id	sid	tid	token	lemma	pos
ejpam-5528	1	1	european	european	PROPN
ejpam-5528	1	2	journal	journal	PROPN
ejpam-5528	1	3	of	of	ADP
ejpam-5528	1	4	pure	pure	ADJ
ejpam-5528	1	5	and	and	CCONJ
ejpam-5528	1	6	applied	applied	ADJ
ejpam-5528	1	7	mathematics	mathematic	NOUN
ejpam-5528	1	8	2025	2025	NUM
ejpam-5528	1	9	,	,	PUNCT
ejpam-5528	1	10	vol	vol	NOUN
ejpam-5528	1	11	.	.	PROPN
ejpam-5528	1	12	18	18	NUM
ejpam-5528	1	13	,	,	PUNCT
ejpam-5528	1	14	issue	issue	NOUN
ejpam-5528	1	15	2	2	NUM
ejpam-5528	1	16	,	,	PUNCT
ejpam-5528	1	17	article	article	NOUN
ejpam-5528	1	18	number	number	NOUN
ejpam-5528	1	19	5528	5528	NUM
ejpam-5528	1	20	issn	issn	VERB
ejpam-5528	1	21	1307	1307	NUM
ejpam-5528	1	22	-	-	SYM
ejpam-5528	1	23	5543	5543	NUM
ejpam-5528	1	24	–	–	PUNCT
ejpam-5528	1	25	ejpam.com	ejpam.com	X
ejpam-5528	1	26	published	publish	VERB
ejpam-5528	1	27	by	by	ADP
ejpam-5528	1	28	new	new	PROPN
ejpam-5528	1	29	york	york	PROPN
ejpam-5528	1	30	business	business	PROPN
ejpam-5528	1	31	global	global	ADJ
ejpam-5528	1	32	characterizations	characterization	NOUN
ejpam-5528	1	33	of	of	ADP
ejpam-5528	1	34	nonadditive	nonadditive	ADJ
ejpam-5528	1	35	mappings	mapping	NOUN
ejpam-5528	1	36	in	in	ADP
ejpam-5528	1	37	prime	prime	ADJ
ejpam-5528	1	38	∗-rings	∗-ring	NOUN
ejpam-5528	1	39	involving	involve	VERB
ejpam-5528	1	40	bi	bi	ADJ
ejpam-5528	1	41	-	-	ADJ
ejpam-5528	1	42	skew	skew	ADJ
ejpam-5528	1	43	products	product	NOUN
ejpam-5528	1	44	moin	moin	NOUN
ejpam-5528	1	45	a.	a.	PROPN
ejpam-5528	1	46	ansari1	ansari1	PROPN
ejpam-5528	1	47	,	,	PUNCT
ejpam-5528	1	48	abbas	abbas	PROPN
ejpam-5528	1	49	hussain	hussain	PROPN
ejpam-5528	1	50	shikeh2	shikeh2	PROPN
ejpam-5528	1	51	,	,	PUNCT
ejpam-5528	1	52	junaid	junaid	VERB
ejpam-5528	1	53	nisar3,∗	nisar3,∗	NOUN
ejpam-5528	1	54	,	,	PUNCT
ejpam-5528	1	55	shahid	shahid	NOUN
ejpam-5528	1	56	tamboli4	tamboli4	NOUN
ejpam-5528	1	57	1	1	NUM
ejpam-5528	1	58	department	department	NOUN
ejpam-5528	1	59	of	of	ADP
ejpam-5528	1	60	mathematics	mathematics	PROPN
ejpam-5528	1	61	college	college	PROPN
ejpam-5528	1	62	of	of	ADP
ejpam-5528	1	63	science	science	PROPN
ejpam-5528	1	64	,	,	PUNCT
ejpam-5528	1	65	jazan	jazan	PROPN
ejpam-5528	1	66	university	university	PROPN
ejpam-5528	1	67	jazan	jazan	NOUN
ejpam-5528	1	68	45142	45142	NUM
ejpam-5528	1	69	,	,	PUNCT
ejpam-5528	1	70	kingdom	kingdom	NOUN
ejpam-5528	1	71	of	of	ADP
ejpam-5528	1	72	saudi	saudi	PROPN
ejpam-5528	1	73	arabia	arabia	PROPN
ejpam-5528	1	74	2	2	NUM
ejpam-5528	1	75	department	department	NOUN
ejpam-5528	1	76	of	of	ADP
ejpam-5528	1	77	mathematics	mathematics	PROPN
ejpam-5528	1	78	,	,	PUNCT
ejpam-5528	1	79	aligarh	aligarh	PROPN
ejpam-5528	1	80	muslim	muslim	PROPN
ejpam-5528	1	81	university	university	PROPN
ejpam-5528	1	82	,	,	PUNCT
ejpam-5528	1	83	aligarh-202002	aligarh-202002	NOUN
ejpam-5528	1	84	india	india	PROPN
ejpam-5528	1	85	3	3	NUM
ejpam-5528	1	86	department	department	NOUN
ejpam-5528	1	87	of	of	ADP
ejpam-5528	1	88	applied	apply	VERB
ejpam-5528	1	89	sciences	science	NOUN
ejpam-5528	1	90	,	,	PUNCT
ejpam-5528	1	91	symbiosis	symbiosis	NOUN
ejpam-5528	1	92	institute	institute	PROPN
ejpam-5528	1	93	of	of	ADP
ejpam-5528	1	94	technology	technology	PROPN
ejpam-5528	1	95	,	,	PUNCT
ejpam-5528	1	96	symbiosis	symbiosis	NOUN
ejpam-5528	1	97	international	international	ADJ
ejpam-5528	1	98	(	(	PUNCT
ejpam-5528	1	99	deemed	deem	VERB
ejpam-5528	1	100	)	)	PUNCT
ejpam-5528	1	101	university	university	NOUN
ejpam-5528	1	102	,	,	PUNCT
ejpam-5528	1	103	lavale	lavale	NOUN
ejpam-5528	1	104	,	,	PUNCT
ejpam-5528	1	105	pune	pune	NOUN
ejpam-5528	1	106	,	,	PUNCT
ejpam-5528	1	107	india	india	PROPN
ejpam-5528	1	108	4	4	NUM
ejpam-5528	1	109	department	department	NOUN
ejpam-5528	1	110	of	of	ADP
ejpam-5528	1	111	mechanical	mechanical	ADJ
ejpam-5528	1	112	engineering	engineering	NOUN
ejpam-5528	1	113	,	,	PUNCT
ejpam-5528	1	114	symbiosis	symbiosis	NOUN
ejpam-5528	1	115	institute	institute	PROPN
ejpam-5528	1	116	of	of	ADP
ejpam-5528	1	117	technology	technology	PROPN
ejpam-5528	1	118	,	,	PUNCT
ejpam-5528	1	119	symbiosis	symbiosis	NOUN
ejpam-5528	1	120	international	international	ADJ
ejpam-5528	1	121	(	(	PUNCT
ejpam-5528	1	122	deemed	deem	VERB
ejpam-5528	1	123	)	)	PUNCT
ejpam-5528	1	124	university	university	NOUN
ejpam-5528	1	125	,	,	PUNCT
ejpam-5528	1	126	lavale	lavale	NOUN
ejpam-5528	1	127	,	,	PUNCT
ejpam-5528	1	128	pune	pune	NOUN
ejpam-5528	1	129	,	,	PUNCT
ejpam-5528	1	130	india	india	PROPN
ejpam-5528	1	131	abstract	abstract	NOUN
ejpam-5528	1	132	.	.	PUNCT
ejpam-5528	2	1	the	the	DET
ejpam-5528	2	2	paper	paper	NOUN
ejpam-5528	2	3	investigates	investigate	VERB
ejpam-5528	2	4	nonadditive	nonadditive	ADJ
ejpam-5528	2	5	mappings	mapping	NOUN
ejpam-5528	2	6	ω	ω	NOUN
ejpam-5528	2	7	:	:	PUNCT
ejpam-5528	2	8	ℜ	ℜ	PROPN
ejpam-5528	2	9	→	→	SYM
ejpam-5528	2	10	ℜ	ℜ	PROPN
ejpam-5528	2	11	on	on	ADP
ejpam-5528	2	12	a	a	DET
ejpam-5528	2	13	prime	prime	ADJ
ejpam-5528	2	14	ring	ring	NOUN
ejpam-5528	2	15	ℜ	ℜ	PROPN
ejpam-5528	2	16	with	with	ADP
ejpam-5528	2	17	involution	involution	NOUN
ejpam-5528	2	18	∗	∗	NOUN
ejpam-5528	2	19	,	,	PUNCT
ejpam-5528	2	20	characterized	characterize	VERB
ejpam-5528	2	21	by	by	ADP
ejpam-5528	2	22	satisfying	satisfy	VERB
ejpam-5528	2	23	one	one	NUM
ejpam-5528	2	24	of	of	ADP
ejpam-5528	2	25	the	the	DET
ejpam-5528	2	26	following	following	ADJ
ejpam-5528	2	27	conditions	condition	NOUN
ejpam-5528	2	28	:	:	PUNCT
ejpam-5528	2	29	(	(	PUNCT
ejpam-5528	2	30	i	i	NOUN
ejpam-5528	2	31	)	)	PUNCT
ejpam-5528	3	1	[	[	X
ejpam-5528	3	2	ω(u),ω(v)]•	ω(u),ω(v)]•	NUM
ejpam-5528	3	3	=	=	SYM
ejpam-5528	4	1	[	[	X
ejpam-5528	4	2	u	u	NOUN
ejpam-5528	4	3	,	,	PUNCT
ejpam-5528	4	4	v]•	v]•	PROPN
ejpam-5528	4	5	for	for	ADP
ejpam-5528	4	6	all	all	DET
ejpam-5528	4	7	u	u	NOUN
ejpam-5528	4	8	,	,	PUNCT
ejpam-5528	4	9	v	v	NOUN
ejpam-5528	4	10	∈	∈	NOUN
ejpam-5528	4	11	ℜ.	ℜ.	PROPN
ejpam-5528	4	12	(	(	PUNCT
ejpam-5528	4	13	ii	ii	NOUN
ejpam-5528	4	14	)	)	PUNCT
ejpam-5528	5	1	[	[	X
ejpam-5528	5	2	ω(u	ω(u	NUM
ejpam-5528	5	3	)	)	PUNCT
ejpam-5528	5	4	,	,	PUNCT
ejpam-5528	5	5	v]•	v]•	X
ejpam-5528	5	6	=	=	PUNCT
ejpam-5528	6	1	[	[	X
ejpam-5528	6	2	u	u	NOUN
ejpam-5528	6	3	,	,	PUNCT
ejpam-5528	6	4	ω(v)]•	ω(v)]•	PUNCT
ejpam-5528	6	5	for	for	ADP
ejpam-5528	6	6	all	all	DET
ejpam-5528	6	7	u	u	NOUN
ejpam-5528	6	8	,	,	PUNCT
ejpam-5528	6	9	v	v	NOUN
ejpam-5528	6	10	∈	∈	NOUN
ejpam-5528	6	11	ℜ.	ℜ.	PROPN
ejpam-5528	6	12	(	(	PUNCT
ejpam-5528	6	13	iii	iii	NOUN
ejpam-5528	6	14	)	)	PUNCT
ejpam-5528	6	15	ω(u	ω(u	PROPN
ejpam-5528	6	16	•	•	NUM
ejpam-5528	6	17	v	v	NOUN
ejpam-5528	6	18	)	)	PUNCT
ejpam-5528	6	19	=	=	SYM
ejpam-5528	6	20	ω(u	ω(u	PROPN
ejpam-5528	6	21	)	)	PUNCT
ejpam-5528	6	22	•	•	NUM
ejpam-5528	6	23	v	v	NOUN
ejpam-5528	6	24	for	for	ADP
ejpam-5528	6	25	all	all	DET
ejpam-5528	6	26	u	u	NOUN
ejpam-5528	6	27	,	,	PUNCT
ejpam-5528	6	28	v	v	NOUN
ejpam-5528	6	29	∈	∈	NOUN
ejpam-5528	6	30	ℜ.	ℜ.	PROPN
ejpam-5528	6	31	furthermore	furthermore	ADV
ejpam-5528	6	32	,	,	PUNCT
ejpam-5528	6	33	the	the	DET
ejpam-5528	6	34	paper	paper	NOUN
ejpam-5528	6	35	characterizes	characterize	VERB
ejpam-5528	6	36	generalized	generalized	ADJ
ejpam-5528	6	37	bi	bi	ADJ
ejpam-5528	6	38	-	-	ADJ
ejpam-5528	6	39	skew	skew	ADJ
ejpam-5528	6	40	jordan	jordan	PROPN
ejpam-5528	6	41	derivations	derivation	NOUN
ejpam-5528	6	42	within	within	ADP
ejpam-5528	6	43	prime	prime	ADJ
ejpam-5528	6	44	∗-rings	∗-ring	NOUN
ejpam-5528	6	45	and	and	CCONJ
ejpam-5528	6	46	examines	examine	VERB
ejpam-5528	6	47	the	the	DET
ejpam-5528	6	48	implications	implication	NOUN
ejpam-5528	6	49	of	of	ADP
ejpam-5528	6	50	these	these	DET
ejpam-5528	6	51	results	result	NOUN
ejpam-5528	6	52	in	in	ADP
ejpam-5528	6	53	the	the	DET
ejpam-5528	6	54	context	context	NOUN
ejpam-5528	6	55	of	of	ADP
ejpam-5528	6	56	various	various	ADJ
ejpam-5528	6	57	operator	operator	NOUN
ejpam-5528	6	58	algebras	algebra	NOUN
ejpam-5528	6	59	.	.	PUNCT
ejpam-5528	7	1	2020	2020	NUM
ejpam-5528	7	2	mathematics	mathematics	PROPN
ejpam-5528	7	3	subject	subject	NOUN
ejpam-5528	7	4	classifications	classification	NOUN
ejpam-5528	7	5	:	:	PUNCT
ejpam-5528	7	6	16n60	16n60	NUM
ejpam-5528	7	7	,	,	PUNCT
ejpam-5528	7	8	16w10	16w10	NUM
ejpam-5528	7	9	,	,	PUNCT
ejpam-5528	7	10	47b47	47b47	VERB
ejpam-5528	7	11	key	key	ADJ
ejpam-5528	7	12	words	word	NOUN
ejpam-5528	7	13	and	and	CCONJ
ejpam-5528	7	14	phrases	phrase	NOUN
ejpam-5528	7	15	:	:	PUNCT
ejpam-5528	7	16	involution	involution	NOUN
ejpam-5528	7	17	,	,	PUNCT
ejpam-5528	7	18	prime	prime	ADJ
ejpam-5528	7	19	ring	ring	NOUN
ejpam-5528	7	20	,	,	PUNCT
ejpam-5528	7	21	strong	strong	ADJ
ejpam-5528	7	22	bi	bi	ADJ
ejpam-5528	7	23	-	-	ADJ
ejpam-5528	7	24	skew	skew	ADJ
ejpam-5528	7	25	commutativity	commutativity	NOUN
ejpam-5528	7	26	preserving	preserve	VERB
ejpam-5528	7	27	map	map	NOUN
ejpam-5528	7	28	,	,	PUNCT
ejpam-5528	7	29	bi	bi	ADJ
ejpam-5528	7	30	-	-	ADJ
ejpam-5528	7	31	skew	skew	ADJ
ejpam-5528	7	32	commuting	commuting	NOUN
ejpam-5528	7	33	map	map	NOUN
ejpam-5528	7	34	,	,	PUNCT
ejpam-5528	7	35	bi	bi	ADJ
ejpam-5528	7	36	-	-	ADJ
ejpam-5528	7	37	skew	skew	ADJ
ejpam-5528	7	38	jordan	jordan	PROPN
ejpam-5528	7	39	derivation	derivation	PROPN
ejpam-5528	7	40	1	1	NUM
ejpam-5528	7	41	.	.	PUNCT
ejpam-5528	7	42	introduction	introduction	NOUN
ejpam-5528	7	43	in	in	ADP
ejpam-5528	7	44	this	this	DET
ejpam-5528	7	45	paper	paper	NOUN
ejpam-5528	7	46	,	,	PUNCT
ejpam-5528	7	47	unless	unless	SCONJ
ejpam-5528	7	48	stated	state	VERB
ejpam-5528	7	49	otherwise	otherwise	ADV
ejpam-5528	7	50	,	,	PUNCT
ejpam-5528	7	51	ℜ	ℜ	PROPN
ejpam-5528	7	52	represents	represent	VERB
ejpam-5528	7	53	a	a	DET
ejpam-5528	7	54	prime	prime	ADJ
ejpam-5528	7	55	ring	ring	NOUN
ejpam-5528	7	56	with	with	ADP
ejpam-5528	7	57	z(ℜ	z(ℜ	NUM
ejpam-5528	7	58	)	)	PUNCT
ejpam-5528	7	59	as	as	ADP
ejpam-5528	7	60	its	its	PRON
ejpam-5528	7	61	center	center	NOUN
ejpam-5528	7	62	.	.	PUNCT
ejpam-5528	8	1	a	a	DET
ejpam-5528	8	2	ring	ring	NOUN
ejpam-5528	8	3	ℜ	ℜ	PROPN
ejpam-5528	8	4	is	be	AUX
ejpam-5528	8	5	defined	define	VERB
ejpam-5528	8	6	as	as	ADP
ejpam-5528	8	7	prime	prime	ADJ
ejpam-5528	8	8	if	if	SCONJ
ejpam-5528	8	9	,	,	PUNCT
ejpam-5528	8	10	for	for	ADP
ejpam-5528	8	11	any	any	DET
ejpam-5528	8	12	u	u	NOUN
ejpam-5528	8	13	,	,	PUNCT
ejpam-5528	8	14	v	v	NOUN
ejpam-5528	8	15	∈	∈	PROPN
ejpam-5528	8	16	ℜ	ℜ	PROPN
ejpam-5528	8	17	,	,	PUNCT
ejpam-5528	8	18	the	the	DET
ejpam-5528	8	19	condition	condition	NOUN
ejpam-5528	8	20	uℜv	uℜv	NOUN
ejpam-5528	8	21	=	=	SYM
ejpam-5528	8	22	{	{	PUNCT
ejpam-5528	8	23	0	0	NUM
ejpam-5528	8	24	}	}	PUNCT
ejpam-5528	8	25	implies	imply	VERB
ejpam-5528	8	26	that	that	SCONJ
ejpam-5528	8	27	either	either	CCONJ
ejpam-5528	8	28	u	u	PROPN
ejpam-5528	8	29	=	=	NOUN
ejpam-5528	8	30	0	0	NUM
ejpam-5528	8	31	or	or	CCONJ
ejpam-5528	8	32	v	v	NOUN
ejpam-5528	8	33	=	=	SYM
ejpam-5528	8	34	0	0	NUM
ejpam-5528	8	35	.	.	PUNCT
ejpam-5528	9	1	we	we	PRON
ejpam-5528	9	2	denote	denote	VERB
ejpam-5528	9	3	the	the	DET
ejpam-5528	9	4	maximal	maximal	ADJ
ejpam-5528	9	5	left	left	NOUN
ejpam-5528	9	6	and	and	CCONJ
ejpam-5528	9	7	right	right	ADJ
ejpam-5528	9	8	rings	ring	NOUN
ejpam-5528	9	9	of	of	ADP
ejpam-5528	9	10	quotients	quotient	NOUN
ejpam-5528	9	11	of	of	ADP
ejpam-5528	9	12	ℜ	ℜ	NOUN
ejpam-5528	9	13	by	by	ADP
ejpam-5528	9	14	qml(ℜ	qml(ℜ	NOUN
ejpam-5528	9	15	)	)	PUNCT
ejpam-5528	9	16	and	and	CCONJ
ejpam-5528	9	17	qmr(ℜ	qmr(ℜ	NOUN
ejpam-5528	9	18	)	)	PUNCT
ejpam-5528	9	19	,	,	PUNCT
ejpam-5528	9	20	respectively	respectively	ADV
ejpam-5528	9	21	.	.	PUNCT
ejpam-5528	10	1	the	the	DET
ejpam-5528	10	2	maximal	maximal	ADJ
ejpam-5528	10	3	symmetric	symmetric	ADJ
ejpam-5528	10	4	ring	ring	NOUN
ejpam-5528	10	5	of	of	ADP
ejpam-5528	10	6	quotients	quotient	NOUN
ejpam-5528	10	7	of	of	ADP
ejpam-5528	10	8	ℜ	ℜ	PROPN
ejpam-5528	10	9	is	be	AUX
ejpam-5528	10	10	denoted	denote	VERB
ejpam-5528	10	11	by	by	ADP
ejpam-5528	10	12	qms(ℜ	qms(ℜ	PROPN
ejpam-5528	10	13	)	)	PUNCT
ejpam-5528	10	14	.	.	PUNCT
ejpam-5528	11	1	it	it	PRON
ejpam-5528	11	2	is	be	AUX
ejpam-5528	11	3	well	well	ADV
ejpam-5528	11	4	established	establish	VERB
ejpam-5528	11	5	that	that	SCONJ
ejpam-5528	11	6	ℜ	ℜ	PROPN
ejpam-5528	11	7	⊆	⊆	NUM
ejpam-5528	11	8	qms(ℜ	qms(ℜ	NUM
ejpam-5528	11	9	)	)	PUNCT
ejpam-5528	11	10	⊆	⊆	NUM
ejpam-5528	11	11	qml(ℜ	qml(ℜ	NOUN
ejpam-5528	11	12	)	)	PUNCT
ejpam-5528	11	13	and	and	CCONJ
ejpam-5528	11	14	that	that	SCONJ
ejpam-5528	11	15	qms(ℜ	qms(ℜ	PROPN
ejpam-5528	11	16	)	)	PUNCT
ejpam-5528	11	17	=	=	SYM
ejpam-5528	11	18	qml(ℜ	qml(ℜ	NOUN
ejpam-5528	11	19	)	)	PUNCT
ejpam-5528	11	20	∩	∩	NOUN
ejpam-5528	11	21	qmr(ℜ	qmr(ℜ	NOUN
ejpam-5528	11	22	)	)	PUNCT
ejpam-5528	11	23	.	.	PUNCT
ejpam-5528	12	1	both	both	DET
ejpam-5528	12	2	qms(ℜ	qms(ℜ	NUM
ejpam-5528	12	3	)	)	PUNCT
ejpam-5528	12	4	and	and	CCONJ
ejpam-5528	12	5	qml(ℜ	qml(ℜ	NOUN
ejpam-5528	12	6	)	)	PUNCT
ejpam-5528	12	7	are	be	AUX
ejpam-5528	12	8	also	also	ADV
ejpam-5528	12	9	recognized	recognize	VERB
ejpam-5528	12	10	as	as	ADP
ejpam-5528	12	11	prime	prime	ADJ
ejpam-5528	12	12	rings	ring	NOUN
ejpam-5528	12	13	and	and	CCONJ
ejpam-5528	12	14	share	share	VERB
ejpam-5528	12	15	a	a	DET
ejpam-5528	12	16	common	common	ADJ
ejpam-5528	12	17	center	center	NOUN
ejpam-5528	12	18	,	,	PUNCT
