	NOUN
ejpam-3341	287	2	to	to	ADP
ejpam-3341	287	3	semigroups	semigroup	NOUN
ejpam-3341	287	4	.	.	PUNCT
ejpam-3341	288	1	merrill	merrill	NOUN
ejpam-3341	288	2	research	research	NOUN
ejpam-3341	288	3	and	and	CCONJ
ejpam-3341	288	4	lecture	lecture	NOUN
ejpam-3341	288	5	series	series	NOUN
ejpam-3341	288	6	.	.	PUNCT
ejpam-3341	289	1	charles	charles	PROPN
ejpam-3341	289	2	e.	e.	PROPN
ejpam-3341	289	3	merrill	merrill	PROPN
ejpam-3341	289	4	publishing	publishing	PROPN
ejpam-3341	289	5	co.	co.	PROPN
ejpam-3341	289	6	,	,	PUNCT
ejpam-3341	289	7	columbus	columbus	PROPN
ejpam-3341	289	8	,	,	PUNCT
ejpam-3341	289	9	ohio	ohio	PROPN
ejpam-3341	289	10	,	,	PUNCT
ejpam-3341	289	11	1973	1973	NUM
ejpam-3341	289	12	viii+198	viii+198	PROPN
ejpam-3341	289	13	pp	pp	NOUN
ejpam-3341	289	14	.	.	PUNCT