ejpam-5528	12	19	∗corresponding	∗corresponde	VERB
ejpam-5528	12	20	author	author	NOUN
ejpam-5528	12	21	.	.	PUNCT
ejpam-5528	13	1	doi	doi	NOUN
ejpam-5528	13	2	:	:	PUNCT
ejpam-5528	13	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5528	https://doi.org/10.29020/nybg.ejpam.v18i2.5528	PUNCT
ejpam-5528	13	4	email	email	NOUN
ejpam-5528	13	5	addresses	address	NOUN
ejpam-5528	13	6	:	:	PUNCT
ejpam-5528	13	7	maansari@jazanu.edu.sa	maansari@jazanu.edu.sa	PROPN
ejpam-5528	13	8	(	(	PUNCT
ejpam-5528	13	9	m.	m.	NOUN
ejpam-5528	13	10	ansari	ansari	PROPN
ejpam-5528	13	11	)	)	PUNCT
ejpam-5528	13	12	,	,	PUNCT
ejpam-5528	13	13	abbasnabi94@gmail.com	abbasnabi94@gmail.com	X
ejpam-5528	13	14	(	(	PUNCT
ejpam-5528	13	15	a.	a.	PROPN
ejpam-5528	13	16	shikeh	shikeh	PROPN
ejpam-5528	13	17	)	)	PUNCT
ejpam-5528	13	18	,	,	PUNCT
ejpam-5528	13	19	junaidnisar73@gmail.com	junaidnisar73@gmail.com	X
ejpam-5528	13	20	(	(	PUNCT
ejpam-5528	13	21	j.	j.	PROPN
ejpam-5528	13	22	nisar	nisar	PROPN
ejpam-5528	13	23	)	)	PUNCT
ejpam-5528	13	24	,	,	PUNCT
ejpam-5528	13	25	shahidt@sitpune.edu.in	shahidt@sitpune.edu.in	ADV
ejpam-5528	13	26	(	(	PUNCT
ejpam-5528	13	27	s.	s.	PROPN
ejpam-5528	13	28	tamboli	tamboli	PROPN
ejpam-5528	13	29	)	)	PUNCT
ejpam-5528	13	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5528	14	1	1	1	NUM
ejpam-5528	14	2	copyright	copyright	NOUN
ejpam-5528	14	3	:	:	PUNCT
ejpam-5528	14	4	©	©	PROPN
ejpam-5528	14	5	2025	2025	NUM
ejpam-5528	14	6	the	the	DET
ejpam-5528	14	7	author(s	author(s	NOUN
ejpam-5528	14	8	)	)	PUNCT
ejpam-5528	14	9	.	.	PUNCT
ejpam-5528	15	1	(	(	PUNCT
ejpam-5528	15	2	cc	cc	NOUN
ejpam-5528	15	3	by	by	ADP
ejpam-5528	15	4	-	-	PUNCT
ejpam-5528	15	5	nc	nc	PROPN
ejpam-5528	15	6	4.0	4.0	NUM
ejpam-5528	15	7	)	)	PUNCT
ejpam-5528	15	8	moin	moin	NOUN
ejpam-5528	15	9	a.	a.	NOUN
ejpam-5528	15	10	ansari	ansari	PROPN
ejpam-5528	15	11	et	et	PROPN
ejpam-5528	15	12	al	al	PROPN
ejpam-5528	15	13	.	.	PUNCT
ejpam-5528	15	14	/	/	SYM
ejpam-5528	15	15	eur	eur	PROPN
ejpam-5528	15	16	.	.	PUNCT
ejpam-5528	16	1	j.	j.	PROPN
ejpam-5528	16	2	pure	pure	PROPN
ejpam-5528	16	3	appl	appl	PROPN
ejpam-5528	16	4	.	.	PROPN
ejpam-5528	16	5	math	math	PROPN
ejpam-5528	16	6	,	,	PUNCT
ejpam-5528	16	7	18	18	NUM
ejpam-5528	16	8	(	(	PUNCT
ejpam-5528	16	9	2	2	NUM
ejpam-5528	16	10	)	)	PUNCT
ejpam-5528	16	11	(	(	PUNCT
ejpam-5528	16	12	2025	2025	NUM
ejpam-5528	16	13	)	)	PUNCT
ejpam-5528	16	14	,	,	PUNCT
ejpam-5528	16	15	5528	5528	NUM
ejpam-5528	16	16	2	2	NUM
ejpam-5528	16	17	of	of	ADP
ejpam-5528	16	18	14	14	NUM
ejpam-5528	16	19	denoted	denote	VERB
ejpam-5528	16	20	by	by	ADP
ejpam-5528	16	21	c	c	PROPN
ejpam-5528	16	22	,	,	PUNCT
ejpam-5528	16	23	which	which	PRON
ejpam-5528	16	24	is	be	AUX
ejpam-5528	16	25	the	the	DET
ejpam-5528	16	26	extended	extended	ADJ
ejpam-5528	16	27	centroid	centroid	NOUN
ejpam-5528	16	28	of	of	ADP
ejpam-5528	16	29	ℜ.	ℜ.	PROPN
ejpam-5528	16	30	the	the	DET
ejpam-5528	16	31	set	set	NOUN
ejpam-5528	16	32	c	c	PROPN
ejpam-5528	16	33	is	be	AUX
ejpam-5528	16	34	defined	define	VERB
ejpam-5528	16	35	as	as	ADP
ejpam-5528	16	36	{	{	PUNCT
ejpam-5528	16	37	λ	λ	X
ejpam-5528	16	38	∈	∈	PROPN
ejpam-5528	16	39	qms(ℜ	qms(ℜ	PROPN
ejpam-5528	16	40	)	)	PUNCT
ejpam-5528	17	1	|	|	ADV
ejpam-5528	17	2	λa	λa	INTJ
ejpam-5528	17	3	=	=	PUNCT
ejpam-5528	17	4	aλ	aλ	X
ejpam-5528	17	5	for	for	ADP
ejpam-5528	17	6	all	all	DET
ejpam-5528	17	7	a	a	DET
ejpam-5528	17	8	∈	∈	PROPN
ejpam-5528	17	9	ℜ	ℜ	PROPN
ejpam-5528	17	10	}	}	PUNCT
ejpam-5528	17	11	.	.	PUNCT
ejpam-5528	18	1	the	the	DET
ejpam-5528	18	2	ring	ring	NOUN
ejpam-5528	18	3	ℜ	ℜ	PROPN
ejpam-5528	18	4	is	be	AUX
ejpam-5528	18	5	prime	prime	ADJ
ejpam-5528	18	6	if	if	SCONJ
ejpam-5528	19	1	and	and	CCONJ
ejpam-5528	19	2	only	only	ADV
ejpam-5528	19	3	if	if	SCONJ
ejpam-5528	19	4	c	c	PROPN
ejpam-5528	19	5	is	be	AUX
ejpam-5528	19	6	a	a	DET
ejpam-5528	19	7	field	field	NOUN
ejpam-5528	19	8	(	(	PUNCT
ejpam-5528	19	9	see	see	VERB
ejpam-5528	19	10	[	[	X
ejpam-5528	19	11	1–3	1–3	NOUN
ejpam-5528	19	12	]	]	X
ejpam-5528	19	13	for	for	ADP
ejpam-5528	19	14	more	more	ADJ
ejpam-5528	19	15	details	detail	NOUN
ejpam-5528	19	16	)	)	PUNCT
ejpam-5528	19	17	.	.	PUNCT
ejpam-5528	20	1	an	an	DET
ejpam-5528	20	2	involution	involution	NOUN
ejpam-5528	20	3	‘	'	PUNCT
ejpam-5528	20	4	∗	∗	NOUN
ejpam-5528	20	5	’	'	PUNCT
ejpam-5528	20	6	on	on	ADP
ejpam-5528	20	7	ℜ	ℜ	PROPN
ejpam-5528	20	8	is	be	AUX
ejpam-5528	20	9	defined	define	VERB
ejpam-5528	20	10	as	as	ADP
ejpam-5528	20	11	an	an	DET
ejpam-5528	20	12	anti	anti	ADJ
ejpam-5528	20	13	-	-	ADJ
ejpam-5528	20	14	automorphism	automorphism	NOUN
ejpam-5528	20	15	of	of	ADP
ejpam-5528	20	16	order	order	NOUN
ejpam-5528	20	17	1	1	NUM
ejpam-5528	20	18	or	or	CCONJ
ejpam-5528	20	19	2	2	NUM
ejpam-5528	20	20	.	.	PUNCT
ejpam-5528	21	1	an	an	DET
ejpam-5528	21	2	antiautomorphism	antiautomorphism	NOUN
ejpam-5528	21	3	∇	∇	X
ejpam-5528	21	4	of	of	ADP
ejpam-5528	21	5	ℜ	ℜ	PROPN
ejpam-5528	21	6	is	be	AUX
ejpam-5528	21	7	classified	classify	VERB
ejpam-5528	21	8	as	as	ADP
ejpam-5528	21	9	being	be	AUX
ejpam-5528	21	10	of	of	ADP
ejpam-5528	21	11	the	the	DET
ejpam-5528	21	12	first	first	ADJ
ejpam-5528	21	13	kind	kind	NOUN
ejpam-5528	21	14	with	with	ADP
ejpam-5528	21	15	respect	respect	NOUN
ejpam-5528	21	16	to	to	ADP
ejpam-5528	21	17	z(ℜ	z(ℜ	NUM
ejpam-5528	21	18	)	)	PUNCT
ejpam-5528	21	19	if	if	SCONJ
ejpam-5528	21	20	it	it	PRON
ejpam-5528	21	21	acts	act	VERB
ejpam-5528	21	22	as	as	ADP
ejpam-5528	21	23	the	the	DET
ejpam-5528	21	24	identity	identity	NOUN
ejpam-5528	21	25	map	map	NOUN
ejpam-5528	21	26	on	on	ADP
ejpam-5528	21	27	z(ℜ	z(ℜ	NUM
ejpam-5528	21	28	)	)	PUNCT
ejpam-5528	21	29	;	;	PUNCT
ejpam-5528	21	30	otherwise	otherwise	ADV
ejpam-5528	21	31	,	,	PUNCT
ejpam-5528	21	32	it	it	PRON
ejpam-5528	21	33	is	be	AUX
ejpam-5528	21	34	considered	consider	VERB
ejpam-5528	21	35	of	of	ADP
ejpam-5528	21	36	the	the	DET
ejpam-5528	21	37	second	second	ADJ
ejpam-5528	21	38	kind	kind	NOUN
ejpam-5528	21	39	on	on	ADP
ejpam-5528	21	40	z(ℜ	z(ℜ	NUM
ejpam-5528	21	41	)	)	PUNCT
ejpam-5528	21	42	.	.	PUNCT
ejpam-5528	22	1	for	for	ADP
ejpam-5528	22	2	a	a	DET
ejpam-5528	22	3	semiprime	semiprime	NOUN
ejpam-5528	22	4	ring	ring	NOUN
ejpam-5528	22	5	ℜ	ℜ	PROPN
ejpam-5528	22	6	,	,	PUNCT
ejpam-5528	22	7	if	if	SCONJ
ejpam-5528	22	8	∇	∇	PRON
ejpam-5528	22	9	is	be	AUX
ejpam-5528	22	10	an	an	DET
ejpam-5528	22	11	anti	anti	ADJ
ejpam-5528	22	12	-	-	ADJ
ejpam-5528	22	13	automorphism	automorphism	ADJ
ejpam-5528	22	14	,	,	PUNCT
ejpam-5528	22	15	then	then	ADV
ejpam-5528	22	16	a	a	DET
ejpam-5528	22	17	right	right	ADJ
ejpam-5528	22	18	ideal	ideal	NOUN
ejpam-5528	22	19	i	i	PRON
ejpam-5528	22	20	of	of	ADP
ejpam-5528	22	21	ℜ	ℜ	PROPN
ejpam-5528	22	22	is	be	AUX
ejpam-5528	22	23	dense	dense	ADJ
ejpam-5528	22	24	if	if	SCONJ
ejpam-5528	22	25	and	and	CCONJ
ejpam-5528	22	26	only	only	ADV
ejpam-5528	22	27	if	if	SCONJ
ejpam-5528	22	28	∇(i	∇(i	NOUN
ejpam-5528	22	29	)	)	PUNCT
ejpam-5528	22	30	is	be	AUX
ejpam-5528	22	31	a	a	DET
ejpam-5528	22	32	dense	dense	ADJ
ejpam-5528	22	33	left	left	ADJ
ejpam-5528	22	34	ideal	ideal	NOUN
ejpam-5528	22	35	of	of	ADP
ejpam-5528	22	36	ℜ	ℜ	PROPN
ejpam-5528	22	37	,	,	PUNCT
ejpam-5528	22	38	and	and	CCONJ
ejpam-5528	22	39	a	a	DET
ejpam-5528	22	40	left	left	ADJ
ejpam-5528	22	41	ideal	ideal	NOUN
ejpam-5528	22	42	j	j	PROPN
ejpam-5528	22	43	of	of	ADP
ejpam-5528	22	44	ℜ	ℜ	PROPN
ejpam-5528	22	45	is	be	AUX
ejpam-5528	22	46	dense	dense	ADJ
ejpam-5528	22	47	if	if	SCONJ
ejpam-5528	22	48	and	and	CCONJ
ejpam-5528	22	49	only	only	ADV
ejpam-5528	22	50	if	if	SCONJ
ejpam-5528	22	51	∇(j	∇(j	NOUN
ejpam-5528	22	52	)	)	PUNCT
ejpam-5528	22	53	is	be	AUX
ejpam-5528	22	54	a	a	DET
ejpam-5528	22	55	dense	dense	ADJ
ejpam-5528	22	56	right	right	ADJ
ejpam-5528	22	57	ideal	ideal	NOUN
ejpam-5528	22	58	of	of	ADP
ejpam-5528	22	59	ℜ.	ℜ.	PROPN
ejpam-5528	22	60	consequently	consequently	ADV
ejpam-5528	22	61	,	,	PUNCT
ejpam-5528	22	62	with	with	ADP
ejpam-5528	22	63	a	a	DET
ejpam-5528	22	64	straightforward	straightforward	ADJ
ejpam-5528	22	65	modification	modification	NOUN
ejpam-5528	22	66	of	of	ADP
ejpam-5528	22	67	the	the	DET
ejpam-5528	22	68	proof	proof	NOUN
ejpam-5528	22	69	in	in	ADP
ejpam-5528	22	70	[	[	X
ejpam-5528	22	71	1	1	NUM
ejpam-5528	22	72	,	,	PUNCT
ejpam-5528	22	73	proposition	proposition	NOUN
ejpam-5528	22	74	2.5.4	2.5.4	NUM
ejpam-5528	22	75	]	]	PUNCT
ejpam-5528	22	76	,	,	PUNCT
ejpam-5528	22	77	it	it	PRON
ejpam-5528	22	78	follows	follow	VERB
ejpam-5528	22	79	that	that	SCONJ
ejpam-5528	22	80	∇	∇	PROPN
ejpam-5528	22	81	can	can	AUX
ejpam-5528	22	82	be	be	AUX
ejpam-5528	22	83	uniquely	uniquely	ADV
ejpam-5528	22	84	extended	extend	VERB
ejpam-5528	22	85	to	to	ADP
ejpam-5528	22	86	an	an	DET
ejpam-5528	22	87	anti	anti	ADJ
ejpam-5528	22	88	-	-	ADJ
ejpam-5528	22	89	automorphism	automorphism	NOUN
ejpam-5528	22	90	of	of	ADP
ejpam-5528	22	91	qms(ℜ	qms(ℜ	PROPN
ejpam-5528	22	92	)	)	PUNCT
ejpam-5528	22	93	.	.	PUNCT
ejpam-5528	23	1	an	an	DET
ejpam-5528	23	2	anti	anti	ADJ
ejpam-5528	23	3	-	-	ADJ
ejpam-5528	23	4	automorphism	automorphism	ADJ
ejpam-5528	23	5	∇	∇	NOUN
ejpam-5528	23	6	of	of	ADP
ejpam-5528	23	7	ℜ	ℜ	PROPN
ejpam-5528	23	8	is	be	AUX
ejpam-5528	23	9	said	say	VERB
ejpam-5528	23	10	to	to	PART
ejpam-5528	23	11	be	be	AUX
ejpam-5528	23	12	of	of	ADP
ejpam-5528	23	13	the	the	DET
ejpam-5528	23	14	first	first	ADJ
ejpam-5528	23	15	kind	kind	NOUN
ejpam-5528	23	16	if	if	SCONJ
ejpam-5528	23	17	it	it	PRON
ejpam-5528	23	18	acts	act	VERB
ejpam-5528	23	19	as	as	ADP
ejpam-5528	23	20	the	the	DET
ejpam-5528	23	21	identity	identity	NOUN
ejpam-5528	23	22	on	on	ADP
ejpam-5528	23	23	c	c	NOUN
ejpam-5528	23	24	,	,	PUNCT
ejpam-5528	23	25	and	and	CCONJ
ejpam-5528	23	26	of	of	ADP
ejpam-5528	23	27	the	the	DET
ejpam-5528	23	28	second	second	ADJ
ejpam-5528	23	29	kind	kind	NOUN
ejpam-5528	23	30	otherwise	otherwise	ADV
ejpam-5528	23	31	.	.	PUNCT
ejpam-5528	24	1	for	for	ADP
ejpam-5528	24	2	elements	element	NOUN
ejpam-5528	24	3	u	u	NOUN
ejpam-5528	24	4	,	,	PUNCT
ejpam-5528	24	5	v	v	NOUN
ejpam-5528	24	6	∈	∈	PROPN
ejpam-5528	24	7	ℜ	ℜ	PROPN
ejpam-5528	24	8	,	,	PUNCT
ejpam-5528	24	9	the	the	DET
ejpam-5528	24	10	following	follow	VERB
ejpam-5528	24	11	products	product	NOUN
ejpam-5528	24	12	are	be	AUX
ejpam-5528	24	13	defined	define	VERB
ejpam-5528	24	14	:	:	PUNCT
ejpam-5528	24	15	the	the	DET
ejpam-5528	24	16	lie	lie	NOUN
ejpam-5528	24	17	product	product	NOUN
ejpam-5528	24	18	[	[	X
ejpam-5528	24	19	u	u	NOUN
ejpam-5528	24	20	,	,	PUNCT
ejpam-5528	24	21	v	v	NOUN
ejpam-5528	24	22	]	]	X
ejpam-5528	24	23	=	=	SYM
ejpam-5528	24	24	uv−	uv−	SYM
ejpam-5528	24	25	vu	vu	X
ejpam-5528	24	26	,	,	PUNCT
ejpam-5528	24	27	the	the	DET
ejpam-5528	24	28	skew	skew	ADJ
ejpam-5528	24	29	lie	lie	NOUN
ejpam-5528	24	30	product	product	NOUN
ejpam-5528	24	31	[	[	X
ejpam-5528	24	32	u	u	NOUN
ejpam-5528	24	33	,	,	PUNCT
ejpam-5528	24	34	v]∗	v]∗	X
ejpam-5528	24	35	=	=	SYM
ejpam-5528	25	1	uv	uv	NOUN
ejpam-5528	25	2	−	−	PROPN
ejpam-5528	25	3	vu∗	vu∗	NOUN
ejpam-5528	25	4	,	,	PUNCT
ejpam-5528	25	5	the	the	DET
ejpam-5528	25	6	skew	skew	ADJ
ejpam-5528	25	7	jordan	jordan	PROPN
ejpam-5528	25	8	product	product	PROPN
ejpam-5528	25	9	u	u	PROPN
ejpam-5528	25	10	⋄	⋄	PROPN
ejpam-5528	25	11	v	v	ADP
ejpam-5528	25	12	=	=	SYM
ejpam-5528	25	13	uv	uv	NOUN
ejpam-5528	25	14	+	+	NUM
ejpam-5528	25	15	vu∗	vu∗	NOUN
ejpam-5528	25	16	,	,	PUNCT
ejpam-5528	25	17	the	the	DET
ejpam-5528	25	18	bi	bi	ADJ
ejpam-5528	25	19	-	-	ADJ
ejpam-5528	25	20	skew	skew	ADJ
ejpam-5528	25	21	lie	lie	NOUN
ejpam-5528	25	22	product	product	NOUN
ejpam-5528	25	23	[	[	X
ejpam-5528	25	24	u	u	NOUN
ejpam-5528	25	25	,	,	PUNCT
ejpam-5528	25	26	v]•	v]•	PROPN
ejpam-5528	25	27	=	=	PUNCT
ejpam-5528	25	28	uv∗	uv∗	ADJ
ejpam-5528	25	29	−	−	NOUN
ejpam-5528	25	30	vu∗	vu∗	NOUN
ejpam-5528	25	31	,	,	PUNCT
ejpam-5528	25	32	and	and	CCONJ
ejpam-5528	25	33	the	the	DET
ejpam-5528	25	34	bi	bi	ADJ
ejpam-5528	25	35	-	-	ADJ
ejpam-5528	25	36	skew	skew	ADJ
ejpam-5528	25	37	jordan	jordan	PROPN
ejpam-5528	25	38	product	product	PROPN
ejpam-5528	25	39	u	u	PROPN
ejpam-5528	25	40	•	•	NOUN
ejpam-5528	25	41	v	v	NOUN
ejpam-5528	25	42	=	=	PUNCT
ejpam-5528	25	43	uv∗	uv∗	ADJ
ejpam-5528	25	44	+	+	CCONJ
ejpam-5528	25	45	vu∗.	vu∗.	ADP
ejpam-5528	25	46	these	these	DET
ejpam-5528	25	47	types	type	NOUN
ejpam-5528	25	48	of	of	ADP
ejpam-5528	25	49	products	product	NOUN
ejpam-5528	25	50	have	have	AUX
ejpam-5528	25	51	been	be	AUX
ejpam-5528	25	52	the	the	DET
ejpam-5528	25	53	focus	focus	NOUN
ejpam-5528	25	54	of	of	ADP
ejpam-5528	25	55	extensive	extensive	ADJ
ejpam-5528	25	56	research	research	NOUN
ejpam-5528	25	57	by	by	ADP
ejpam-5528	25	58	various	various	ADJ
ejpam-5528	25	59	authors	author	NOUN
ejpam-5528	25	60	(	(	PUNCT
ejpam-5528	25	61	see	see	VERB
ejpam-5528	25	62	[	[	X
ejpam-5528	25	63	4–15	4–15	NOUN
ejpam-5528	25	64	]	]	PUNCT
ejpam-5528	25	65	)	)	PUNCT
ejpam-5528	25	66	.	.	PUNCT
ejpam-5528	26	1	a	a	DET
ejpam-5528	26	2	map	map	NOUN
ejpam-5528	26	3	ω	ω	NOUN
ejpam-5528	26	4	:	:	PUNCT
ejpam-5528	26	5	ℜ	ℜ	PROPN
ejpam-5528	26	6	→	→	SYM
ejpam-5528	26	7	ℜ	ℜ	PROPN
ejpam-5528	26	8	is	be	AUX
ejpam-5528	26	9	termed	term	VERB
ejpam-5528	26	10	a	a	DET
ejpam-5528	26	11	strong	strong	ADJ
ejpam-5528	26	12	commutativity	commutativity	NOUN
ejpam-5528	26	13	preserving	preserve	VERB
ejpam-5528	26	14	map	map	NOUN
ejpam-5528	26	15	if	if	SCONJ
ejpam-5528	26	16	it	it	PRON
ejpam-5528	26	17	satisfies	satisfy	VERB
ejpam-5528	26	18	ω([u	ω([u	PROPN
ejpam-5528	26	19	,	,	PUNCT
ejpam-5528	26	20	v	v	NOUN
ejpam-5528	26	21	]	]	X
ejpam-5528	26	22	)	)	PUNCT
ejpam-5528	27	1	=	=	PUNCT
ejpam-5528	28	1	[	[	X
ejpam-5528	28	2	u	u	NOUN
ejpam-5528	28	3	,	,	PUNCT
ejpam-5528	28	4	v	v	ADP
ejpam-5528	28	5	]	]	PUNCT
ejpam-5528	28	6	for	for	ADP
ejpam-5528	28	7	all	all	DET
ejpam-5528	28	8	u	u	NOUN
ejpam-5528	28	9	,	,	PUNCT
ejpam-5528	28	10	v	v	NOUN
ejpam-5528	28	11	∈	∈	NOUN
ejpam-5528	28	12	ℜ.	ℜ.	PROPN
ejpam-5528	28	13	in	in	ADP
ejpam-5528	28	14	the	the	DET
ejpam-5528	28	15	context	context	NOUN
ejpam-5528	28	16	of	of	ADP
ejpam-5528	28	17	∗-rings	∗-ring	NOUN
ejpam-5528	28	18	,	,	PUNCT
ejpam-5528	28	19	ω	ω	PROPN
ejpam-5528	28	20	is	be	AUX
ejpam-5528	28	21	referred	refer	VERB
ejpam-5528	28	22	to	to	ADP
ejpam-5528	28	23	as	as	ADP
ejpam-5528	28	24	a	a	DET
ejpam-5528	28	25	strong	strong	ADJ
ejpam-5528	28	26	skew	skew	NOUN
ejpam-5528	28	27	commutativity	commutativity	NOUN
ejpam-5528	28	28	preserving	preserve	VERB
ejpam-5528	28	29	map	map	NOUN
ejpam-5528	28	30	if	if	SCONJ
ejpam-5528	28	31	ω([u	ω([u	NOUN
ejpam-5528	28	32	,	,	PUNCT
ejpam-5528	28	33	v]∗	v]∗	NOUN
ejpam-5528	28	34	)	)	PUNCT
ejpam-5528	29	1	=	=	PUNCT
ejpam-5528	30	1	[	[	X
ejpam-5528	30	2	u	u	NOUN
ejpam-5528	30	3	,	,	PUNCT
ejpam-5528	30	4	v]∗	v]∗	VERB
ejpam-5528	30	5	for	for	ADP
ejpam-5528	30	6	all	all	DET
ejpam-5528	30	7	u	u	NOUN
ejpam-5528	30	8	,	,	PUNCT
ejpam-5528	30	9	v	v	NOUN
ejpam-5528	30	10	∈	∈	PROPN
ejpam-5528	30	11	ℜ	ℜ	PROPN
ejpam-5528	30	12	,	,	PUNCT
ejpam-5528	30	13	and	and	CCONJ
ejpam-5528	30	14	as	as	ADP
ejpam-5528	30	15	a	a	DET
ejpam-5528	30	16	strong	strong	ADJ
ejpam-5528	30	17	bi	bi	ADJ
ejpam-5528	30	18	-	-	ADJ
ejpam-5528	30	19	skew	skew	ADJ
ejpam-5528	30	20	commutativity	commutativity	NOUN
ejpam-5528	30	21	preserving	preserve	VERB
ejpam-5528	30	22	map	map	NOUN
ejpam-5528	30	23	if	if	SCONJ
ejpam-5528	30	24	ω([u	ω([u	NOUN
ejpam-5528	30	25	,	,	PUNCT
ejpam-5528	30	26	v]•	v]•	NOUN
ejpam-5528	30	27	)	)	PUNCT
ejpam-5528	30	28	=	=	PUNCT
ejpam-5528	31	1	[	[	X
ejpam-5528	31	2	u	u	NOUN
ejpam-5528	31	3	,	,	PUNCT
ejpam-5528	31	4	v]•	v]•	PROPN
ejpam-5528	31	5	for	for	ADP
ejpam-5528	31	6	all	all	DET
ejpam-5528	31	7	u	u	NOUN
ejpam-5528	31	8	,	,	PUNCT
ejpam-5528	31	9	v	v	NOUN
ejpam-5528	31	10	∈	∈	PROPN
ejpam-5528	31	11	ℜ	ℜ	PROPN
ejpam-5528	31	12	(	(	PUNCT
ejpam-5528	31	13	see	see	VERB
ejpam-5528	31	14	[	[	X
ejpam-5528	31	15	9	9	NUM
ejpam-5528	31	16	,	,	PUNCT
ejpam-5528	31	17	12	12	NUM
ejpam-5528	31	18	,	,	PUNCT
ejpam-5528	31	19	14	14	NUM
ejpam-5528	31	20	,	,	PUNCT
ejpam-5528	31	21	16	16	NUM
ejpam-5528	31	22	]	]	PUNCT
ejpam-5528	31	23	)	)	PUNCT
ejpam-5528	31	24	.	.	PUNCT
ejpam-5528	32	1	a	a	DET
ejpam-5528	32	2	map	map	NOUN
ejpam-5528	32	3	ω	ω	NOUN
ejpam-5528	32	4	:	:	PUNCT
ejpam-5528	32	5	ℜ	ℜ	PROPN
ejpam-5528	32	6	→	→	SYM
ejpam-5528	32	7	ℜ	ℜ	PROPN
ejpam-5528	32	8	is	be	AUX
ejpam-5528	32	9	called	call	VERB
ejpam-5528	32	10	a	a	DET
ejpam-5528	32	11	skew	skew	ADJ
ejpam-5528	32	12	commuting	commuting	NOUN
ejpam-5528	32	13	map	map	NOUN
ejpam-5528	32	14	if	if	SCONJ
ejpam-5528	32	15	it	it	PRON
ejpam-5528	32	16	satisfies	satisfy	VERB
ejpam-5528	32	17	[	[	X
ejpam-5528	32	18	ω(u	ω(u	NUM
ejpam-5528	32	19	)	)	PUNCT
ejpam-5528	32	20	,	,	PUNCT
ejpam-5528	32	21	v]∗	v]∗	X
ejpam-5528	33	1	=	=	PUNCT
ejpam-5528	34	1	[	[	X
ejpam-5528	34	2	u	u	NOUN
ejpam-5528	34	3	,	,	PUNCT
ejpam-5528	34	4	ω(v)]∗	ω(v)]∗	NUM
ejpam-5528	34	5	for	for	ADP
ejpam-5528	34	6	all	all	DET
ejpam-5528	34	7	u	u	NOUN
ejpam-5528	34	8	,	,	PUNCT
ejpam-5528	34	9	v	v	NOUN
ejpam-5528	34	10	∈	∈	PROPN
ejpam-5528	34	11	ℜ	ℜ	PROPN
ejpam-5528	34	12	(	(	PUNCT
ejpam-5528	34	13	see	see	VERB
ejpam-5528	34	14	[	[	X
ejpam-5528	34	15	17	17	NUM
ejpam-5528	34	16	]	]	NUM
ejpam-5528	34	17	)	)	PUNCT
ejpam-5528	34	18	.	.	PUNCT
ejpam-5528	35	1	similarly	similarly	ADV
ejpam-5528	35	2	,	,	PUNCT
ejpam-5528	35	3	ω	ω	PROPN
ejpam-5528	35	4	is	be	AUX
ejpam-5528	35	5	termed	term	VERB
ejpam-5528	35	6	a	a	DET
ejpam-5528	35	7	bi	bi	ADJ
ejpam-5528	35	8	-	-	ADJ
ejpam-5528	35	9	skew	skew	ADJ
ejpam-5528	35	10	commuting	commuting	NOUN
ejpam-5528	35	11	map	map	NOUN
ejpam-5528	35	12	if	if	SCONJ
ejpam-5528	35	13	[	[	X
ejpam-5528	35	14	ω(u	ω(u	NUM
ejpam-5528	35	15	)	)	PUNCT
ejpam-5528	35	16	,	,	PUNCT
ejpam-5528	35	17	v]•	v]•	X
ejpam-5528	36	1	=	=	PUNCT
ejpam-5528	37	1	[	[	X
ejpam-5528	37	2	u	u	NOUN
ejpam-5528	37	3	,	,	PUNCT
ejpam-5528	37	4	ω(v)]•	ω(v)]•	PUNCT
ejpam-5528	37	5	for	for	ADP
ejpam-5528	37	6	all	all	DET
ejpam-5528	37	7	u	u	NOUN
ejpam-5528	37	8	,	,	PUNCT
ejpam-5528	37	9	v	v	NOUN
ejpam-5528	37	10	∈	∈	NOUN
ejpam-5528	37	11	ℜ.	ℜ.	VERB
ejpam-5528	37	12	a	a	DET
ejpam-5528	37	13	map	map	NOUN
ejpam-5528	38	1	ω	ω	NOUN
ejpam-5528	38	2	:	:	PUNCT
ejpam-5528	38	3	ℜ	ℜ	PROPN
ejpam-5528	38	4	→	→	SYM
ejpam-5528	38	5	qms(ℜ	qms(ℜ	NUM
ejpam-5528	38	6	)	)	PUNCT
ejpam-5528	38	7	is	be	AUX
ejpam-5528	38	8	described	describe	VERB
ejpam-5528	38	9	as	as	ADP
ejpam-5528	38	10	∗-linear	∗-linear	ADJ
ejpam-5528	38	11	if	if	SCONJ
ejpam-5528	38	12	it	it	PRON
ejpam-5528	38	13	holds	hold	VERB
ejpam-5528	38	14	that	that	SCONJ
ejpam-5528	38	15	ω(u∗	ω(u∗	VERB
ejpam-5528	38	16	)	)	PUNCT
ejpam-5528	38	17	=	=	PUNCT
ejpam-5528	39	1	ω(u)∗	ω(u)∗	NOUN
ejpam-5528	39	2	for	for	ADP
ejpam-5528	39	3	all	all	DET
ejpam-5528	39	4	u	u	NOUN
ejpam-5528	39	5	∈	∈	PROPN
ejpam-5528	39	6	ℜ.	ℜ.	PROPN
ejpam-5528	39	7	furthermore	furthermore	ADV
ejpam-5528	39	8	,	,	PUNCT
ejpam-5528	39	9	a	a	DET
ejpam-5528	39	10	map	map	NOUN
ejpam-5528	39	11	ω	ω	NOUN
ejpam-5528	39	12	:	:	PUNCT
ejpam-5528	39	13	ℜ	ℜ	PROPN
ejpam-5528	39	14	→	→	SYM
ejpam-5528	39	15	ℜ	ℜ	PROPN
ejpam-5528	39	16	is	be	AUX
ejpam-5528	39	17	known	know	VERB
ejpam-5528	39	18	as	as	ADP
ejpam-5528	39	19	a	a	DET
ejpam-5528	39	20	derivation	derivation	NOUN
ejpam-5528	39	21	if	if	SCONJ
ejpam-5528	39	22	it	it	PRON
ejpam-5528	39	23	satisfies	satisfy	VERB
ejpam-5528	39	24	ω(uv	ω(uv	NOUN
ejpam-5528	39	25	)	)	PUNCT
ejpam-5528	39	26	=	=	PUNCT
ejpam-5528	39	27	ω(u)v	ω(u)v	X
ejpam-5528	39	28	+	+	CCONJ
ejpam-5528	39	29	uω(v	uω(v	NOUN
ejpam-5528	39	30	)	)	PUNCT
ejpam-5528	39	31	for	for	ADP
ejpam-5528	39	32	all	all	DET
ejpam-5528	39	33	u	u	NOUN
ejpam-5528	39	34	,	,	PUNCT
ejpam-5528	39	35	v	v	NOUN
ejpam-5528	39	36	∈	∈	NOUN
ejpam-5528	39	37	ℜ.	ℜ.	PROPN
ejpam-5528	39	38	in	in	ADP
ejpam-5528	39	39	∗-rings	∗-ring	NOUN
ejpam-5528	39	40	,	,	PUNCT
ejpam-5528	39	41	a	a	DET
ejpam-5528	39	42	map	map	NOUN
ejpam-5528	39	43	ω	ω	NOUN
ejpam-5528	39	44	:	:	PUNCT
ejpam-5528	39	45	ℜ	ℜ	PROPN
ejpam-5528	39	46	→	→	SYM
ejpam-5528	39	47	ℜ	ℜ	PROPN
ejpam-5528	39	48	is	be	AUX
ejpam-5528	39	49	called	call	VERB
ejpam-5528	39	50	a	a	DET
ejpam-5528	39	51	skew	skew	ADJ
ejpam-5528	39	52	lie	lie	NOUN
ejpam-5528	39	53	derivation	derivation	NOUN
ejpam-5528	39	54	if	if	SCONJ
ejpam-5528	39	55	ω([u	ω([u	NOUN
ejpam-5528	39	56	,	,	PUNCT
ejpam-5528	39	57	v]∗	v]∗	NOUN
ejpam-5528	39	58	)	)	PUNCT
ejpam-5528	40	1	=	=	PUNCT
ejpam-5528	41	1	[	[	X
ejpam-5528	41	2	ω(u	ω(u	NUM
ejpam-5528	41	3	)	)	PUNCT
ejpam-5528	41	4	,	,	PUNCT
ejpam-5528	41	5	v]∗	v]∗	X
ejpam-5528	41	6	+	+	PUNCT
ejpam-5528	42	1	[	[	X
ejpam-5528	42	2	u	u	NOUN
ejpam-5528	42	3	,	,	PUNCT
ejpam-5528	42	4	ω(v)]∗	ω(v)]∗	NUM
ejpam-5528	42	5	for	for	ADP
ejpam-5528	42	6	all	all	DET
ejpam-5528	42	7	u	u	NOUN
ejpam-5528	42	8	,	,	PUNCT
ejpam-5528	42	9	v	v	NOUN
ejpam-5528	42	10	∈	∈	PROPN
ejpam-5528	42	11	ℜ	ℜ	PROPN
ejpam-5528	42	12	(	(	PUNCT
ejpam-5528	42	13	see	see	VERB
ejpam-5528	42	14	[	[	X
ejpam-5528	42	15	7	7	NUM
ejpam-5528	42	16	,	,	PUNCT
ejpam-5528	42	17	18	18	NUM
ejpam-5528	42	18	]	]	NUM
ejpam-5528	42	19	)	)	PUNCT
ejpam-5528	42	20	.	.	PUNCT
ejpam-5528	43	1	similarly	similarly	ADV
ejpam-5528	43	2	,	,	PUNCT
ejpam-5528	43	3	it	it	PRON
ejpam-5528	43	4	is	be	AUX
ejpam-5528	43	5	called	call	VERB
ejpam-5528	43	6	a	a	DET
ejpam-5528	43	7	skew	skew	ADJ
ejpam-5528	43	8	jordan	jordan	PROPN
ejpam-5528	43	9	derivation	derivation	NOUN
ejpam-5528	43	10	if	if	SCONJ
ejpam-5528	43	11	ω(u	ω(u	PROPN
ejpam-5528	43	12	⋄	⋄	PROPN
ejpam-5528	43	13	v	v	NOUN
ejpam-5528	43	14	)	)	PUNCT
ejpam-5528	43	15	=	=	SYM
ejpam-5528	43	16	ω(u	ω(u	PROPN
ejpam-5528	43	17	)	)	PUNCT
ejpam-5528	44	1	⋄	⋄	NOUN
ejpam-5528	44	2	v	v	ADJ
ejpam-5528	44	3	+	+	CCONJ
ejpam-5528	44	4	u	u	NOUN
ejpam-5528	44	5	⋄	⋄	PROPN
ejpam-5528	44	6	ω(v	ω(v	NOUN
ejpam-5528	44	7	)	)	PUNCT
ejpam-5528	44	8	for	for	ADP
ejpam-5528	44	9	all	all	DET
ejpam-5528	44	10	u	u	NOUN
ejpam-5528	44	11	,	,	PUNCT
ejpam-5528	44	12	v	v	NOUN
ejpam-5528	44	13	∈	∈	NOUN
ejpam-5528	44	14	ℜ.	ℜ.	VERB
ejpam-5528	44	15	a	a	DET
ejpam-5528	44	16	map	map	NOUN
ejpam-5528	44	17	ω	ω	NOUN
ejpam-5528	44	18	:	:	PUNCT
ejpam-5528	44	19	ℜ	ℜ	PROPN
ejpam-5528	44	20	→	→	SYM
ejpam-5528	44	21	ℜ	ℜ	PROPN
ejpam-5528	44	22	is	be	AUX
ejpam-5528	44	23	defined	define	VERB
ejpam-5528	44	24	as	as	ADP
ejpam-5528	44	25	a	a	DET
ejpam-5528	44	26	bi	bi	ADJ
ejpam-5528	44	27	-	-	ADJ
ejpam-5528	44	28	skew	skew	ADJ
ejpam-5528	44	29	jordan	jordan	PROPN
ejpam-5528	44	30	derivation	derivation	NOUN
ejpam-5528	44	31	if	if	SCONJ
ejpam-5528	44	32	ω(u	ω(u	PROPN
ejpam-5528	44	33	•	•	NUM
ejpam-5528	44	34	v	v	NOUN
ejpam-5528	44	35	)	)	PUNCT
ejpam-5528	44	36	=	=	SYM
ejpam-5528	44	37	ω(u	ω(u	PROPN
ejpam-5528	44	38	)	)	PUNCT
ejpam-5528	44	39	•	•	NOUN
ejpam-5528	44	40	v+	v+	ADP
ejpam-5528	44	41	u	u	PROPN
ejpam-5528	44	42	•ω(v	•ω(v	NOUN
ejpam-5528	44	43	)	)	PUNCT
ejpam-5528	44	44	for	for	ADP
ejpam-5528	44	45	all	all	DET
ejpam-5528	44	46	u	u	NOUN
ejpam-5528	44	47	,	,	PUNCT
ejpam-5528	44	48	v	v	NOUN
ejpam-5528	44	49	∈	∈	PROPN
ejpam-5528	44	50	ℜ	ℜ	PROPN
ejpam-5528	44	51	(	(	PUNCT
ejpam-5528	44	52	see	see	VERB
ejpam-5528	44	53	[	[	X
ejpam-5528	44	54	19–22	19–22	NUM
ejpam-5528	44	55	]	]	X
ejpam-5528	44	56	)	)	PUNCT
ejpam-5528	44	57	.	.	PUNCT
ejpam-5528	45	1	additionally	additionally	ADV
ejpam-5528	45	2	,	,	PUNCT
ejpam-5528	45	3	a	a	DET
ejpam-5528	45	4	map	map	NOUN
ejpam-5528	45	5	ψ	ψ	X
ejpam-5528	45	6	:	:	PUNCT
ejpam-5528	45	7	ℜ	ℜ	X
ejpam-5528	45	8	→	→	SYM
ejpam-5528	45	9	ℜ	ℜ	PROPN
ejpam-5528	45	10	is	be	AUX
ejpam-5528	45	11	termed	term	VERB
ejpam-5528	45	12	a	a	DET
ejpam-5528	45	13	generalized	generalized	ADJ
ejpam-5528	45	14	bi	bi	ADJ
ejpam-5528	45	15	-	-	ADJ
ejpam-5528	45	16	skew	skew	ADJ
ejpam-5528	45	17	jordan	jordan	PROPN
ejpam-5528	45	18	derivation	derivation	PROPN
ejpam-5528	45	19	if	if	SCONJ
ejpam-5528	45	20	there	there	PRON
ejpam-5528	45	21	exists	exist	VERB
ejpam-5528	45	22	a	a	DET
ejpam-5528	45	23	bi	bi	ADJ
ejpam-5528	45	24	-	-	ADJ
ejpam-5528	45	25	skew	skew	ADJ
ejpam-5528	45	26	jordan	jordan	PROPN
ejpam-5528	45	27	derivation	derivation	PROPN
ejpam-5528	45	28	ω	ω	PROPN
ejpam-5528	45	29	:	:	PUNCT
ejpam-5528	45	30	ℜ	ℜ	PROPN
ejpam-5528	45	31	→	→	SYM
ejpam-5528	45	32	ℜ	ℜ	PROPN
ejpam-5528	45	33	such	such	ADJ
ejpam-5528	45	34	that	that	DET
ejpam-5528	45	35	ψ([u	ψ([u	PROPN
ejpam-5528	45	36	,	,	PUNCT
ejpam-5528	45	37	v]•	v]•	NOUN
ejpam-5528	45	38	)	)	PUNCT
ejpam-5528	45	39	=	=	PUNCT
ejpam-5528	46	1	[	[	X
ejpam-5528	46	2	ψ(u	ψ(u	NOUN
ejpam-5528	46	3	)	)	PUNCT
ejpam-5528	46	4	,	,	PUNCT
ejpam-5528	47	1	v]•	v]•	PROPN
ejpam-5528	48	1	+	+	PUNCT
ejpam-5528	49	1	[	[	X
ejpam-5528	49	2	u	u	NOUN
ejpam-5528	49	3	,	,	PUNCT
ejpam-5528	49	4	ω(v)]•	ω(v)]•	PUNCT
ejpam-5528	49	5	for	for	ADP
ejpam-5528	49	6	all	all	DET
ejpam-5528	49	7	u	u	NOUN
ejpam-5528	49	8	,	,	PUNCT
ejpam-5528	49	9	v	v	NOUN
ejpam-5528	49	10	∈	∈	PROPN
ejpam-5528	49	11	ℜ	ℜ	PROPN
ejpam-5528	49	12	(	(	PUNCT
ejpam-5528	49	13	see	see	VERB
ejpam-5528	49	14	[	[	X
ejpam-5528	49	15	22	22	NUM
ejpam-5528	49	16	]	]	PUNCT
ejpam-5528	49	17	)	)	PUNCT
ejpam-5528	49	18	.	.	PUNCT
ejpam-5528	50	1	a	a	DET
ejpam-5528	50	2	derivation	derivation	NOUN
ejpam-5528	50	3	ω	ω	NOUN
ejpam-5528	50	4	:	:	PUNCT
ejpam-5528	50	5	ℜ	ℜ	PROPN
ejpam-5528	50	6	→	→	SYM
ejpam-5528	50	7	ℜ	ℜ	PROPN
ejpam-5528	50	8	is	be	AUX
ejpam-5528	50	9	called	call	VERB
ejpam-5528	50	10	an	an	DET
ejpam-5528	50	11	additive	additive	ADJ
ejpam-5528	50	12	∗-derivation	∗-derivation	NOUN
ejpam-5528	50	13	if	if	SCONJ
ejpam-5528	50	14	ω	ω	PROPN
ejpam-5528	50	15	is	be	AUX
ejpam-5528	50	16	both	both	PRON
ejpam-5528	50	17	additive	additive	ADJ
ejpam-5528	50	18	and	and	CCONJ
ejpam-5528	50	19	∗-linear	∗-linear	NOUN
ejpam-5528	50	20	.	.	PUNCT
ejpam-5528	51	1	a	a	DET
ejpam-5528	51	2	map	map	NOUN
ejpam-5528	51	3	ω	ω	NOUN
ejpam-5528	51	4	:	:	PUNCT
ejpam-5528	51	5	ℜ	ℜ	PROPN
ejpam-5528	51	6	→	→	SYM
ejpam-5528	51	7	ℜ	ℜ	PROPN
ejpam-5528	51	8	is	be	AUX
ejpam-5528	51	9	called	call	VERB
ejpam-5528	51	10	a	a	DET
ejpam-5528	51	11	left	left	ADJ
ejpam-5528	51	12	(	(	PUNCT
ejpam-5528	51	13	resp	resp	NOUN
ejpam-5528	51	14	.	.	PUNCT
ejpam-5528	52	1	right	right	ADJ
ejpam-5528	52	2	)	)	PUNCT
ejpam-5528	52	3	centralizer	centralizer	NOUN
ejpam-5528	52	4	if	if	SCONJ
ejpam-5528	52	5	ω(uv	ω(uv	NUM
ejpam-5528	52	6	)	)	PUNCT
ejpam-5528	52	7	=	=	SYM
ejpam-5528	53	1	ω(u)v	ω(u)v	X
ejpam-5528	53	2	(	(	PUNCT
ejpam-5528	53	3	resp	resp	NOUN
ejpam-5528	53	4	.	.	PUNCT
ejpam-5528	54	1	ω(uv	ω(uv	NUM
ejpam-5528	54	2	)	)	PUNCT
ejpam-5528	54	3	=	=	SYM
ejpam-5528	54	4	uω(v	uω(v	NOUN
ejpam-5528	54	5	)	)	PUNCT
ejpam-5528	54	6	)	)	PUNCT
ejpam-5528	54	7	for	for	ADP
ejpam-5528	54	8	all	all	DET
ejpam-5528	54	9	u	u	NOUN
ejpam-5528	54	10	,	,	PUNCT
ejpam-5528	54	11	v	v	NOUN
ejpam-5528	54	12	∈	∈	PROPN
ejpam-5528	54	13	ℜ	ℜ	PROPN
ejpam-5528	54	14	(	(	PUNCT
ejpam-5528	54	15	see	see	VERB
ejpam-5528	54	16	[	[	X
ejpam-5528	54	17	23	23	NUM
ejpam-5528	54	18	]	]	NUM
ejpam-5528	54	19	)	)	PUNCT
ejpam-5528	54	20	.	.	PUNCT
ejpam-5528	55	1	similarly	similarly	ADV
ejpam-5528	55	2	,	,	PUNCT
ejpam-5528	55	3	ω	ω	PROPN
ejpam-5528	55	4	is	be	AUX
ejpam-5528	55	5	termed	term	VERB
ejpam-5528	55	6	a	a	DET
ejpam-5528	55	7	left	left	ADJ
ejpam-5528	55	8	(	(	PUNCT
ejpam-5528	55	9	resp	resp	NOUN
ejpam-5528	55	10	.	.	PUNCT
ejpam-5528	56	1	right	right	ADJ
ejpam-5528	56	2	)	)	PUNCT
ejpam-5528	56	3	bi	bi	ADJ
ejpam-5528	56	4	-	-	ADJ
ejpam-5528	56	5	skew	skew	ADJ
ejpam-5528	56	6	jordan	jordan	PROPN
ejpam-5528	56	7	centralizer	centralizer	NOUN
ejpam-5528	56	8	if	if	SCONJ
ejpam-5528	56	9	ω(u	ω(u	PROPN
ejpam-5528	56	10	•	•	NUM
ejpam-5528	56	11	v	v	NOUN
ejpam-5528	56	12	)	)	PUNCT
ejpam-5528	56	13	=	=	SYM
ejpam-5528	56	14	ω(u	ω(u	PROPN
ejpam-5528	56	15	)	)	PUNCT
ejpam-5528	56	16	•	•	NUM
ejpam-5528	56	17	v	v	NOUN
ejpam-5528	56	18	(	(	PUNCT
ejpam-5528	56	19	resp	resp	NOUN
ejpam-5528	56	20	.	.	PUNCT
ejpam-5528	57	1	ω(u	ω(u	NOUN
ejpam-5528	57	2	•	•	NUM
ejpam-5528	57	3	v	v	NOUN
ejpam-5528	57	4	)	)	PUNCT
ejpam-5528	57	5	=	=	SYM
ejpam-5528	57	6	u	u	NOUN
ejpam-5528	57	7	•	•	NOUN
ejpam-5528	57	8	ω(v	ω(v	NOUN
ejpam-5528	57	9	)	)	PUNCT
ejpam-5528	57	10	)	)	PUNCT
ejpam-5528	57	11	for	for	ADP
ejpam-5528	57	12	all	all	DET
ejpam-5528	57	13	u	u	NOUN
ejpam-5528	57	14	,	,	PUNCT
ejpam-5528	57	15	v	v	NOUN
ejpam-5528	57	16	∈	∈	NOUN
ejpam-5528	57	17	ℜ.	ℜ.	ADJ
ejpam-5528	57	18	brešar	brešar	NOUN
ejpam-5528	57	19	and	and	CCONJ
ejpam-5528	57	20	miers	mier	NOUN
ejpam-5528	57	21	[	[	X
ejpam-5528	57	22	24	24	NUM
ejpam-5528	57	23	,	,	PUNCT
ejpam-5528	57	24	theorem	theorem	VERB
ejpam-5528	57	25	5	5	NUM
ejpam-5528	57	26	]	]	PUNCT
ejpam-5528	57	27	proved	prove	VERB
ejpam-5528	57	28	that	that	SCONJ
ejpam-5528	57	29	if	if	SCONJ
ejpam-5528	57	30	ℜ	ℜ	PROPN
ejpam-5528	57	31	is	be	AUX
ejpam-5528	57	32	a	a	DET
ejpam-5528	57	33	semiprime	semiprime	NOUN
ejpam-5528	57	34	ring	ring	NOUN
ejpam-5528	57	35	and	and	CCONJ
ejpam-5528	57	36	ω	ω	NUM
ejpam-5528	57	37	:	:	PUNCT
ejpam-5528	57	38	ℜ	ℜ	PROPN
ejpam-5528	57	39	→	→	SYM
ejpam-5528	57	40	ℜ	ℜ	PROPN
ejpam-5528	57	41	is	be	AUX
ejpam-5528	57	42	an	an	DET
ejpam-5528	57	43	additive	additive	ADJ
ejpam-5528	57	44	strong	strong	ADJ
ejpam-5528	57	45	commutativity	commutativity	NOUN
ejpam-5528	57	46	preserving	preserve	VERB
ejpam-5528	57	47	map	map	NOUN
ejpam-5528	57	48	,	,	PUNCT
ejpam-5528	57	49	then	then	ADV
ejpam-5528	57	50	ω(u	ω(u	PROPN
ejpam-5528	57	51	)	)	PUNCT
ejpam-5528	58	1	=	=	SYM
ejpam-5528	58	2	λu+µ(u	λu+µ(u	PROPN
ejpam-5528	58	3	)	)	PUNCT
ejpam-5528	58	4	for	for	ADP
ejpam-5528	58	5	all	all	DET
ejpam-5528	58	6	u	u	PRON
ejpam-5528	58	7	∈	∈	PROPN
ejpam-5528	58	8	ℜ	ℜ	PROPN
ejpam-5528	58	9	,	,	PUNCT
ejpam-5528	58	10	where	where	SCONJ
ejpam-5528	58	11	λ	λ	PROPN
ejpam-5528	58	12	∈	∈	PROPN
ejpam-5528	58	13	c	c	PROPN
ejpam-5528	58	14	and	and	CCONJ
ejpam-5528	58	15	µ	µ	ADJ
ejpam-5528	58	16	:	:	PUNCT
ejpam-5528	58	17	ℜ	ℜ	PROPN
ejpam-5528	58	18	→	→	SYM
ejpam-5528	58	19	c	c	NOUN
ejpam-5528	58	20	is	be	AUX
ejpam-5528	58	21	an	an	DET
ejpam-5528	58	22	additive	additive	ADJ
ejpam-5528	58	23	map	map	NOUN
ejpam-5528	58	24	.	.	PUNCT
ejpam-5528	59	1	recently	recently	ADV
ejpam-5528	59	2	,	,	PUNCT
ejpam-5528	59	3	several	several	ADJ
ejpam-5528	59	4	authors	author	NOUN
ejpam-5528	59	5	have	have	AUX
ejpam-5528	59	6	studied	study	VERB
ejpam-5528	59	7	strong	strong	ADJ
ejpam-5528	59	8	commutativity	commutativity	NOUN
ejpam-5528	59	9	preserving	preserve	VERB
ejpam-5528	59	10	maps	map	NOUN
ejpam-5528	59	11	(	(	PUNCT
ejpam-5528	59	12	see	see	VERB
ejpam-5528	59	13	[	[	X
ejpam-5528	59	14	8	8	NUM
ejpam-5528	59	15	,	,	PUNCT
ejpam-5528	59	16	10	10	NUM
ejpam-5528	59	17	,	,	PUNCT
ejpam-5528	59	18	11	11	NUM
ejpam-5528	59	19	,	,	PUNCT
ejpam-5528	59	20	15	15	NUM
ejpam-5528	59	21	]	]	NUM
ejpam-5528	59	22	)	)	PUNCT
ejpam-5528	59	23	.	.	PUNCT
ejpam-5528	60	1	strong	strong	ADJ
ejpam-5528	60	2	skew	skew	ADJ
ejpam-5528	60	3	commutativity	commutativity	NOUN
ejpam-5528	60	4	preserving	preserve	VERB
ejpam-5528	60	5	maps	map	NOUN
ejpam-5528	60	6	have	have	AUX
ejpam-5528	60	7	received	receive	VERB
ejpam-5528	60	8	a	a	DET
ejpam-5528	60	9	lot	lot	NOUN
ejpam-5528	60	10	of	of	ADP
ejpam-5528	60	11	attention	attention	NOUN
ejpam-5528	60	12	from	from	ADP
ejpam-5528	60	13	various	various	ADJ
ejpam-5528	60	14	algebraists	algebraist	NOUN
ejpam-5528	60	15	and	and	CCONJ
ejpam-5528	60	16	have	have	AUX
ejpam-5528	60	17	been	be	AUX
ejpam-5528	60	18	widely	widely	ADV
ejpam-5528	60	19	studied	study	VERB
ejpam-5528	60	20	in	in	ADP
ejpam-5528	60	21	the	the	DET
ejpam-5528	60	22	context	context	NOUN
ejpam-5528	60	23	of	of	ADP
ejpam-5528	60	24	rings	ring	NOUN
ejpam-5528	60	25	and	and	CCONJ
ejpam-5528	60	26	algebras	algebras	PROPN
ejpam-5528	60	27	(	(	PUNCT
ejpam-5528	60	28	see	see	VERB
ejpam-5528	60	29	[	[	X
ejpam-5528	60	30	4	4	NUM
ejpam-5528	60	31	,	,	PUNCT
ejpam-5528	60	32	6	6	NUM
ejpam-5528	60	33	,	,	PUNCT
ejpam-5528	60	34	9	9	NUM
ejpam-5528	60	35	,	,	PUNCT
ejpam-5528	60	36	12	12	NUM
ejpam-5528	60	37	,	,	PUNCT
ejpam-5528	60	38	14	14	NUM
ejpam-5528	60	39	]	]	PUNCT
ejpam-5528	60	40	)	)	PUNCT
ejpam-5528	60	41	.	.	PUNCT
ejpam-5528	61	1	quiet	quiet	ADJ
ejpam-5528	61	2	recently	recently	ADV
ejpam-5528	61	3	,	,	PUNCT
ejpam-5528	61	4	siddeeque	siddeeque	NOUN
ejpam-5528	61	5	et	et	PROPN
ejpam-5528	61	6	al	al	PROPN
ejpam-5528	61	7	.	.	PUNCT
ejpam-5528	62	1	[	[	X
ejpam-5528	62	2	25	25	NUM
ejpam-5528	62	3	,	,	PUNCT
ejpam-5528	62	4	theorem	theorem	VERB
ejpam-5528	62	5	2.2	2.2	NUM
ejpam-5528	62	6	]	]	PUNCT
ejpam-5528	62	7	characterized	characterize	VERB
ejpam-5528	62	8	surjective	surjective	ADJ
ejpam-5528	62	9	strong	strong	ADJ
ejpam-5528	62	10	skew	skew	NOUN
ejpam-5528	62	11	commutativity	commutativity	NOUN
ejpam-5528	62	12	moin	moin	PROPN
ejpam-5528	62	13	a.	a.	NOUN
ejpam-5528	62	14	ansari	ansari	PROPN
ejpam-5528	62	15	et	et	PROPN
ejpam-5528	62	16	al	al	PROPN
ejpam-5528	62	17	.	.	PUNCT
ejpam-5528	62	18	/	/	SYM
ejpam-5528	62	19	eur	eur	PROPN
ejpam-5528	62	20	.	.	PUNCT
ejpam-5528	63	1	j.	j.	PROPN
ejpam-5528	63	2	pure	pure	PROPN
ejpam-5528	63	3	appl	appl	PROPN
ejpam-5528	63	4	.	.	PROPN
ejpam-5528	63	5	math	math	PROPN
ejpam-5528	63	6	,	,	PUNCT
ejpam-5528	63	7	18	18	NUM
ejpam-5528	63	8	(	(	PUNCT
ejpam-5528	63	9	2	2	NUM
ejpam-5528	63	10	)	)	PUNCT
ejpam-5528	63	11	(	(	PUNCT
ejpam-5528	63	12	2025	2025	NUM
ejpam-5528	63	13	)	)	PUNCT
ejpam-5528	63	14	,	,	PUNCT
ejpam-5528	63	15	5528	5528	NUM
ejpam-5528	63	16	3	3	NUM
ejpam-5528	63	17	of	of	ADP
ejpam-5528	63	18	14	14	NUM
ejpam-5528	63	19	preserving	preserve	VERB
ejpam-5528	63	20	maps	map	NOUN
ejpam-5528	63	21	in	in	ADP
ejpam-5528	63	22	prime	prime	ADJ
ejpam-5528	63	23	rings	ring	NOUN
ejpam-5528	63	24	without	without	ADP
ejpam-5528	63	25	assuming	assume	VERB
ejpam-5528	63	26	the	the	DET
ejpam-5528	63	27	existence	existence	NOUN
ejpam-5528	63	28	of	of	ADP
ejpam-5528	63	29	the	the	DET
ejpam-5528	63	30	unity	unity	NOUN
ejpam-5528	63	31	and	and	CCONJ
ejpam-5528	63	32	a	a	DET
ejpam-5528	63	33	nontrivial	nontrivial	ADJ
ejpam-5528	63	34	symmetric	symmetric	ADJ
ejpam-5528	63	35	idempotent	idempotent	NOUN
ejpam-5528	63	36	.	.	PUNCT
ejpam-5528	64	1	they	they	PRON
ejpam-5528	64	2	established	establish	VERB
ejpam-5528	64	3	that	that	SCONJ
ejpam-5528	64	4	if	if	SCONJ
ejpam-5528	64	5	ℜ	ℜ	PROPN
ejpam-5528	64	6	is	be	AUX
ejpam-5528	64	7	a	a	DET
ejpam-5528	64	8	prime	prime	ADJ
ejpam-5528	64	9	ring	ring	NOUN
ejpam-5528	64	10	with	with	ADP
ejpam-5528	64	11	an	an	DET
ejpam-5528	64	12	involution	involution	NOUN
ejpam-5528	64	13	‘	'	PUNCT
ejpam-5528	64	14	∗	∗	NOUN
ejpam-5528	64	15	’	'	PUNCT
ejpam-5528	64	16	and	and	CCONJ
ejpam-5528	64	17	ω	ω	NUM
ejpam-5528	64	18	:	:	PUNCT
ejpam-5528	64	19	ℜ	ℜ	PROPN
ejpam-5528	64	20	→	→	SYM
ejpam-5528	64	21	ℜ	ℜ	PROPN
ejpam-5528	64	22	is	be	AUX
ejpam-5528	64	23	a	a	DET
ejpam-5528	64	24	surjective	surjective	ADJ
ejpam-5528	64	25	strong	strong	ADJ
ejpam-5528	64	26	skew	skew	ADJ
ejpam-5528	64	27	commutativity	commutativity	NOUN
ejpam-5528	64	28	preserving	preserve	VERB
ejpam-5528	64	29	map	map	NOUN
ejpam-5528	64	30	,	,	PUNCT
ejpam-5528	64	31	then	then	ADV
ejpam-5528	64	32	there	there	PRON
ejpam-5528	64	33	exists	exist	VERB
ejpam-5528	64	34	λ	λ	PROPN
ejpam-5528	64	35	∈	∈	PROPN
ejpam-5528	64	36	{	{	PUNCT
ejpam-5528	64	37	1,−1	1,−1	NUM
ejpam-5528	64	38	}	}	PUNCT
ejpam-5528	64	39	such	such	ADJ
ejpam-5528	64	40	that	that	SCONJ
ejpam-5528	64	41	ω(a	ω(a	NUM
ejpam-5528	64	42	)	)	PUNCT
ejpam-5528	64	43	=	=	SYM
ejpam-5528	65	1	λa	λa	NOUN
ejpam-5528	65	2	for	for	ADP
ejpam-5528	65	3	all	all	DET
ejpam-5528	65	4	a	a	DET
ejpam-5528	65	5	∈	∈	NOUN
ejpam-5528	65	6	ℜ.	ℜ.	PROPN
ejpam-5528	65	7	qi	qi	PROPN
ejpam-5528	65	8	and	and	CCONJ
ejpam-5528	65	9	chen	chen	PROPN
ejpam-5528	66	1	[	[	X
ejpam-5528	66	2	16	16	NUM
ejpam-5528	66	3	,	,	PUNCT
ejpam-5528	66	4	theorem	theorem	VERB
ejpam-5528	66	5	2.1	2.1	NUM
ejpam-5528	66	6	]	]	PUNCT
ejpam-5528	66	7	characterized	characterize	VERB
ejpam-5528	66	8	surjective	surjective	ADJ
ejpam-5528	66	9	strong	strong	ADJ
ejpam-5528	66	10	bi	bi	ADJ
ejpam-5528	66	11	-	-	ADJ
ejpam-5528	66	12	skew	skew	ADJ
ejpam-5528	66	13	commutativity	commutativity	NOUN
ejpam-5528	66	14	preserving	preserve	VERB
ejpam-5528	66	15	maps	map	NOUN
ejpam-5528	66	16	on	on	ADP
ejpam-5528	66	17	prime	prime	ADJ
ejpam-5528	66	18	∗algebras	∗algebra	NOUN
ejpam-5528	66	19	.	.	PUNCT
ejpam-5528	67	1	consequently	consequently	ADV
ejpam-5528	67	2	,	,	PUNCT
ejpam-5528	67	3	they	they	PRON
ejpam-5528	67	4	proved	prove	VERB
ejpam-5528	67	5	the	the	DET
ejpam-5528	67	6	following	follow	VERB
ejpam-5528	67	7	result	result	NOUN
ejpam-5528	67	8	:	:	PUNCT
ejpam-5528	67	9	let	let	VERB
ejpam-5528	67	10	a	a	PRON
ejpam-5528	67	11	be	be	AUX
ejpam-5528	67	12	a	a	DET
ejpam-5528	67	13	prime	prime	ADJ
ejpam-5528	67	14	∗-algebra	∗-algebra	NOUN
ejpam-5528	67	15	,	,	PUNCT
ejpam-5528	67	16	over	over	ADP
ejpam-5528	67	17	a	a	DET
ejpam-5528	67	18	field	field	NOUN
ejpam-5528	67	19	k	k	NOUN
ejpam-5528	67	20	,	,	PUNCT
ejpam-5528	67	21	with	with	ADP
ejpam-5528	67	22	unity	unity	NOUN
ejpam-5528	67	23	i	i	PRON
ejpam-5528	67	24	and	and	CCONJ
ejpam-5528	67	25	containing	contain	VERB
ejpam-5528	67	26	a	a	DET
ejpam-5528	67	27	nontrivial	nontrivial	ADJ
ejpam-5528	67	28	symmetric	symmetric	ADJ
ejpam-5528	67	29	idempotent	idempotent	NOUN
ejpam-5528	67	30	.	.	PUNCT
ejpam-5528	68	1	suppose	suppose	VERB
ejpam-5528	68	2	that	that	SCONJ
ejpam-5528	68	3	‘	'	PUNCT
ejpam-5528	68	4	∗	∗	NOUN
ejpam-5528	68	5	’	'	PUNCT
ejpam-5528	68	6	is	be	AUX
ejpam-5528	68	7	of	of	ADP
ejpam-5528	68	8	the	the	DET
ejpam-5528	68	9	second	second	ADJ
ejpam-5528	68	10	kind	kind	NOUN
ejpam-5528	68	11	on	on	ADP
ejpam-5528	68	12	z(a	z(a	NOUN
ejpam-5528	68	13	)	)	PUNCT
ejpam-5528	68	14	and	and	CCONJ
ejpam-5528	68	15	ψ(i)ψ(i)∗	ψ(i)ψ(i)∗	X
ejpam-5528	68	16	=	=	SYM
ejpam-5528	68	17	ψ(i)∗ψ(i	ψ(i)∗ψ(i	PROPN
ejpam-5528	68	18	)	)	PUNCT
ejpam-5528	69	1	=	=	SYM
ejpam-5528	69	2	i.	i.	NOUN
ejpam-5528	69	3	if	if	SCONJ
ejpam-5528	69	4	ψ	ψ	X
ejpam-5528	69	5	:	:	PUNCT
ejpam-5528	69	6	a	a	PRON
ejpam-5528	69	7	→	→	X
ejpam-5528	69	8	a	a	PRON
ejpam-5528	69	9	is	be	AUX
ejpam-5528	69	10	a	a	DET
ejpam-5528	69	11	surjective	surjective	ADJ
ejpam-5528	69	12	strong	strong	ADJ
ejpam-5528	69	13	bi	bi	ADJ
ejpam-5528	69	14	-	-	ADJ
ejpam-5528	69	15	skew	skew	ADJ
ejpam-5528	69	16	commutativity	commutativity	NOUN
ejpam-5528	69	17	preserving	preserve	VERB
ejpam-5528	69	18	map	map	NOUN
ejpam-5528	69	19	,	,	PUNCT
ejpam-5528	69	20	then	then	ADV
ejpam-5528	69	21	ψ(u	ψ(u	PROPN
ejpam-5528	69	22	)	)	PUNCT
ejpam-5528	69	23	=	=	SYM
ejpam-5528	69	24	αuψ(i	αuψ(i	PROPN
ejpam-5528	69	25	)	)	PUNCT
ejpam-5528	69	26	for	for	ADP
ejpam-5528	69	27	all	all	PRON
ejpam-5528	69	28	u	u	PROPN
ejpam-5528	69	29	∈	∈	PROPN
ejpam-5528	69	30	a	a	PRON
ejpam-5528	69	31	,	,	PUNCT
ejpam-5528	69	32	where	where	SCONJ
ejpam-5528	69	33	α∗	α∗	NOUN
ejpam-5528	69	34	=	=	PUNCT
ejpam-5528	69	35	α	α	NOUN
ejpam-5528	69	36	∈	∈	PROPN
ejpam-5528	69	37	c	c	PROPN
ejpam-5528	69	38	and	and	CCONJ
ejpam-5528	69	39	α2	α2	PROPN
ejpam-5528	69	40	=	=	SYM
ejpam-5528	69	41	i.	i.	PROPN
ejpam-5528	69	42	khong	khong	PROPN
ejpam-5528	69	43	and	and	CCONJ
ejpam-5528	69	44	zhang	zhang	PROPN
ejpam-5528	70	1	[	[	X
ejpam-5528	70	2	17	17	NUM
ejpam-5528	70	3	]	]	PUNCT
ejpam-5528	70	4	showed	show	VERB
ejpam-5528	70	5	,	,	PUNCT
ejpam-5528	70	6	under	under	ADP
ejpam-5528	70	7	certain	certain	ADJ
ejpam-5528	70	8	restrictions	restriction	NOUN
ejpam-5528	70	9	,	,	PUNCT
ejpam-5528	70	10	that	that	SCONJ
ejpam-5528	70	11	if	if	SCONJ
ejpam-5528	70	12	ℜ	ℜ	PROPN
ejpam-5528	70	13	is	be	AUX
ejpam-5528	70	14	a	a	DET
ejpam-5528	70	15	unital	unital	ADJ
ejpam-5528	70	16	∗-ring	∗-ring	NOUN
ejpam-5528	70	17	containing	contain	VERB
ejpam-5528	70	18	a	a	DET
ejpam-5528	70	19	nontrivial	nontrivial	ADJ
ejpam-5528	70	20	symmetric	symmetric	ADJ
ejpam-5528	70	21	idempotent	idempotent	NOUN
ejpam-5528	70	22	and	and	CCONJ
ejpam-5528	70	23	ω	ω	NUM
ejpam-5528	70	24	:	:	PUNCT
ejpam-5528	70	25	ℜ	ℜ	PROPN
ejpam-5528	70	26	→	→	SYM
ejpam-5528	70	27	ℜ	ℜ	PROPN
ejpam-5528	70	28	is	be	AUX
ejpam-5528	70	29	a	a	DET
ejpam-5528	70	30	skew	skew	ADJ
ejpam-5528	70	31	commutating	commutate	VERB
ejpam-5528	70	32	map	map	NOUN
ejpam-5528	70	33	,	,	PUNCT
ejpam-5528	70	34	then	then	ADV
ejpam-5528	70	35	there	there	PRON
ejpam-5528	70	36	exists	exist	VERB
ejpam-5528	70	37	λ∗	λ∗	NOUN
ejpam-5528	70	38	=	=	PUNCT
ejpam-5528	70	39	λ	λ	X
ejpam-5528	70	40	∈	∈	PROPN
ejpam-5528	70	41	z(ℜ	z(ℜ	NUM
ejpam-5528	70	42	)	)	PUNCT
ejpam-5528	70	43	such	such	ADJ
ejpam-5528	70	44	that	that	SCONJ
ejpam-5528	70	45	ω(a	ω(a	NUM
ejpam-5528	70	46	)	)	PUNCT
ejpam-5528	70	47	=	=	SYM
ejpam-5528	71	1	λa	λa	NOUN
ejpam-5528	71	2	for	for	ADP
ejpam-5528	71	3	all	all	DET
ejpam-5528	71	4	a	a	DET
ejpam-5528	71	5	∈	∈	NOUN
ejpam-5528	71	6	ℜ.	ℜ.	PROPN
ejpam-5528	71	7	recently	recently	ADV
ejpam-5528	71	8	,	,	PUNCT
ejpam-5528	71	9	siddeeque	siddeeque	NOUN
ejpam-5528	71	10	et	et	PROPN
ejpam-5528	71	11	al	al	PROPN
ejpam-5528	71	12	.	.	PUNCT
ejpam-5528	72	1	[	[	X
ejpam-5528	72	2	25	25	NUM
ejpam-5528	72	3	,	,	PUNCT
ejpam-5528	72	4	theorem	theorem	VERB
ejpam-5528	72	5	2.3	2.3	NUM
ejpam-5528	72	6	]	]	PUNCT
ejpam-5528	72	7	characterized	characterize	VERB
ejpam-5528	72	8	skew	skew	NOUN
ejpam-5528	72	9	commutating	commutate	VERB
ejpam-5528	72	10	maps	map	NOUN
ejpam-5528	72	11	in	in	ADP
ejpam-5528	72	12	prime	prime	ADJ
ejpam-5528	72	13	rings	ring	NOUN
ejpam-5528	72	14	without	without	ADP
ejpam-5528	72	15	assuming	assume	VERB
ejpam-5528	72	16	the	the	DET
ejpam-5528	72	17	existence	existence	NOUN
ejpam-5528	72	18	of	of	ADP
ejpam-5528	72	19	the	the	DET
ejpam-5528	72	20	unity	unity	NOUN
ejpam-5528	72	21	and	and	CCONJ
ejpam-5528	72	22	a	a	DET
ejpam-5528	72	23	nontrivial	nontrivial	ADJ
ejpam-5528	72	24	symmetric	symmetric	ADJ
ejpam-5528	72	25	idempotent	idempotent	NOUN
ejpam-5528	72	26	.	.	PUNCT
ejpam-5528	73	1	they	they	PRON
ejpam-5528	73	2	established	establish	VERB
ejpam-5528	73	3	that	that	SCONJ
ejpam-5528	73	4	if	if	SCONJ
ejpam-5528	73	5	ℜ	ℜ	PROPN
ejpam-5528	73	6	is	be	AUX
ejpam-5528	73	7	a	a	DET
ejpam-5528	73	8	prime	prime	ADJ
ejpam-5528	73	9	ring	ring	NOUN
ejpam-5528	73	10	with	with	ADP
ejpam-5528	73	11	an	an	DET
ejpam-5528	73	12	involution	involution	NOUN
ejpam-5528	73	13	‘	'	PUNCT
ejpam-5528	73	14	∗	∗	NOUN
ejpam-5528	73	15	’	'	PUNCT
ejpam-5528	73	16	and	and	CCONJ
ejpam-5528	73	17	ω	ω	NUM
ejpam-5528	73	18	:	:	PUNCT
ejpam-5528	73	19	ℜ	ℜ	PROPN
ejpam-5528	73	20	→	→	SYM
ejpam-5528	73	21	ℜ	ℜ	PROPN
ejpam-5528	73	22	is	be	AUX
ejpam-5528	73	23	a	a	DET
ejpam-5528	73	24	skew	skew	ADJ
ejpam-5528	73	25	commutating	commutate	VERB
ejpam-5528	73	26	map	map	NOUN
ejpam-5528	73	27	,	,	PUNCT
ejpam-5528	73	28	then	then	ADV
ejpam-5528	73	29	there	there	PRON
ejpam-5528	73	30	exists	exist	VERB
ejpam-5528	73	31	λ∗	λ∗	NOUN
ejpam-5528	74	1	=	=	PUNCT
ejpam-5528	74	2	λ	λ	X
ejpam-5528	74	3	∈	∈	PROPN
ejpam-5528	74	4	c	c	NOUN
ejpam-5528	74	5	such	such	ADJ
ejpam-5528	74	6	that	that	SCONJ
ejpam-5528	74	7	ω(a	ω(a	NUM
ejpam-5528	74	8	)	)	PUNCT
ejpam-5528	74	9	=	=	SYM
ejpam-5528	75	1	λa	λa	NOUN
ejpam-5528	75	2	for	for	ADP
ejpam-5528	75	3	all	all	DET
ejpam-5528	75	4	a	a	DET
ejpam-5528	75	5	∈	∈	NOUN
ejpam-5528	75	6	ℜ.	ℜ.	PROPN
ejpam-5528	75	7	motivated	motivate	VERB
ejpam-5528	75	8	by	by	ADP
ejpam-5528	75	9	the	the	DET
ejpam-5528	75	10	above	above	ADJ
ejpam-5528	75	11	results	result	NOUN
ejpam-5528	75	12	,	,	PUNCT
ejpam-5528	75	13	in	in	ADP
ejpam-5528	75	14	section	section	NOUN
ejpam-5528	75	15	2	2	NUM
ejpam-5528	75	16	of	of	ADP
ejpam-5528	75	17	the	the	DET
ejpam-5528	75	18	present	present	ADJ
ejpam-5528	75	19	paper	paper	NOUN
ejpam-5528	75	20	,	,	PUNCT
ejpam-5528	75	21	we	we	PRON
ejpam-5528	75	22	will	will	AUX
ejpam-5528	75	23	characterize	characterize	VERB
ejpam-5528	75	24	surjective	surjective	ADJ
ejpam-5528	75	25	strong	strong	ADJ
ejpam-5528	75	26	bi	bi	ADJ
ejpam-5528	75	27	-	-	ADJ
ejpam-5528	75	28	skew	skew	ADJ
ejpam-5528	75	29	commutativity	commutativity	NOUN
ejpam-5528	75	30	preserving	preserve	VERB
ejpam-5528	75	31	maps	map	NOUN
ejpam-5528	75	32	and	and	CCONJ
ejpam-5528	75	33	bi	bi	NOUN
ejpam-5528	75	34	-	-	ADJ
ejpam-5528	75	35	skew	skew	ADJ
ejpam-5528	75	36	commutating	commutating	NOUN
ejpam-5528	75	37	maps	map	NOUN
ejpam-5528	75	38	in	in	ADP
ejpam-5528	75	39	prime	prime	ADJ
ejpam-5528	75	40	rings	ring	NOUN
ejpam-5528	75	41	without	without	ADP
ejpam-5528	75	42	assuming	assume	VERB
ejpam-5528	75	43	the	the	DET
ejpam-5528	75	44	existence	existence	NOUN
ejpam-5528	75	45	of	of	ADP
ejpam-5528	75	46	the	the	DET
ejpam-5528	75	47	unity	unity	NOUN
ejpam-5528	75	48	and	and	CCONJ
ejpam-5528	75	49	a	a	DET
ejpam-5528	75	50	nontrivial	nontrivial	ADJ
ejpam-5528	75	51	symmetric	symmetric	ADJ
ejpam-5528	75	52	idempotent	idempotent	NOUN
ejpam-5528	75	53	(	(	PUNCT
ejpam-5528	75	54	see	see	VERB
ejpam-5528	75	55	theorems	theorem	NOUN
ejpam-5528	75	56	2.1	2.1	NUM
ejpam-5528	75	57	and	and	CCONJ
ejpam-5528	75	58	2.2	2.2	NUM
ejpam-5528	75	59	)	)	PUNCT
ejpam-5528	75	60	.	.	PUNCT
ejpam-5528	76	1	as	as	ADP
ejpam-5528	76	2	applications	application	NOUN
ejpam-5528	76	3	,	,	PUNCT
ejpam-5528	76	4	we	we	PRON
ejpam-5528	76	5	will	will	AUX
ejpam-5528	76	6	characterize	characterize	VERB
ejpam-5528	76	7	such	such	ADJ
ejpam-5528	76	8	maps	map	NOUN
ejpam-5528	76	9	in	in	ADP
ejpam-5528	76	10	different	different	ADJ
ejpam-5528	76	11	operator	operator	NOUN
ejpam-5528	76	12	algebras	algebra	NOUN
ejpam-5528	76	13	.	.	PUNCT
ejpam-5528	77	1	skew	skew	PROPN
ejpam-5528	77	2	lie	lie	NOUN
ejpam-5528	77	3	,	,	PUNCT
ejpam-5528	77	4	skew	skew	ADJ
ejpam-5528	77	5	jordan	jordan	PROPN
ejpam-5528	77	6	and	and	CCONJ
ejpam-5528	77	7	bi	bi	PROPN
ejpam-5528	77	8	-	-	ADJ
ejpam-5528	77	9	skew	skew	ADJ
ejpam-5528	77	10	jordan	jordan	PROPN
ejpam-5528	77	11	derivations	derivation	NOUN
ejpam-5528	77	12	have	have	AUX
ejpam-5528	77	13	been	be	AUX
ejpam-5528	77	14	explored	explore	VERB
ejpam-5528	77	15	by	by	ADP
ejpam-5528	77	16	various	various	ADJ
ejpam-5528	77	17	algebraists	algebraist	NOUN
ejpam-5528	77	18	in	in	ADP
ejpam-5528	77	19	the	the	DET
ejpam-5528	77	20	context	context	NOUN
ejpam-5528	77	21	of	of	ADP
ejpam-5528	77	22	algebras	algebra	NOUN
ejpam-5528	77	23	and	and	CCONJ
ejpam-5528	77	24	rings	ring	NOUN
ejpam-5528	77	25	(	(	PUNCT
ejpam-5528	77	26	see	see	VERB
ejpam-5528	77	27	[	[	X
ejpam-5528	77	28	7	7	NUM
ejpam-5528	77	29	,	,	PUNCT
ejpam-5528	77	30	18	18	NUM
ejpam-5528	77	31	,	,	PUNCT
ejpam-5528	77	32	21	21	NUM
ejpam-5528	77	33	,	,	PUNCT
ejpam-5528	77	34	22	22	NUM
ejpam-5528	77	35	]	]	PUNCT
ejpam-5528	77	36	and	and	CCONJ
ejpam-5528	77	37	their	their	PRON
ejpam-5528	77	38	bibliographic	bibliographic	ADJ
ejpam-5528	77	39	content	content	NOUN
ejpam-5528	77	40	)	)	PUNCT
ejpam-5528	77	41	.	.	PUNCT
ejpam-5528	78	1	very	very	ADV
ejpam-5528	78	2	recently	recently	ADV
ejpam-5528	78	3	,	,	PUNCT
ejpam-5528	78	4	siddeeque	siddeeque	NOUN
ejpam-5528	78	5	and	and	CCONJ
ejpam-5528	78	6	shikeh	shikeh	NOUN
ejpam-5528	79	1	[	[	X
ejpam-5528	79	2	20	20	NUM
ejpam-5528	79	3	]	]	PUNCT
ejpam-5528	79	4	characterized	characterize	VERB
ejpam-5528	79	5	bi	bi	PROPN
ejpam-5528	79	6	-	-	ADJ
ejpam-5528	79	7	skew	skew	ADJ
ejpam-5528	79	8	jordan	jordan	PROPN
ejpam-5528	79	9	derivations	derivation	NOUN
ejpam-5528	79	10	in	in	ADP
ejpam-5528	79	11	prime	prime	ADJ
ejpam-5528	79	12	rings	ring	NOUN
ejpam-5528	80	1	and	and	CCONJ
ejpam-5528	80	2	proved	prove	VERB
ejpam-5528	80	3	that	that	SCONJ
ejpam-5528	80	4	every	every	DET
ejpam-5528	80	5	bi	bi	ADJ
ejpam-5528	80	6	-	-	ADJ
ejpam-5528	80	7	skew	skew	ADJ
ejpam-5528	80	8	jordan	jordan	PROPN
ejpam-5528	80	9	derivation	derivation	NOUN
ejpam-5528	80	10	on	on	ADP
ejpam-5528	80	11	a	a	DET
ejpam-5528	80	12	unital	unital	ADJ
ejpam-5528	80	13	prime	prime	NOUN
ejpam-5528	80	14	∗-ring	∗-ring	NOUN
ejpam-5528	80	15	containing	contain	VERB
ejpam-5528	80	16	a	a	DET
ejpam-5528	80	17	nontrivial	nontrivial	ADJ
ejpam-5528	80	18	symmetric	symmetric	ADJ
ejpam-5528	80	19	idempotent	idempotent	NOUN
ejpam-5528	80	20	is	be	AUX
ejpam-5528	80	21	an	an	DET
ejpam-5528	80	22	additive	additive	ADJ
ejpam-5528	80	23	∗-derivation	∗-derivation	NOUN
ejpam-5528	80	24	.	.	PUNCT
ejpam-5528	81	1	in	in	ADP
ejpam-5528	81	2	section	section	NOUN
ejpam-5528	81	3	3	3	NUM
ejpam-5528	81	4	,	,	PUNCT
ejpam-5528	81	5	we	we	PRON
ejpam-5528	81	6	will	will	AUX
ejpam-5528	81	7	characterize	characterize	VERB
ejpam-5528	81	8	generalized	generalized	ADJ
ejpam-5528	81	9	bi	bi	ADJ
ejpam-5528	81	10	-	-	ADJ
ejpam-5528	81	11	skew	skew	ADJ
ejpam-5528	81	12	jordan	jordan	PROPN
ejpam-5528	81	13	derivations	derivation	NOUN
ejpam-5528	81	14	in	in	ADP
ejpam-5528	81	15	prime	prime	ADJ
ejpam-5528	81	16	rings	ring	NOUN
ejpam-5528	81	17	(	(	PUNCT
ejpam-5528	81	18	see	see	VERB
ejpam-5528	81	19	theorem	theorem	NOUN
ejpam-5528	81	20	3.2	3.2	NUM
ejpam-5528	81	21	)	)	PUNCT
ejpam-5528	81	22	.	.	PUNCT
ejpam-5528	82	1	as	as	ADP
ejpam-5528	82	2	applications	application	NOUN
ejpam-5528	82	3	,	,	PUNCT
ejpam-5528	82	4	we	we	PRON
ejpam-5528	82	5	will	will	AUX
ejpam-5528	82	6	characterize	characterize	VERB
ejpam-5528	82	7	generalized	generalized	ADJ
ejpam-5528	82	8	bi	bi	ADJ
ejpam-5528	82	9	-	-	ADJ
ejpam-5528	82	10	skew	skew	ADJ
ejpam-5528	82	11	jordan	jordan	PROPN
ejpam-5528	82	12	derivations	derivation	NOUN
ejpam-5528	82	13	in	in	ADP
ejpam-5528	82	14	different	different	ADJ
ejpam-5528	82	15	operator	operator	NOUN
ejpam-5528	82	16	algebras	algebra	NOUN
ejpam-5528	82	17	.	.	PUNCT
ejpam-5528	83	1	2	2	X
ejpam-5528	83	2	.	.	X
ejpam-5528	83	3	strong	strong	ADJ
ejpam-5528	83	4	bi	bi	ADJ
ejpam-5528	83	5	-	-	ADJ
ejpam-5528	83	6	skew	skew	ADJ
ejpam-5528	83	7	commutativity	commutativity	NOUN
ejpam-5528	83	8	preserving	preserve	VERB
ejpam-5528	83	9	maps	map	NOUN
ejpam-5528	83	10	and	and	CCONJ
ejpam-5528	83	11	bi	bi	NOUN
ejpam-5528	83	12	-	-	ADJ
ejpam-5528	83	13	skew	skew	ADJ
ejpam-5528	83	14	commuting	commuting	NOUN
ejpam-5528	83	15	maps	map	NOUN
ejpam-5528	83	16	in	in	ADP
ejpam-5528	83	17	prime	prime	ADJ
ejpam-5528	83	18	rings	ring	NOUN
ejpam-5528	83	19	we	we	PRON
ejpam-5528	83	20	facilitate	facilitate	VERB
ejpam-5528	83	21	our	our	PRON
ejpam-5528	83	22	discussion	discussion	NOUN
ejpam-5528	83	23	with	with	ADP
ejpam-5528	83	24	the	the	DET
ejpam-5528	83	25	following	follow	VERB
ejpam-5528	83	26	lemma	lemma	PROPN
ejpam-5528	83	27	which	which	PRON
ejpam-5528	83	28	plays	play	VERB
ejpam-5528	83	29	a	a	DET
ejpam-5528	83	30	crucial	crucial	ADJ
ejpam-5528	83	31	role	role	NOUN
ejpam-5528	83	32	in	in	ADP
ejpam-5528	83	33	the	the	DET
ejpam-5528	83	34	proof	proof	NOUN
ejpam-5528	83	35	of	of	ADP
ejpam-5528	83	36	our	our	PRON
ejpam-5528	83	37	main	main	ADJ
ejpam-5528	83	38	results	result	NOUN
ejpam-5528	83	39	.	.	PUNCT
ejpam-5528	84	1	lemma	lemma	PROPN
ejpam-5528	84	2	2.1	2.1	NUM
ejpam-5528	84	3	.	.	PUNCT
ejpam-5528	85	1	let	let	VERB
ejpam-5528	85	2	ℜ	ℜ	PROPN
ejpam-5528	85	3	be	be	AUX
ejpam-5528	85	4	a	a	DET
ejpam-5528	85	5	prime	prime	ADJ
ejpam-5528	85	6	ring	ring	NOUN
ejpam-5528	85	7	with	with	ADP
ejpam-5528	85	8	an	an	DET
ejpam-5528	85	9	involution	involution	NOUN
ejpam-5528	85	10	‘	'	PUNCT
ejpam-5528	85	11	∗	∗	NOUN
ejpam-5528	85	12	’	'	PUNCT
ejpam-5528	85	13	of	of	ADP
ejpam-5528	85	14	order	order	NOUN
ejpam-5528	85	15	2	2	NUM
ejpam-5528	85	16	and	and	CCONJ
ejpam-5528	85	17	let	let	VERB
ejpam-5528	85	18	a	a	DET
ejpam-5528	85	19	,	,	PUNCT
ejpam-5528	85	20	b	b	PROPN
ejpam-5528	85	21	∈	∈	PROPN
ejpam-5528	85	22	qml(ℜ	qml(ℜ	NOUN
ejpam-5528	85	23	)	)	PUNCT
ejpam-5528	85	24	such	such	ADJ
ejpam-5528	85	25	that	that	DET
ejpam-5528	85	26	bu∗	bu∗	NOUN
ejpam-5528	85	27	=	=	PUNCT
ejpam-5528	85	28	ua	ua	PROPN
ejpam-5528	85	29	for	for	ADP
ejpam-5528	85	30	all	all	DET
ejpam-5528	85	31	u	u	NOUN
ejpam-5528	85	32	∈	∈	PROPN
ejpam-5528	85	33	ℜ.	ℜ.	PROPN
ejpam-5528	85	34	then	then	ADV
ejpam-5528	85	35	a	a	DET
ejpam-5528	85	36	=	=	SYM
ejpam-5528	85	37	b	b	NOUN
ejpam-5528	85	38	=	=	SYM
ejpam-5528	85	39	0	0	PROPN
ejpam-5528	85	40	.	.	PUNCT
ejpam-5528	86	1	proof	proof	NOUN
ejpam-5528	86	2	.	.	PUNCT
ejpam-5528	87	1	if	if	SCONJ
ejpam-5528	87	2	ℜ	ℜ	PROPN
ejpam-5528	87	3	is	be	AUX
ejpam-5528	87	4	noncommutative	noncommutative	ADJ
ejpam-5528	87	5	,	,	PUNCT
ejpam-5528	87	6	then	then	ADV
ejpam-5528	87	7	by	by	ADP
ejpam-5528	87	8	[	[	X
ejpam-5528	87	9	20	20	NUM
ejpam-5528	87	10	,	,	PUNCT
ejpam-5528	87	11	lemma	lemma	PROPN
ejpam-5528	87	12	2.1	2.1	NUM
ejpam-5528	87	13	]	]	PUNCT
ejpam-5528	87	14	,	,	PUNCT
ejpam-5528	87	15	the	the	DET
ejpam-5528	87	16	result	result	NOUN
ejpam-5528	87	17	follows	follow	VERB
ejpam-5528	87	18	.	.	PUNCT
ejpam-5528	88	1	therefore	therefore	ADV
ejpam-5528	88	2	,	,	PUNCT
ejpam-5528	88	3	let	let	VERB
ejpam-5528	88	4	’s	’s	PRON
ejpam-5528	88	5	assume	assume	VERB
ejpam-5528	88	6	that	that	SCONJ
ejpam-5528	88	7	ℜ	ℜ	PROPN
ejpam-5528	88	8	is	be	AUX
ejpam-5528	88	9	commutative	commutative	ADJ
ejpam-5528	88	10	.	.	PUNCT
ejpam-5528	89	1	thus	thus	ADV
ejpam-5528	89	2	,	,	PUNCT
ejpam-5528	89	3	α∗	α∗	VERB
ejpam-5528	89	4	̸=	̸=	PROPN
ejpam-5528	89	5	α	α	NOUN
ejpam-5528	89	6	for	for	ADP
ejpam-5528	89	7	some	some	DET
ejpam-5528	89	8	α	α	NOUN
ejpam-5528	89	9	∈	∈	NOUN
ejpam-5528	89	10	ℜ.	ℜ.	PROPN
ejpam-5528	89	11	substituting	substitute	VERB
ejpam-5528	89	12	αu	αu	NOUN
ejpam-5528	89	13	for	for	ADP
ejpam-5528	89	14	u	u	PROPN
ejpam-5528	89	15	in	in	ADP
ejpam-5528	89	16	the	the	DET
ejpam-5528	89	17	given	give	VERB
ejpam-5528	89	18	relation	relation	NOUN
ejpam-5528	89	19	,	,	PUNCT
ejpam-5528	89	20	we	we	PRON
ejpam-5528	89	21	find	find	VERB
ejpam-5528	89	22	that	that	SCONJ
ejpam-5528	89	23	bα∗u∗	bα∗u∗	NOUN
ejpam-5528	89	24	=	=	SYM
ejpam-5528	89	25	αua	αua	NOUN
ejpam-5528	89	26	for	for	ADP
ejpam-5528	89	27	all	all	DET
ejpam-5528	89	28	u	u	NOUN
ejpam-5528	89	29	∈	∈	PROPN
ejpam-5528	89	30	ℜ.	ℜ.	PROPN
ejpam-5528	89	31	also	also	ADV
ejpam-5528	89	32	,	,	PUNCT
ejpam-5528	89	33	αbu∗	αbu∗	NOUN
ejpam-5528	89	34	=	=	SYM
ejpam-5528	89	35	αua	αua	NOUN
ejpam-5528	89	36	for	for	ADP
ejpam-5528	89	37	all	all	PRON
ejpam-5528	89	38	u	u	NOUN
ejpam-5528	89	39	∈	∈	NOUN
ejpam-5528	89	40	ℜ.	ℜ.	PROPN
ejpam-5528	89	41	hence	hence	ADV
ejpam-5528	89	42	,	,	PUNCT
ejpam-5528	89	43	(	(	PUNCT
ejpam-5528	89	44	α∗	α∗	VERB
ejpam-5528	89	45	−	−	NOUN
ejpam-5528	89	46	α)bu∗	α)bu∗	NOUN
ejpam-5528	89	47	=	=	NOUN
ejpam-5528	89	48	0	0	NUM
ejpam-5528	89	49	for	for	ADP
ejpam-5528	89	50	all	all	DET
ejpam-5528	89	51	u	u	PROPN
ejpam-5528	89	52	∈	∈	PROPN
ejpam-5528	89	53	ℜ.	ℜ.	PROPN
ejpam-5528	89	54	therefore	therefore	ADV
ejpam-5528	89	55	,	,	PUNCT
ejpam-5528	89	56	b	b	X
ejpam-5528	89	57	=	=	SYM
ejpam-5528	89	58	0	0	NUM
ejpam-5528	89	59	and	and	CCONJ
ejpam-5528	89	60	consequently	consequently	ADV
ejpam-5528	89	61	,	,	PUNCT
ejpam-5528	89	62	a	a	PRON
ejpam-5528	89	63	=	=	SYM
ejpam-5528	89	64	0	0	NUM
ejpam-5528	89	65	.	.	PUNCT
ejpam-5528	90	1	moin	moin	PROPN
ejpam-5528	90	2	a.	a.	PROPN
ejpam-5528	90	3	ansari	ansari	PROPN
ejpam-5528	90	4	et	et	PROPN
ejpam-5528	90	5	al	al	PROPN
ejpam-5528	90	6	.	.	PUNCT
ejpam-5528	90	7	/	/	SYM
ejpam-5528	90	8	eur	eur	PROPN
ejpam-5528	90	9	.	.	PUNCT
ejpam-5528	91	1	j.	j.	PROPN
ejpam-5528	91	2	pure	pure	PROPN
ejpam-5528	91	3	appl	appl	PROPN
ejpam-5528	91	4	.	.	PROPN
ejpam-5528	91	5	math	math	PROPN
ejpam-5528	91	6	,	,	PUNCT
ejpam-5528	91	7	18	18	NUM
ejpam-5528	91	8	(	(	PUNCT
ejpam-5528	91	9	2	2	NUM
ejpam-5528	91	10	)	)	PUNCT
ejpam-5528	91	11	(	(	PUNCT
ejpam-5528	91	12	2025	2025	NUM
ejpam-5528	91	13	)	)	PUNCT
ejpam-5528	91	14	,	,	PUNCT
ejpam-5528	91	15	5528	5528	NUM
ejpam-5528	91	16	4	4	NUM
ejpam-5528	91	17	of	of	ADP
ejpam-5528	91	18	14	14	NUM
ejpam-5528	91	19	lemma	lemma	PROPN
ejpam-5528	91	20	2.2	2.2	NUM
ejpam-5528	91	21	.	.	PUNCT
ejpam-5528	92	1	let	let	VERB
ejpam-5528	92	2	ℜ	ℜ	PROPN
ejpam-5528	92	3	be	be	AUX
ejpam-5528	92	4	a	a	DET
ejpam-5528	92	5	prime	prime	ADJ
ejpam-5528	92	6	pi	pi	NOUN
ejpam-5528	92	7	-	-	PUNCT
ejpam-5528	92	8	ring	ring	NOUN
ejpam-5528	92	9	with	with	ADP
ejpam-5528	92	10	an	an	DET
ejpam-5528	92	11	anti	anti	ADJ
ejpam-5528	92	12	-	-	ADJ
ejpam-5528	92	13	automorphism	automorphism	ADJ
ejpam-5528	92	14	∇.	∇.	NOUN
ejpam-5528	92	15	then	then	ADV
ejpam-5528	92	16	∇	∇	PROPN
ejpam-5528	92	17	is	be	AUX
ejpam-5528	92	18	of	of	ADP
ejpam-5528	92	19	first	first	ADJ
ejpam-5528	92	20	kind	kind	NOUN
ejpam-5528	92	21	if	if	SCONJ
ejpam-5528	92	22	and	and	CCONJ
ejpam-5528	92	23	only	only	ADV
ejpam-5528	92	24	if	if	SCONJ
ejpam-5528	92	25	∇	∇	NOUN
ejpam-5528	92	26	is	be	AUX
ejpam-5528	92	27	of	of	ADP
ejpam-5528	92	28	the	the	DET
ejpam-5528	92	29	first	first	ADJ
ejpam-5528	92	30	kind	kind	NOUN
ejpam-5528	92	31	on	on	ADP
ejpam-5528	92	32	z(ℜ	z(ℜ	NUM
ejpam-5528	92	33	)	)	PUNCT
ejpam-5528	92	34	.	.	PUNCT
ejpam-5528	93	1	proof	proof	NOUN
ejpam-5528	93	2	.	.	PUNCT
ejpam-5528	94	1	by	by	ADP
ejpam-5528	94	2	[	[	X
ejpam-5528	94	3	26	26	NUM
ejpam-5528	94	4	,	,	PUNCT
ejpam-5528	94	5	corollary	corollary	ADJ
ejpam-5528	94	6	1	1	NUM
ejpam-5528	94	7	]	]	PUNCT
ejpam-5528	94	8	,	,	PUNCT
ejpam-5528	94	9	qml(ℜ	qml(ℜ	PROPN
ejpam-5528	94	10	)	)	PUNCT
ejpam-5528	94	11	=	=	SYM
ejpam-5528	94	12	ℜc	ℜc	PROPN
ejpam-5528	94	13	=	=	SYM
ejpam-5528	94	14	{	{	PUNCT
ejpam-5528	94	15	u	u	NOUN
ejpam-5528	94	16	α	α	NOUN
ejpam-5528	94	17	|	|	ADV
ejpam-5528	94	18	u	u	NOUN
ejpam-5528	94	19	∈	∈	PROPN
ejpam-5528	94	20	ℜ	ℜ	PROPN
ejpam-5528	94	21	and	and	CCONJ
ejpam-5528	94	22	0	0	NUM
ejpam-5528	94	23	̸=	̸=	PROPN
ejpam-5528	94	24	α	α	PROPN
ejpam-5528	94	25	∈	∈	PROPN
ejpam-5528	94	26	z(ℜ	z(ℜ	NUM
ejpam-5528	94	27	)	)	PUNCT
ejpam-5528	94	28	}	}	PUNCT
ejpam-5528	94	29	.	.	PUNCT
ejpam-5528	95	1	therefore	therefore	ADV
ejpam-5528	95	2	if	if	SCONJ
ejpam-5528	95	3	∇	∇	X
ejpam-5528	95	4	is	be	AUX
ejpam-5528	95	5	of	of	ADP
ejpam-5528	95	6	the	the	DET
ejpam-5528	95	7	first	first	ADJ
ejpam-5528	95	8	kind	kind	NOUN
ejpam-5528	95	9	on	on	ADP
ejpam-5528	95	10	z(ℜ	z(ℜ	NUM
ejpam-5528	95	11	)	)	PUNCT
ejpam-5528	95	12	,	,	PUNCT
ejpam-5528	95	13	then	then	ADV
ejpam-5528	95	14	∇	∇	PROPN
ejpam-5528	95	15	can	can	AUX
ejpam-5528	95	16	be	be	AUX
ejpam-5528	95	17	uniquely	uniquely	ADV
ejpam-5528	95	18	extended	extend	VERB
ejpam-5528	95	19	to	to	ADP
ejpam-5528	95	20	an	an	DET
ejpam-5528	95	21	antiautomorphism	antiautomorphism	NOUN
ejpam-5528	95	22	of	of	ADP
ejpam-5528	95	23	ℜc	ℜc	PROPN
ejpam-5528	95	24	,	,	PUNCT
ejpam-5528	95	25	denoted	denote	VERB
ejpam-5528	95	26	by	by	ADP
ejpam-5528	95	27	∇	∇	X
ejpam-5528	95	28	also	also	ADV
ejpam-5528	95	29	,	,	PUNCT
ejpam-5528	95	30	by	by	ADP
ejpam-5528	95	31	defining	define	VERB
ejpam-5528	95	32	∇	∇	NOUN
ejpam-5528	95	33	(	(	PUNCT
ejpam-5528	95	34	a	a	DET
ejpam-5528	95	35	α	α	NOUN
ejpam-5528	95	36	)	)	PUNCT
ejpam-5528	95	37	=	=	SYM
ejpam-5528	95	38	∇(u	∇(u	PROPN
ejpam-5528	95	39	)	)	PUNCT
ejpam-5528	95	40	α	α	NOUN
ejpam-5528	95	41	.	.	PUNCT
ejpam-5528	96	1	hence	hence	ADV
ejpam-5528	96	2	∇	∇	PROPN
ejpam-5528	96	3	is	be	AUX
ejpam-5528	96	4	of	of	ADP
ejpam-5528	96	5	the	the	DET
ejpam-5528	96	6	first	first	ADJ
ejpam-5528	96	7	kind	kind	NOUN
ejpam-5528	96	8	.	.	PUNCT
ejpam-5528	97	1	the	the	DET
ejpam-5528	97	2	converse	converse	NOUN
ejpam-5528	97	3	holds	hold	VERB
ejpam-5528	97	4	trivially	trivially	ADV
ejpam-5528	97	5	.	.	PUNCT
ejpam-5528	98	1	lemma	lemma	PROPN
ejpam-5528	98	2	2.3	2.3	NUM
ejpam-5528	98	3	.	.	PUNCT
ejpam-5528	99	1	[	[	X
ejpam-5528	99	2	20	20	NUM
ejpam-5528	99	3	,	,	PUNCT
ejpam-5528	99	4	lemma	lemma	PROPN
ejpam-5528	99	5	2.2	2.2	NUM
ejpam-5528	99	6	]	]	PUNCT
ejpam-5528	99	7	let	let	VERB
ejpam-5528	99	8	ℜ	ℜ	PROPN
ejpam-5528	99	9	be	be	AUX
ejpam-5528	99	10	a	a	DET
ejpam-5528	99	11	ring	ring	NOUN
ejpam-5528	99	12	with	with	ADP
ejpam-5528	99	13	an	an	DET
ejpam-5528	99	14	involution	involution	NOUN
ejpam-5528	99	15	‘	'	PUNCT
ejpam-5528	99	16	∗	∗	NOUN
ejpam-5528	99	17	’	'	PUNCT
ejpam-5528	99	18	and	and	CCONJ
ejpam-5528	99	19	let	let	VERB
ejpam-5528	99	20	ω	ω	NOUN
ejpam-5528	99	21	:	:	PUNCT
ejpam-5528	99	22	ℜ×ℜ	ℜ×ℜ	PROPN
ejpam-5528	99	23	→	→	PUNCT
ejpam-5528	99	24	g	g	NOUN
ejpam-5528	99	25	be	be	AUX
ejpam-5528	99	26	a	a	DET
ejpam-5528	99	27	map	map	NOUN
ejpam-5528	99	28	,	,	PUNCT
ejpam-5528	99	29	where	where	SCONJ
ejpam-5528	99	30	g	g	PROPN
ejpam-5528	99	31	is	be	AUX
ejpam-5528	99	32	an	an	DET
ejpam-5528	99	33	additive	additive	ADJ
ejpam-5528	99	34	group	group	NOUN
ejpam-5528	99	35	.	.	PUNCT
ejpam-5528	100	1	suppose	suppose	VERB
ejpam-5528	100	2	f	f	X
ejpam-5528	100	3	,	,	PUNCT
ejpam-5528	100	4	h	h	NOUN
ejpam-5528	100	5	:	:	PUNCT
ejpam-5528	100	6	ℜ	ℜ	PROPN
ejpam-5528	100	7	→	→	SYM
ejpam-5528	100	8	g	g	NOUN
ejpam-5528	100	9	are	be	AUX
ejpam-5528	100	10	maps	map	NOUN
ejpam-5528	100	11	such	such	ADJ
ejpam-5528	100	12	that	that	DET
ejpam-5528	100	13	ω(u	ω(u	PROPN
ejpam-5528	100	14	,	,	PUNCT
ejpam-5528	100	15	v	v	NOUN
ejpam-5528	100	16	)	)	PUNCT
ejpam-5528	100	17	=	=	PUNCT
ejpam-5528	100	18	f(uv∗)+h(vu∗	f(uv∗)+h(vu∗	NOUN
ejpam-5528	100	19	)	)	PUNCT
ejpam-5528	100	20	for	for	ADP
ejpam-5528	100	21	all	all	DET
ejpam-5528	100	22	u	u	NOUN
ejpam-5528	100	23	,	,	PUNCT
ejpam-5528	100	24	v	v	NOUN
ejpam-5528	100	25	∈	∈	NOUN
ejpam-5528	100	26	ℜ.	ℜ.	PROPN
ejpam-5528	100	27	then	then	ADV
ejpam-5528	100	28	ω(uw	ω(uw	NUM
ejpam-5528	100	29	,	,	PUNCT
ejpam-5528	100	30	v	v	NOUN
ejpam-5528	100	31	)	)	PUNCT
ejpam-5528	100	32	=	=	SYM
ejpam-5528	100	33	ω(u	ω(u	PROPN
ejpam-5528	100	34	,	,	PUNCT
ejpam-5528	100	35	vw∗	vw∗	NOUN
ejpam-5528	100	36	)	)	PUNCT
ejpam-5528	100	37	for	for	ADP
ejpam-5528	100	38	all	all	DET
ejpam-5528	100	39	u	u	PROPN
ejpam-5528	100	40	,	,	PUNCT
ejpam-5528	100	41	w	w	PROPN
ejpam-5528	100	42	,	,	PUNCT
ejpam-5528	100	43	v	v	NOUN
ejpam-5528	100	44	∈	∈	NOUN
ejpam-5528	100	45	ℜ.	ℜ.	VERB
ejpam-5528	100	46	the	the	DET
ejpam-5528	100	47	following	follow	VERB
ejpam-5528	100	48	result	result	NOUN
ejpam-5528	100	49	provides	provide	VERB
ejpam-5528	100	50	a	a	DET
ejpam-5528	100	51	characterization	characterization	NOUN
ejpam-5528	100	52	of	of	ADP
ejpam-5528	100	53	strong	strong	ADJ
ejpam-5528	100	54	bi	bi	ADJ
ejpam-5528	100	55	-	-	ADJ
ejpam-5528	100	56	skew	skew	ADJ
ejpam-5528	100	57	commutativity	commutativity	NOUN
ejpam-5528	100	58	preserving	preserve	VERB
ejpam-5528	100	59	maps	map	NOUN
ejpam-5528	100	60	in	in	ADP
ejpam-5528	100	61	prime	prime	ADJ
ejpam-5528	100	62	rings	ring	NOUN
ejpam-5528	100	63	without	without	ADP
ejpam-5528	100	64	assuming	assume	VERB
ejpam-5528	100	65	the	the	DET
ejpam-5528	100	66	existence	existence	NOUN
ejpam-5528	100	67	of	of	ADP
ejpam-5528	100	68	the	the	DET
ejpam-5528	100	69	unity	unity	NOUN
ejpam-5528	100	70	and	and	CCONJ
ejpam-5528	100	71	a	a	DET
ejpam-5528	100	72	nontrivial	nontrivial	ADJ
ejpam-5528	100	73	symmetric	symmetric	ADJ
ejpam-5528	100	74	idempotent	idempotent	NOUN
ejpam-5528	100	75	,	,	PUNCT
ejpam-5528	100	76	thereby	thereby	ADV
ejpam-5528	100	77	generalizing	generalize	VERB
ejpam-5528	100	78	,	,	PUNCT
ejpam-5528	100	79	improving	improve	VERB
ejpam-5528	100	80	and	and	CCONJ
ejpam-5528	100	81	extending	extend	VERB
ejpam-5528	100	82	[	[	PUNCT
ejpam-5528	100	83	16	16	NUM
ejpam-5528	100	84	,	,	PUNCT
ejpam-5528	100	85	theorem	theorem	VERB
ejpam-5528	100	86	2.1	2.1	NUM
ejpam-5528	100	87	]	]	PUNCT
ejpam-5528	100	88	to	to	ADP
ejpam-5528	100	89	prime	prime	ADJ
ejpam-5528	100	90	rings	ring	NOUN
ejpam-5528	100	91	.	.	PUNCT
ejpam-5528	101	1	theorem	theorem	VERB
ejpam-5528	101	2	2.1	2.1	NUM
ejpam-5528	101	3	.	.	PUNCT
ejpam-5528	102	1	let	let	VERB
ejpam-5528	102	2	ℜ	ℜ	PROPN
ejpam-5528	102	3	be	be	AUX
ejpam-5528	102	4	a	a	DET
ejpam-5528	102	5	prime	prime	ADJ
ejpam-5528	102	6	ring	ring	NOUN
ejpam-5528	102	7	with	with	ADP
ejpam-5528	102	8	an	an	DET
ejpam-5528	102	9	involution	involution	NOUN
ejpam-5528	102	10	‘	'	PUNCT
ejpam-5528	102	11	∗	∗	NOUN
ejpam-5528	102	12	’	'	PUNCT
ejpam-5528	102	13	of	of	ADP
ejpam-5528	102	14	order	order	NOUN
ejpam-5528	102	15	2	2	NUM
ejpam-5528	102	16	,	,	PUNCT
ejpam-5528	102	17	and	and	CCONJ
ejpam-5528	102	18	let	let	VERB
ejpam-5528	102	19	ω	ω	NOUN
ejpam-5528	102	20	:	:	PUNCT
ejpam-5528	102	21	ℜ	ℜ	PROPN
ejpam-5528	102	22	→	→	SYM
ejpam-5528	102	23	ℜ	ℜ	PROPN
ejpam-5528	102	24	be	be	AUX
ejpam-5528	102	25	a	a	DET
ejpam-5528	102	26	surjective	surjective	ADJ
ejpam-5528	102	27	strong	strong	ADJ
ejpam-5528	102	28	bi	bi	ADJ
ejpam-5528	102	29	-	-	ADJ
ejpam-5528	102	30	skew	skew	ADJ
ejpam-5528	102	31	commutativity	commutativity	NOUN
ejpam-5528	102	32	preserving	preserve	VERB
ejpam-5528	102	33	map	map	NOUN
ejpam-5528	102	34	.	.	PUNCT
ejpam-5528	103	1	then	then	ADV
ejpam-5528	103	2	there	there	PRON
ejpam-5528	103	3	exists	exist	VERB
ejpam-5528	103	4	q	q	PROPN
ejpam-5528	103	5	∈	∈	PROPN
ejpam-5528	103	6	qms(ℜ	qms(ℜ	PROPN
ejpam-5528	103	7	)	)	PUNCT
ejpam-5528	103	8	such	such	ADJ
ejpam-5528	103	9	that	that	SCONJ
ejpam-5528	103	10	qq∗	qq∗	ADJ
ejpam-5528	103	11	=	=	NOUN
ejpam-5528	103	12	1	1	NUM
ejpam-5528	103	13	and	and	CCONJ
ejpam-5528	103	14	ω(u	ω(u	NUM
ejpam-5528	103	15	)	)	PUNCT
ejpam-5528	103	16	=	=	SYM
ejpam-5528	103	17	uq	uq	NOUN
ejpam-5528	103	18	for	for	ADP
ejpam-5528	103	19	all	all	DET
ejpam-5528	103	20	u	u	NOUN
ejpam-5528	103	21	∈	∈	PROPN
ejpam-5528	103	22	ℜ	ℜ	PROPN
ejpam-5528	103	23	provided	provide	VERB
ejpam-5528	103	24	that	that	SCONJ
ejpam-5528	103	25	either	either	CCONJ
ejpam-5528	103	26	dimcℜc	dimcℜc	VERB
ejpam-5528	103	27	>	>	X
ejpam-5528	103	28	4	4	NUM
ejpam-5528	103	29	or	or	CCONJ
ejpam-5528	103	30	both	both	PRON
ejpam-5528	103	31	char(ℜ	char(ℜ	NOUN
ejpam-5528	103	32	)	)	PUNCT
ejpam-5528	103	33	̸=	̸=	PROPN
ejpam-5528	103	34	2	2	NUM
ejpam-5528	103	35	and	and	CCONJ
ejpam-5528	103	36	’	'	PUNCT
ejpam-5528	103	37	∗	∗	NOUN
ejpam-5528	103	38	‘	'	PUNCT
ejpam-5528	103	39	is	be	AUX
ejpam-5528	103	40	of	of	ADP
ejpam-5528	103	41	the	the	DET
ejpam-5528	103	42	second	second	ADJ
ejpam-5528	103	43	kind	kind	NOUN
ejpam-5528	103	44	.	.	PUNCT
ejpam-5528	104	1	proof	proof	NOUN
ejpam-5528	104	2	.	.	PUNCT
ejpam-5528	105	1	by	by	ADP
ejpam-5528	105	2	the	the	DET
ejpam-5528	105	3	given	give	VERB
ejpam-5528	105	4	hypothesis	hypothesis	NOUN
ejpam-5528	105	5	,	,	PUNCT
ejpam-5528	105	6	we	we	PRON
ejpam-5528	105	7	have	have	VERB
ejpam-5528	105	8	[	[	X
ejpam-5528	105	9	ω(u),ω(v)]•	ω(u),ω(v)]•	NUM
ejpam-5528	105	10	=	=	SYM
ejpam-5528	106	1	[	[	X
ejpam-5528	106	2	u	u	NOUN
ejpam-5528	106	3	,	,	PUNCT
ejpam-5528	106	4	v]•	v]•	PROPN
ejpam-5528	106	5	(	(	PUNCT
ejpam-5528	106	6	2.1	2.1	NUM
ejpam-5528	106	7	)	)	PUNCT
ejpam-5528	106	8	for	for	ADP
ejpam-5528	106	9	all	all	DET
ejpam-5528	106	10	u	u	NOUN
ejpam-5528	106	11	,	,	PUNCT
ejpam-5528	106	12	v	v	NOUN
ejpam-5528	106	13	∈	∈	NOUN
ejpam-5528	106	14	ℜ.	ℜ.	PROPN
ejpam-5528	106	15	firstly	firstly	ADV
ejpam-5528	106	16	we	we	PRON
ejpam-5528	106	17	establish	establish	VERB
ejpam-5528	106	18	some	some	DET
ejpam-5528	106	19	facts	fact	NOUN
ejpam-5528	106	20	about	about	ADP
ejpam-5528	106	21	ω	ω	NUM
ejpam-5528	106	22	.	.	PUNCT
ejpam-5528	107	1	fact	fact	NOUN
ejpam-5528	107	2	i.	i.	PROPN
ejpam-5528	107	3	ω	ω	PROPN
ejpam-5528	107	4	is	be	AUX
ejpam-5528	107	5	additive	additive	ADJ
ejpam-5528	107	6	.	.	PUNCT
ejpam-5528	108	1	for	for	ADP
ejpam-5528	108	2	every	every	DET
ejpam-5528	108	3	u	u	NOUN
ejpam-5528	108	4	,	,	PUNCT
ejpam-5528	108	5	v	v	NOUN
ejpam-5528	108	6	,	,	PUNCT
ejpam-5528	108	7	w	w	PROPN
ejpam-5528	108	8	∈	∈	PROPN
ejpam-5528	108	9	ℜ	ℜ	PROPN
ejpam-5528	108	10	,	,	PUNCT
ejpam-5528	108	11	we	we	PRON
ejpam-5528	108	12	have	have	VERB
ejpam-5528	108	13	[	[	X
ejpam-5528	108	14	ω(u),ω(v	ω(u),ω(v	X
ejpam-5528	108	15	+	+	CCONJ
ejpam-5528	108	16	w)−	w)−	PROPN
ejpam-5528	108	17	ω(v)−	ω(v)−	PROPN
ejpam-5528	108	18	ω(w)]•	ω(w)]•	ADP
ejpam-5528	109	1	=	=	PUNCT
ejpam-5528	110	1	[	[	X
ejpam-5528	110	2	ω(u),ω(v	ω(u),ω(v	X
ejpam-5528	110	3	+	+	CCONJ
ejpam-5528	110	4	w)]•	w)]•	PROPN
ejpam-5528	110	5	−	−	NOUN
ejpam-5528	111	1	[	[	X
ejpam-5528	111	2	ω(u),ω(v)]•	ω(u),ω(v)]•	NUM
ejpam-5528	111	3	−	−	NOUN
ejpam-5528	111	4	[	[	X
ejpam-5528	111	5	ω(u),ω(w)]•	ω(u),ω(w)]•	NUM
ejpam-5528	111	6	=	=	SYM
ejpam-5528	111	7	[	[	X
ejpam-5528	111	8	u	u	NOUN
ejpam-5528	111	9	,	,	PUNCT
ejpam-5528	111	10	v	v	ADP
ejpam-5528	111	11	+	+	CCONJ
ejpam-5528	111	12	w]•	w]•	NOUN
ejpam-5528	111	13	−	−	PROPN
ejpam-5528	112	1	[	[	X
ejpam-5528	112	2	u	u	NOUN
ejpam-5528	112	3	,	,	PUNCT
ejpam-5528	112	4	v]•	v]•	PROPN
ejpam-5528	112	5	−	−	PROPN
ejpam-5528	113	1	[	[	X
ejpam-5528	113	2	u	u	NOUN
ejpam-5528	113	3	,	,	PUNCT
ejpam-5528	113	4	w]•	w]•	NOUN
ejpam-5528	113	5	=	=	SYM
ejpam-5528	113	6	0	0	X
ejpam-5528	113	7	.	.	PUNCT
ejpam-5528	113	8	therefore	therefore	ADV
ejpam-5528	113	9	by	by	ADP
ejpam-5528	113	10	the	the	DET
ejpam-5528	113	11	surjectiveness	surjectiveness	NOUN
ejpam-5528	113	12	of	of	ADP
ejpam-5528	113	13	ω	ω	PROPN
ejpam-5528	113	14	,	,	PUNCT
ejpam-5528	113	15	we	we	PRON
ejpam-5528	113	16	find	find	VERB
ejpam-5528	113	17	that	that	SCONJ
ejpam-5528	114	1	[	[	X
ejpam-5528	114	2	u	u	NOUN
ejpam-5528	114	3	,	,	PUNCT
ejpam-5528	114	4	ω(v	ω(v	NOUN
ejpam-5528	114	5	+	+	CCONJ
ejpam-5528	114	6	w)−	w)−	PROPN
ejpam-5528	114	7	ω(v)−	ω(v)−	PROPN
ejpam-5528	114	8	ω(w)]•	ω(w)]•	NUM
ejpam-5528	114	9	=	=	SYM
ejpam-5528	114	10	0	0	NUM
ejpam-5528	114	11	for	for	ADP
ejpam-5528	114	12	all	all	DET
ejpam-5528	114	13	u	u	NOUN
ejpam-5528	114	14	,	,	PUNCT
ejpam-5528	114	15	v	v	NOUN
ejpam-5528	114	16	,	,	PUNCT
ejpam-5528	114	17	w	w	PROPN
ejpam-5528	114	18	∈	∈	PROPN
ejpam-5528	114	19	r.	r.	NOUN
ejpam-5528	114	20	now	now	ADV
ejpam-5528	114	21	in	in	ADP
ejpam-5528	114	22	view	view	NOUN
ejpam-5528	114	23	of	of	ADP
ejpam-5528	114	24	lemma	lemma	PROPN
ejpam-5528	114	25	2.1	2.1	NUM
ejpam-5528	114	26	,	,	PUNCT
ejpam-5528	114	27	it	it	PRON
ejpam-5528	114	28	follows	follow	VERB
ejpam-5528	114	29	that	that	SCONJ
ejpam-5528	114	30	ω(u+	ω(u+	NUM
ejpam-5528	114	31	v	v	NOUN
ejpam-5528	114	32	)	)	PUNCT
ejpam-5528	114	33	=	=	SYM
ejpam-5528	114	34	ω(u	ω(u	PROPN
ejpam-5528	114	35	)	)	PUNCT
ejpam-5528	115	1	+	+	CCONJ
ejpam-5528	115	2	ω(v	ω(v	NOUN
ejpam-5528	115	3	)	)	PUNCT
ejpam-5528	115	4	for	for	ADP
ejpam-5528	115	5	all	all	DET
ejpam-5528	115	6	u	u	NOUN
ejpam-5528	115	7	,	,	PUNCT
ejpam-5528	115	8	v	v	NOUN
ejpam-5528	115	9	∈	∈	PROPN
ejpam-5528	115	10	ℜ	ℜ	PROPN
ejpam-5528	115	11	,	,	PUNCT
ejpam-5528	115	12	that	that	ADV
ejpam-5528	115	13	is	is	ADV
ejpam-5528	115	14	,	,	PUNCT
ejpam-5528	115	15	ω	ω	PROPN
ejpam-5528	115	16	is	be	AUX
ejpam-5528	115	17	additive	additive	ADJ
ejpam-5528	115	18	.	.	PUNCT
ejpam-5528	116	1	fact	fact	NOUN
ejpam-5528	116	2	ii	ii	PROPN
ejpam-5528	116	3	.	.	PUNCT
ejpam-5528	117	1	ω	ω	PROPN
ejpam-5528	117	2	is	be	AUX
ejpam-5528	117	3	injective	injective	ADJ
ejpam-5528	117	4	.	.	PUNCT
ejpam-5528	118	1	let	let	VERB
ejpam-5528	118	2	a	a	DET
ejpam-5528	118	3	∈	∈	PROPN
ejpam-5528	118	4	ℜ	ℜ	NOUN
ejpam-5528	118	5	be	be	AUX
ejpam-5528	118	6	such	such	ADJ
ejpam-5528	118	7	that	that	SCONJ
ejpam-5528	118	8	ω(a	ω(a	NUM
ejpam-5528	118	9	)	)	PUNCT
ejpam-5528	118	10	=	=	SYM
ejpam-5528	119	1	0	0	X
ejpam-5528	119	2	.	.	PUNCT
ejpam-5528	120	1	then	then	ADV
ejpam-5528	120	2	[	[	X
ejpam-5528	120	3	a	a	X
ejpam-5528	120	4	,	,	PUNCT
ejpam-5528	120	5	v]•	v]•	PROPN
ejpam-5528	120	6	=	=	PUNCT
ejpam-5528	121	1	[	[	X
ejpam-5528	121	2	ω(a),ω(v)]•	ω(a),ω(v)]•	NUM
ejpam-5528	121	3	=	=	SYM
ejpam-5528	121	4	0	0	NUM
ejpam-5528	121	5	for	for	SCONJ
ejpam-5528	121	6	all	all	PRON
ejpam-5528	121	7	v	v	NOUN
ejpam-5528	121	8	∈	∈	NOUN
ejpam-5528	121	9	ℜ.	ℜ.	PROPN
ejpam-5528	121	10	hence	hence	ADV
ejpam-5528	121	11	by	by	ADP
ejpam-5528	121	12	lemma	lemma	PROPN
ejpam-5528	121	13	2.1	2.1	NUM
ejpam-5528	121	14	,	,	PUNCT
ejpam-5528	121	15	a	a	DET
ejpam-5528	121	16	=	=	NOUN
ejpam-5528	121	17	0	0	NUM
ejpam-5528	121	18	.	.	PUNCT
ejpam-5528	122	1	thus	thus	ADV
ejpam-5528	122	2	ω	ω	X
ejpam-5528	122	3	is	be	AUX
ejpam-5528	122	4	injective	injective	ADJ
ejpam-5528	122	5	.	.	PUNCT
ejpam-5528	123	1	therefore	therefore	ADV
ejpam-5528	123	2	from	from	ADP
ejpam-5528	123	3	(	(	PUNCT
ejpam-5528	123	4	2.1	2.1	NUM
ejpam-5528	123	5	)	)	PUNCT
ejpam-5528	123	6	,	,	PUNCT
ejpam-5528	123	7	we	we	PRON
ejpam-5528	123	8	have	have	VERB
ejpam-5528	123	9	ω(u)v∗	ω(u)v∗	NOUN
ejpam-5528	124	1	+	+	ADP
ejpam-5528	124	2	ω−1(v)u∗	ω−1(v)u∗	NOUN
ejpam-5528	124	3	−	−	PROPN
ejpam-5528	124	4	uω−1(v)∗	uω−1(v)∗	NOUN
ejpam-5528	124	5	−	−	PROPN
ejpam-5528	124	6	vω(u)∗	vω(u)∗	NOUN
ejpam-5528	124	7	=	=	SYM
ejpam-5528	124	8	0	0	NUM
ejpam-5528	124	9	,	,	PUNCT
ejpam-5528	124	10	(	(	PUNCT
ejpam-5528	124	11	2.2	2.2	NUM
ejpam-5528	124	12	)	)	PUNCT
ejpam-5528	124	13	moin	moin	NOUN
ejpam-5528	124	14	a.	a.	NOUN
ejpam-5528	124	15	ansari	ansari	PROPN
ejpam-5528	124	16	et	et	PROPN
ejpam-5528	124	17	al	al	PROPN
ejpam-5528	124	18	.	.	PUNCT
ejpam-5528	124	19	/	/	SYM
ejpam-5528	124	20	eur	eur	PROPN
ejpam-5528	124	21	.	.	PUNCT
ejpam-5528	125	1	j.	j.	PROPN
ejpam-5528	125	2	pure	pure	PROPN
ejpam-5528	125	3	appl	appl	PROPN
ejpam-5528	125	4	.	.	PROPN
ejpam-5528	125	5	math	math	PROPN
ejpam-5528	125	6	,	,	PUNCT
ejpam-5528	125	7	18	18	NUM
ejpam-5528	125	8	(	(	PUNCT
ejpam-5528	125	9	2	2	NUM
ejpam-5528	125	10	)	)	PUNCT
ejpam-5528	125	11	(	(	PUNCT
ejpam-5528	125	12	2025	2025	NUM
ejpam-5528	125	13	)	)	PUNCT
ejpam-5528	125	14	,	,	PUNCT
ejpam-5528	125	15	5528	5528	NUM
ejpam-5528	125	16	5	5	NUM
ejpam-5528	125	17	of	of	ADP
ejpam-5528	125	18	14	14	NUM
ejpam-5528	125	19	for	for	ADP
ejpam-5528	125	20	all	all	DET
ejpam-5528	125	21	u	u	NOUN
ejpam-5528	125	22	,	,	PUNCT
ejpam-5528	125	23	v	v	X
ejpam-5528	125	24	∈	∈	NOUN
ejpam-5528	125	25	ℜ.	ℜ.	PROPN
ejpam-5528	125	26	next	next	ADV
ejpam-5528	125	27	,	,	PUNCT
ejpam-5528	125	28	we	we	PRON
ejpam-5528	125	29	advance	advance	VERB
ejpam-5528	125	30	by	by	ADP
ejpam-5528	125	31	examining	examine	VERB
ejpam-5528	125	32	the	the	DET
ejpam-5528	125	33	following	follow	VERB
ejpam-5528	125	34	two	two	NUM
ejpam-5528	125	35	scenarios	scenario	NOUN
ejpam-5528	125	36	:	:	PUNCT
ejpam-5528	125	37	case	case	NOUN
ejpam-5528	125	38	i.	i.	NOUN
ejpam-5528	125	39	dimcℜc	dimcℜc	PROPN
ejpam-5528	125	40	>	>	X
ejpam-5528	126	1	4	4	X
ejpam-5528	126	2	.	.	PUNCT
ejpam-5528	127	1	in	in	ADP
ejpam-5528	127	2	view	view	NOUN
ejpam-5528	127	3	of	of	ADP
ejpam-5528	127	4	[	[	X
ejpam-5528	127	5	27	27	NUM
ejpam-5528	127	6	,	,	PUNCT
ejpam-5528	127	7	theorem	theorem	VERB
ejpam-5528	127	8	3.5	3.5	NUM
ejpam-5528	127	9	]	]	PUNCT
ejpam-5528	127	10	,	,	PUNCT
ejpam-5528	127	11	it	it	PRON
ejpam-5528	127	12	follows	follow	VERB
ejpam-5528	127	13	that	that	SCONJ
ejpam-5528	127	14	there	there	PRON
ejpam-5528	127	15	exists	exist	VERB
ejpam-5528	127	16	q	q	PROPN
ejpam-5528	127	17	∈	∈	PROPN
ejpam-5528	127	18	qml(ℜ	qml(ℜ	NOUN
ejpam-5528	127	19	)	)	PUNCT
ejpam-5528	127	20	such	such	ADJ
ejpam-5528	127	21	that	that	DET
ejpam-5528	127	22	ω(u	ω(u	NOUN
ejpam-5528	127	23	)	)	PUNCT
ejpam-5528	128	1	=	=	SYM
ejpam-5528	128	2	uq	uq	NOUN
ejpam-5528	128	3	for	for	ADP
ejpam-5528	128	4	all	all	DET
ejpam-5528	128	5	u	u	PRON
ejpam-5528	128	6	∈	∈	PROPN
ejpam-5528	128	7	ℜ	ℜ	PROPN
ejpam-5528	128	8	and	and	CCONJ
ejpam-5528	128	9	ω−1(v)∗	ω−1(v)∗	PUNCT
ejpam-5528	128	10	=	=	SYM
ejpam-5528	128	11	qv∗	qv∗	ADJ
ejpam-5528	128	12	for	for	ADP
ejpam-5528	128	13	all	all	PRON
ejpam-5528	128	14	v	v	NOUN
ejpam-5528	128	15	∈	∈	NOUN
ejpam-5528	128	16	ℜ.	ℜ.	PROPN
ejpam-5528	128	17	note	note	NOUN
ejpam-5528	128	18	that	that	SCONJ
ejpam-5528	128	19	qv∗	qv∗	ADV
ejpam-5528	128	20	=	=	SYM
ejpam-5528	128	21	ω−1(v)∗	ω−1(v)∗	PUNCT
ejpam-5528	128	22	∈	∈	NOUN
ejpam-5528	128	23	ℜ	ℜ	PROPN
ejpam-5528	128	24	for	for	ADP
ejpam-5528	128	25	all	all	PRON
ejpam-5528	128	26	v	v	NOUN
ejpam-5528	128	27	∈	∈	NOUN
ejpam-5528	128	28	ℜ.	ℜ.	PROPN
ejpam-5528	128	29	hence	hence	ADV
ejpam-5528	128	30	qℜ	qℜ	NOUN
ejpam-5528	128	31	⊆	⊆	X
ejpam-5528	128	32	ℜ.	ℜ.	PROPN
ejpam-5528	128	33	consequently	consequently	ADV
ejpam-5528	128	34	,	,	PUNCT
ejpam-5528	128	35	q	q	PROPN
ejpam-5528	128	36	∈	∈	PROPN
ejpam-5528	128	37	qms(ℜ	qms(ℜ	PROPN
ejpam-5528	128	38	)	)	PUNCT
ejpam-5528	128	39	.	.	PUNCT
ejpam-5528	129	1	therefore	therefore	ADV
ejpam-5528	129	2	ω−1(u	ω−1(u	NUM
ejpam-5528	129	3	)	)	PUNCT
ejpam-5528	130	1	=	=	SYM
ejpam-5528	130	2	uq∗	uq∗	NOUN
ejpam-5528	130	3	for	for	ADP
ejpam-5528	130	4	all	all	DET
ejpam-5528	130	5	u	u	PRON
ejpam-5528	130	6	∈	∈	PROPN
ejpam-5528	130	7	ℜ	ℜ	PROPN
ejpam-5528	130	8	and	and	CCONJ
ejpam-5528	130	9	hence	hence	ADV
ejpam-5528	130	10	ω(u)q∗	ω(u)q∗	PROPN
ejpam-5528	130	11	=	=	SYM
ejpam-5528	130	12	u	u	NOUN
ejpam-5528	130	13	for	for	ADP
ejpam-5528	130	14	all	all	DET
ejpam-5528	130	15	u	u	NOUN
ejpam-5528	130	16	∈	∈	NOUN
ejpam-5528	130	17	ℜ.	ℜ.	PROPN
ejpam-5528	130	18	using	use	VERB
ejpam-5528	130	19	ω(u	ω(u	PROPN
ejpam-5528	130	20	)	)	PUNCT
ejpam-5528	130	21	=	=	SYM
ejpam-5528	130	22	uq	uq	NOUN
ejpam-5528	130	23	in	in	ADP
ejpam-5528	130	24	the	the	DET
ejpam-5528	130	25	last	last	ADJ
ejpam-5528	130	26	relation	relation	NOUN
ejpam-5528	130	27	,	,	PUNCT
ejpam-5528	130	28	we	we	PRON
ejpam-5528	130	29	get	get	VERB
ejpam-5528	130	30	uqq∗	uqq∗	ADJ
ejpam-5528	130	31	=	=	PUNCT
ejpam-5528	130	32	u	u	NOUN
ejpam-5528	130	33	for	for	ADP
ejpam-5528	130	34	all	all	DET
ejpam-5528	130	35	u	u	NOUN
ejpam-5528	130	36	∈	∈	PROPN
ejpam-5528	130	37	ℜ.	ℜ.	PROPN
ejpam-5528	130	38	this	this	PRON
ejpam-5528	130	39	entails	entail	VERB
ejpam-5528	130	40	that	that	SCONJ
ejpam-5528	130	41	qq∗	qq∗	ADV
ejpam-5528	130	42	=	=	VERB
ejpam-5528	130	43	1	1	X
ejpam-5528	130	44	.	.	X
ejpam-5528	130	45	case	case	NOUN
ejpam-5528	130	46	i.	i.	NOUN
ejpam-5528	130	47	dimcℜc	dimcℜc	VERB
ejpam-5528	130	48	≤	≤	ADV
ejpam-5528	130	49	4	4	NUM
ejpam-5528	130	50	.	.	PUNCT
ejpam-5528	131	1	in	in	ADP
ejpam-5528	131	2	this	this	DET
ejpam-5528	131	3	case	case	NOUN
ejpam-5528	131	4	ℜ	ℜ	NOUN
ejpam-5528	131	5	is	be	AUX
ejpam-5528	131	6	a	a	DET
ejpam-5528	131	7	pi	pi	NOUN
ejpam-5528	131	8	-	-	PUNCT
ejpam-5528	131	9	ring	ring	NOUN
ejpam-5528	131	10	and	and	CCONJ
ejpam-5528	131	11	qml(ℜ	qml(ℜ	NOUN
ejpam-5528	131	12	)	)	PUNCT
ejpam-5528	131	13	=	=	SYM
ejpam-5528	131	14	qms(ℜ	qms(ℜ	PROPN
ejpam-5528	131	15	)	)	PUNCT
ejpam-5528	131	16	=	=	SYM
ejpam-5528	131	17	ℜc	ℜc	PROPN
ejpam-5528	131	18	.	.	PUNCT
ejpam-5528	131	19	according	accord	VERB
ejpam-5528	131	20	to	to	ADP
ejpam-5528	131	21	the	the	DET
ejpam-5528	131	22	given	give	VERB
ejpam-5528	131	23	hypothesis	hypothesis	NOUN
ejpam-5528	131	24	char(ℜ	char(ℜ	PART
ejpam-5528	131	25	)	)	PUNCT
ejpam-5528	131	26	̸=	̸=	PROPN
ejpam-5528	131	27	2	2	NUM
ejpam-5528	131	28	and	and	CCONJ
ejpam-5528	131	29	’	'	PUNCT
ejpam-5528	131	30	∗	∗	NOUN
ejpam-5528	131	31	‘	'	PUNCT
ejpam-5528	131	32	is	be	AUX
ejpam-5528	131	33	of	of	ADP
ejpam-5528	131	34	the	the	DET
ejpam-5528	131	35	second	second	ADJ
ejpam-5528	131	36	kind	kind	NOUN
ejpam-5528	131	37	.	.	PUNCT
ejpam-5528	132	1	hence	hence	ADV
ejpam-5528	132	2	by	by	ADP
ejpam-5528	132	3	lemma	lemma	PROPN
ejpam-5528	132	4	2.2	2.2	NUM
ejpam-5528	132	5	,	,	PUNCT
ejpam-5528	132	6	there	there	PRON
ejpam-5528	132	7	is	be	VERB
ejpam-5528	132	8	ζ	ζ	PRON
ejpam-5528	132	9	∈	∈	PROPN
ejpam-5528	132	10	z(ℜ	z(ℜ	NUM
ejpam-5528	132	11	)	)	PUNCT
ejpam-5528	132	12	such	such	ADJ
ejpam-5528	132	13	that	that	DET
ejpam-5528	132	14	ζ∗	ζ∗	PROPN
ejpam-5528	132	15	̸=	̸=	PROPN
ejpam-5528	132	16	ζ	ζ	NOUN
ejpam-5528	132	17	.	.	PUNCT
ejpam-5528	133	1	let	let	VERB
ejpam-5528	133	2	α	α	NOUN
ejpam-5528	133	3	=	=	SYM
ejpam-5528	133	4	ζ∗	ζ∗	ADJ
ejpam-5528	133	5	−	−	PROPN
ejpam-5528	133	6	ζ	ζ	NOUN
ejpam-5528	133	7	and	and	CCONJ
ejpam-5528	133	8	β	β	X
ejpam-5528	133	9	=	=	PUNCT
ejpam-5528	133	10	α2	α2	PROPN
ejpam-5528	133	11	.	.	PUNCT
ejpam-5528	134	1	then	then	ADV
ejpam-5528	134	2	α∗	α∗	VERB
ejpam-5528	134	3	=	=	PUNCT
ejpam-5528	134	4	−α	−α	NOUN
ejpam-5528	134	5	and	and	CCONJ
ejpam-5528	134	6	β∗	β∗	NOUN
ejpam-5528	134	7	=	=	SYM
ejpam-5528	135	1	β	β	X
ejpam-5528	135	2	.	.	PUNCT
ejpam-5528	136	1	setting	set	VERB
ejpam-5528	136	2	v	v	NOUN
ejpam-5528	136	3	=	=	SYM
ejpam-5528	136	4	α	α	X
ejpam-5528	136	5	in	in	ADP
ejpam-5528	136	6	(	(	PUNCT
ejpam-5528	136	7	2.2	2.2	NUM
ejpam-5528	136	8	)	)	PUNCT
ejpam-5528	136	9	,	,	PUNCT
ejpam-5528	136	10	we	we	PRON
ejpam-5528	136	11	get	get	VERB
ejpam-5528	136	12	α(ω(u	α(ω(u	NOUN
ejpam-5528	136	13	)	)	PUNCT
ejpam-5528	137	1	+	+	NUM
ejpam-5528	137	2	ω(u)∗	ω(u)∗	X
ejpam-5528	137	3	)	)	PUNCT
ejpam-5528	137	4	=	=	SYM
ejpam-5528	137	5	ω−1(α)u∗	ω−1(α)u∗	NUM
ejpam-5528	138	1	−	−	NOUN
ejpam-5528	138	2	uω−1(α)∗	uω−1(α)∗	NOUN
ejpam-5528	138	3	,	,	PUNCT
ejpam-5528	138	4	(	(	PUNCT
ejpam-5528	138	5	2.3	2.3	NUM
ejpam-5528	138	6	)	)	PUNCT
ejpam-5528	138	7	for	for	ADP
ejpam-5528	138	8	all	all	DET
ejpam-5528	138	9	u	u	NOUN
ejpam-5528	138	10	∈	∈	PROPN
ejpam-5528	138	11	ℜ.	ℜ.	PROPN
ejpam-5528	138	12	also	also	ADV
ejpam-5528	138	13	taking	take	VERB
ejpam-5528	138	14	v	v	NOUN
ejpam-5528	138	15	=	=	PRON
ejpam-5528	138	16	β	β	X
ejpam-5528	138	17	in	in	ADP
ejpam-5528	138	18	(	(	PUNCT
ejpam-5528	138	19	2.2	2.2	NUM
ejpam-5528	138	20	)	)	PUNCT
ejpam-5528	138	21	,	,	PUNCT
ejpam-5528	138	22	we	we	PRON
ejpam-5528	138	23	get	get	VERB
ejpam-5528	138	24	β(ω(u)−	β(ω(u)−	PUNCT
ejpam-5528	138	25	ω(u)∗	ω(u)∗	X
ejpam-5528	138	26	)	)	PUNCT
ejpam-5528	138	27	=	=	SYM
ejpam-5528	138	28	uω−1(β)∗	uω−1(β)∗	ADJ
ejpam-5528	138	29	−	−	NOUN
ejpam-5528	138	30	ω−1(β)u∗	ω−1(β)u∗	NOUN
ejpam-5528	138	31	(	(	PUNCT
ejpam-5528	138	32	2.4	2.4	NUM
ejpam-5528	138	33	)	)	PUNCT
ejpam-5528	138	34	for	for	ADP
ejpam-5528	138	35	all	all	PRON
ejpam-5528	138	36	u	u	PRON
ejpam-5528	138	37	∈	∈	PROPN
ejpam-5528	138	38	ℜ.	ℜ.	PROPN
ejpam-5528	138	39	multiplying	multiply	VERB
ejpam-5528	138	40	both	both	DET
ejpam-5528	138	41	sides	side	NOUN
ejpam-5528	138	42	of	of	ADP
ejpam-5528	138	43	(	(	PUNCT
ejpam-5528	138	44	2.3	2.3	NUM
ejpam-5528	138	45	)	)	PUNCT
ejpam-5528	138	46	by	by	ADP
ejpam-5528	138	47	β	β	X
ejpam-5528	138	48	and	and	CCONJ
ejpam-5528	138	49	(	(	PUNCT
ejpam-5528	138	50	2.4	2.4	NUM
ejpam-5528	138	51	)	)	PUNCT
ejpam-5528	138	52	by	by	ADP
ejpam-5528	138	53	α	α	X
ejpam-5528	138	54	,	,	PUNCT
ejpam-5528	138	55	we	we	PRON
ejpam-5528	138	56	get	get	VERB
ejpam-5528	138	57	αβ(ω(u	αβ(ω(u	NOUN
ejpam-5528	138	58	)	)	PUNCT
ejpam-5528	138	59	+	+	CCONJ
ejpam-5528	138	60	ω(u)∗	ω(u)∗	NOUN
ejpam-5528	138	61	)	)	PUNCT
ejpam-5528	138	62	=	=	SYM
ejpam-5528	139	1	βω−1(α)u∗	βω−1(α)u∗	NOUN
ejpam-5528	140	1	−	−	NUM
ejpam-5528	140	2	βuω−1(α)∗	βuω−1(α)∗	NOUN
ejpam-5528	140	3	,	,	PUNCT
ejpam-5528	140	4	(	(	PUNCT
ejpam-5528	140	5	2.5	2.5	NUM
ejpam-5528	140	6	)	)	PUNCT
ejpam-5528	140	7	and	and	CCONJ
ejpam-5528	140	8	αβ(ω(u)−	αβ(ω(u)−	NUM
ejpam-5528	140	9	ω(u)∗	ω(u)∗	NOUN
ejpam-5528	140	10	)	)	PUNCT
ejpam-5528	140	11	=	=	SYM
ejpam-5528	141	1	αuω−1(β)∗	αuω−1(β)∗	PRON
ejpam-5528	141	2	−	−	PROPN
ejpam-5528	141	3	αω−1(β)u∗	αω−1(β)u∗	PROPN
ejpam-5528	141	4	(	(	PUNCT
ejpam-5528	141	5	2.6	2.6	NUM
ejpam-5528	141	6	)	)	PUNCT
ejpam-5528	141	7	for	for	ADP
ejpam-5528	141	8	all	all	DET
ejpam-5528	141	9	u	u	PRON
ejpam-5528	141	10	∈	∈	PROPN
ejpam-5528	141	11	ℜ	ℜ	PROPN
ejpam-5528	141	12	,	,	PUNCT
ejpam-5528	141	13	respectively	respectively	ADV
ejpam-5528	141	14	.	.	PUNCT
ejpam-5528	142	1	adding	add	VERB
ejpam-5528	142	2	(	(	PUNCT
ejpam-5528	142	3	2.5	2.5	NUM
ejpam-5528	142	4	)	)	PUNCT
ejpam-5528	142	5	and	and	CCONJ
ejpam-5528	142	6	(	(	PUNCT
ejpam-5528	142	7	2.6	2.6	NUM
ejpam-5528	142	8	)	)	PUNCT
ejpam-5528	142	9	,	,	PUNCT
ejpam-5528	142	10	we	we	PRON
ejpam-5528	142	11	find	find	VERB
ejpam-5528	142	12	that	that	SCONJ
ejpam-5528	142	13	2αβω(u	2αβω(u	NUM
ejpam-5528	142	14	)	)	PUNCT
ejpam-5528	142	15	=	=	PUNCT
ejpam-5528	143	1	αuω−1(β)∗	αuω−1(β)∗	ADV
ejpam-5528	143	2	−	−	PROPN
ejpam-5528	143	3	αω−1(β)u∗	αω−1(β)u∗	PROPN
ejpam-5528	143	4	+	+	CCONJ
ejpam-5528	143	5	βω−1(α)u∗	βω−1(α)u∗	PUNCT
ejpam-5528	143	6	−	−	PROPN
ejpam-5528	143	7	βuω−1(α)∗	βuω−1(α)∗	NOUN
ejpam-5528	143	8	,	,	PUNCT
ejpam-5528	143	9	(	(	PUNCT
ejpam-5528	143	10	2.7	2.7	NUM
ejpam-5528	143	11	)	)	PUNCT
ejpam-5528	143	12	for	for	ADP
ejpam-5528	143	13	all	all	DET
ejpam-5528	143	14	u	u	NOUN
ejpam-5528	143	15	∈	∈	PROPN
ejpam-5528	143	16	ℜ.	ℜ.	PROPN
ejpam-5528	143	17	now	now	ADV
ejpam-5528	143	18	2αβ	2αβ	ADJ
ejpam-5528	143	19	is	be	AUX
ejpam-5528	143	20	invertible	invertible	ADJ
ejpam-5528	143	21	in	in	ADP
ejpam-5528	143	22	c.	c.	PROPN
ejpam-5528	143	23	hence	hence	ADV
ejpam-5528	143	24	,	,	PUNCT
ejpam-5528	143	25	we	we	PRON
ejpam-5528	143	26	have	have	VERB
ejpam-5528	143	27	ω(u	ω(u	NUM
ejpam-5528	143	28	)	)	PUNCT
ejpam-5528	144	1	=	=	PUNCT
ejpam-5528	144	2	uq	uq	NOUN
ejpam-5528	144	3	+	+	PUNCT
ejpam-5528	144	4	q1u	q1u	NOUN
ejpam-5528	144	5	∗	∗	NOUN
ejpam-5528	144	6	,	,	PUNCT
ejpam-5528	144	7	(	(	PUNCT
ejpam-5528	144	8	2.8	2.8	NUM
ejpam-5528	144	9	)	)	PUNCT
ejpam-5528	144	10	for	for	ADP
ejpam-5528	144	11	all	all	DET
ejpam-5528	144	12	u	u	PRON
ejpam-5528	144	13	∈	∈	PROPN
ejpam-5528	144	14	ℜ	ℜ	PROPN
ejpam-5528	144	15	,	,	PUNCT
ejpam-5528	144	16	where	where	SCONJ
ejpam-5528	144	17	q	q	NOUN
ejpam-5528	144	18	=	=	SYM
ejpam-5528	144	19	(	(	PUNCT
ejpam-5528	144	20	2αβ)−1(αω−1(β)∗−βω−1(α)∗	2αβ)−1(αω−1(β)∗−βω−1(α)∗	NUM
ejpam-5528	144	21	)	)	PUNCT
ejpam-5528	144	22	∈	∈	PROPN
ejpam-5528	144	23	ℜc	ℜc	PROPN
ejpam-5528	144	24	and	and	CCONJ
ejpam-5528	144	25	q1	q1	PROPN
ejpam-5528	144	26	=	=	SYM
ejpam-5528	144	27	(	(	PUNCT
ejpam-5528	144	28	2αβ)−1(βω−1(α)−	2αβ)−1(βω−1(α)−	NUM
ejpam-5528	144	29	αω−1(β	αω−1(β	NOUN
ejpam-5528	144	30	)	)	PUNCT
ejpam-5528	144	31	)	)	PUNCT
ejpam-5528	145	1	∈	∈	PROPN
ejpam-5528	145	2	ℜc	ℜc	PROPN
ejpam-5528	145	3	.	.	PUNCT
ejpam-5528	145	4	using	use	VERB
ejpam-5528	145	5	this	this	PRON
ejpam-5528	145	6	in	in	ADP
ejpam-5528	145	7	(	(	PUNCT
ejpam-5528	145	8	2.1	2.1	NUM
ejpam-5528	145	9	)	)	PUNCT
ejpam-5528	145	10	,	,	PUNCT
ejpam-5528	145	11	we	we	PRON
ejpam-5528	145	12	get	get	VERB
ejpam-5528	145	13	(	(	PUNCT
ejpam-5528	145	14	uq	uq	NOUN
ejpam-5528	145	15	+	+	ADJ
ejpam-5528	145	16	q1u	q1u	NOUN
ejpam-5528	145	17	∗)(q∗v∗	∗)(q∗v∗	PROPN
ejpam-5528	145	18	+	+	PROPN
ejpam-5528	145	19	vq∗1)−	vq∗1)−	PROPN
ejpam-5528	145	20	(	(	PUNCT
ejpam-5528	145	21	vq	vq	PROPN
ejpam-5528	146	1	+	+	CCONJ
ejpam-5528	146	2	q1v	q1v	PROPN
ejpam-5528	146	3	∗)(q∗u∗	∗)(q∗u∗	PROPN
ejpam-5528	146	4	+	+	CCONJ
ejpam-5528	146	5	uq∗1	uq∗1	ADJ
ejpam-5528	146	6	)	)	PUNCT
ejpam-5528	146	7	=	=	PUNCT
ejpam-5528	146	8	uv∗	uv∗	ADJ
ejpam-5528	146	9	−	−	NOUN
ejpam-5528	146	10	vu∗	vu∗	NOUN
ejpam-5528	146	11	,	,	PUNCT
ejpam-5528	146	12	(	(	PUNCT
ejpam-5528	146	13	2.9	2.9	NUM
ejpam-5528	146	14	)	)	PUNCT
ejpam-5528	146	15	for	for	ADP
ejpam-5528	146	16	all	all	DET
ejpam-5528	146	17	u	u	NOUN
ejpam-5528	146	18	,	,	PUNCT
ejpam-5528	146	19	v	v	NOUN
ejpam-5528	146	20	∈	∈	NOUN
ejpam-5528	146	21	ℜ.	ℜ.	ADJ
ejpam-5528	146	22	replacing	replace	VERB
ejpam-5528	146	23	v	v	NOUN
ejpam-5528	146	24	by	by	ADP
ejpam-5528	146	25	αv	αv	NOUN
ejpam-5528	146	26	in	in	ADP
ejpam-5528	146	27	(	(	PUNCT
ejpam-5528	146	28	2.9	2.9	NUM
ejpam-5528	146	29	)	)	PUNCT
ejpam-5528	146	30	,	,	PUNCT
ejpam-5528	146	31	we	we	PRON
ejpam-5528	146	32	get	get	VERB
ejpam-5528	146	33	(	(	PUNCT
ejpam-5528	146	34	uq	uq	NOUN
ejpam-5528	146	35	+	+	NOUN
ejpam-5528	146	36	q1u	q1u	NOUN
ejpam-5528	146	37	∗)(−q∗v∗	∗)(−q∗v∗	NOUN
ejpam-5528	146	38	+	+	X
ejpam-5528	146	39	vq∗1)−	vq∗1)−	PROPN
ejpam-5528	146	40	(	(	PUNCT
ejpam-5528	146	41	vq	vq	PROPN
ejpam-5528	146	42	−	−	PROPN
ejpam-5528	146	43	q1v	q1v	PROPN
ejpam-5528	146	44	∗)(q∗u∗	∗)(q∗u∗	PROPN
ejpam-5528	146	45	+	+	CCONJ
ejpam-5528	146	46	uq∗1	uq∗1	ADJ
ejpam-5528	146	47	)	)	PUNCT
ejpam-5528	146	48	=	=	PUNCT
ejpam-5528	147	1	−uv∗	−uv∗	VERB
ejpam-5528	147	2	−	−	PROPN
ejpam-5528	147	3	vu∗	vu∗	NOUN
ejpam-5528	147	4	,	,	PUNCT
ejpam-5528	147	5	(	(	PUNCT
ejpam-5528	147	6	2.10	2.10	NUM
ejpam-5528	147	7	)	)	PUNCT
ejpam-5528	147	8	for	for	ADP
ejpam-5528	147	9	all	all	DET
ejpam-5528	147	10	u	u	NOUN
ejpam-5528	147	11	,	,	PUNCT
ejpam-5528	147	12	v	v	NOUN
ejpam-5528	147	13	∈	∈	NOUN
ejpam-5528	147	14	ℜ.	ℜ.	PROPN
ejpam-5528	147	15	subtracting	subtracting	NOUN
ejpam-5528	147	16	(	(	PUNCT
ejpam-5528	147	17	2.10	2.10	NUM
ejpam-5528	147	18	)	)	PUNCT
ejpam-5528	147	19	and	and	CCONJ
ejpam-5528	147	20	(	(	PUNCT
ejpam-5528	147	21	2.9	2.9	NUM
ejpam-5528	147	22	)	)	PUNCT
ejpam-5528	147	23	,	,	PUNCT
ejpam-5528	147	24	we	we	PRON
ejpam-5528	147	25	find	find	VERB
ejpam-5528	147	26	that	that	SCONJ
ejpam-5528	147	27	(	(	PUNCT
ejpam-5528	147	28	uq	uq	NOUN
ejpam-5528	147	29	+	+	ADJ
ejpam-5528	147	30	q1u	q1u	NOUN
ejpam-5528	147	31	∗)q∗v∗	∗)q∗v∗	NUM
ejpam-5528	147	32	−	−	PROPN
ejpam-5528	147	33	q1v	q1v	NOUN
ejpam-5528	147	34	∗(q∗u∗	∗(q∗u∗	PUNCT
ejpam-5528	147	35	+	+	CCONJ
ejpam-5528	147	36	uq∗1	uq∗1	ADJ
ejpam-5528	147	37	)	)	PUNCT
ejpam-5528	147	38	=	=	PUNCT
ejpam-5528	147	39	uv∗	uv∗	ADJ
ejpam-5528	147	40	,	,	PUNCT
ejpam-5528	147	41	(	(	PUNCT
ejpam-5528	147	42	2.11	2.11	NUM
ejpam-5528	147	43	)	)	PUNCT
ejpam-5528	147	44	moin	moin	NOUN
ejpam-5528	147	45	a.	a.	NOUN
ejpam-5528	147	46	ansari	ansari	PROPN
ejpam-5528	147	47	et	et	PROPN
ejpam-5528	147	48	al	al	PROPN
ejpam-5528	147	49	.	.	PUNCT
ejpam-5528	147	50	/	/	SYM
ejpam-5528	147	51	eur	eur	PROPN
ejpam-5528	147	52	.	.	PUNCT
ejpam-5528	148	1	j.	j.	PROPN
ejpam-5528	148	2	pure	pure	PROPN
ejpam-5528	148	3	appl	appl	PROPN
ejpam-5528	148	4	.	.	PROPN
ejpam-5528	148	5	math	math	PROPN
ejpam-5528	148	6	,	,	PUNCT
ejpam-5528	148	7	18	18	NUM
ejpam-5528	148	8	(	(	PUNCT
ejpam-5528	148	9	2	2	NUM
ejpam-5528	148	10	)	)	PUNCT
ejpam-5528	148	11	(	(	PUNCT
ejpam-5528	148	12	2025	2025	NUM
ejpam-5528	148	13	)	)	PUNCT
ejpam-5528	148	14	,	,	PUNCT
ejpam-5528	148	15	5528	5528	NUM
ejpam-5528	148	16	6	6	NUM
ejpam-5528	148	17	of	of	ADP
ejpam-5528	148	18	14	14	NUM
ejpam-5528	148	19	for	for	ADP
ejpam-5528	148	20	all	all	DET
ejpam-5528	148	21	u	u	NOUN
ejpam-5528	148	22	,	,	PUNCT
ejpam-5528	148	23	v	v	NOUN
ejpam-5528	148	24	∈	∈	PROPN
ejpam-5528	148	25	ℜ.alter	ℜ.alter	NOUN
ejpam-5528	148	26	u	u	NOUN
ejpam-5528	148	27	by	by	ADP
ejpam-5528	148	28	αu	αu	PRON
ejpam-5528	148	29	in	in	ADP
ejpam-5528	148	30	(	(	PUNCT
ejpam-5528	148	31	2.11	2.11	NUM
ejpam-5528	148	32	)	)	PUNCT
ejpam-5528	148	33	,	,	PUNCT
ejpam-5528	148	34	we	we	PRON
ejpam-5528	148	35	have	have	AUX
ejpam-5528	148	36	(	(	PUNCT
ejpam-5528	148	37	uq	uq	NOUN
ejpam-5528	148	38	−	−	PROPN
ejpam-5528	148	39	q1u	q1u	VERB
ejpam-5528	148	40	∗)q∗v∗	∗)q∗v∗	NUM
ejpam-5528	148	41	−	−	PROPN
ejpam-5528	148	42	q1v	q1v	VERB
ejpam-5528	148	43	∗(−q∗u∗	∗(−q∗u∗	NOUN
ejpam-5528	148	44	+	+	CCONJ
ejpam-5528	148	45	uq∗1	uq∗1	ADJ
ejpam-5528	148	46	)	)	PUNCT
ejpam-5528	148	47	=	=	PUNCT
ejpam-5528	148	48	uv∗	uv∗	ADJ
ejpam-5528	148	49	,	,	PUNCT
ejpam-5528	148	50	(	(	PUNCT
ejpam-5528	148	51	2.12	2.12	NUM
ejpam-5528	148	52	)	)	PUNCT
ejpam-5528	148	53	for	for	ADP
ejpam-5528	148	54	all	all	DET
ejpam-5528	148	55	u	u	NOUN
ejpam-5528	148	56	,	,	PUNCT
ejpam-5528	148	57	v	v	NOUN
ejpam-5528	148	58	∈	∈	NOUN
ejpam-5528	148	59	ℜ.	ℜ.	PROPN
ejpam-5528	148	60	subtracting	subtracting	NOUN
ejpam-5528	148	61	(	(	PUNCT
ejpam-5528	148	62	2.12	2.12	NUM
ejpam-5528	148	63	)	)	PUNCT
ejpam-5528	148	64	from	from	ADP
ejpam-5528	148	65	(	(	PUNCT
ejpam-5528	148	66	2.11	2.11	NUM
ejpam-5528	148	67	)	)	PUNCT
ejpam-5528	148	68	,	,	PUNCT
ejpam-5528	148	69	we	we	PRON
ejpam-5528	148	70	obtain	obtain	VERB
ejpam-5528	148	71	q1u	q1u	NOUN
ejpam-5528	148	72	∗q∗v∗	∗q∗v∗	NOUN
ejpam-5528	149	1	=	=	SYM
ejpam-5528	149	2	q1v	q1v	NOUN
ejpam-5528	149	3	∗q∗u∗	∗q∗u∗	PROPN
ejpam-5528	149	4	,	,	PUNCT
ejpam-5528	149	5	(	(	PUNCT
ejpam-5528	149	6	2.13	2.13	NUM
ejpam-5528	149	7	)	)	PUNCT
ejpam-5528	149	8	for	for	ADP
ejpam-5528	149	9	all	all	DET
ejpam-5528	149	10	u	u	NOUN
ejpam-5528	149	11	,	,	PUNCT
ejpam-5528	149	12	v	v	NOUN
ejpam-5528	149	13	∈	∈	NOUN
ejpam-5528	149	14	ℜ.	ℜ.	ADJ
ejpam-5528	149	15	setting	set	VERB
ejpam-5528	149	16	u	u	NOUN
ejpam-5528	149	17	=	=	NOUN
ejpam-5528	149	18	α	α	X
ejpam-5528	149	19	in	in	ADP
ejpam-5528	149	20	(	(	PUNCT
ejpam-5528	149	21	2.13	2.13	NUM
ejpam-5528	149	22	)	)	PUNCT
ejpam-5528	149	23	,	,	PUNCT
ejpam-5528	149	24	we	we	PRON
ejpam-5528	149	25	get	get	VERB
ejpam-5528	149	26	q1[q	q1[q	NOUN
ejpam-5528	149	27	∗	∗	NOUN
ejpam-5528	149	28	,	,	PUNCT
ejpam-5528	149	29	v	v	NOUN
ejpam-5528	149	30	]	]	X
ejpam-5528	149	31	=	=	SYM
ejpam-5528	149	32	0	0	NUM
ejpam-5528	149	33	for	for	ADP
ejpam-5528	149	34	all	all	PRON
ejpam-5528	149	35	v	v	NOUN
ejpam-5528	149	36	∈	∈	NOUN
ejpam-5528	149	37	ℜ.	ℜ.	PROPN
ejpam-5528	149	38	therefore	therefore	ADV
ejpam-5528	149	39	,	,	PUNCT
ejpam-5528	149	40	q1	q1	PROPN
ejpam-5528	149	41	=	=	SYM
ejpam-5528	149	42	0	0	NUM
ejpam-5528	149	43	or	or	CCONJ
ejpam-5528	149	44	q	q	PROPN
ejpam-5528	149	45	∈	∈	PROPN
ejpam-5528	149	46	c.	c.	NOUN
ejpam-5528	149	47	if	if	SCONJ
ejpam-5528	149	48	q1	q1	PROPN
ejpam-5528	149	49	=	=	SYM
ejpam-5528	149	50	0	0	NUM
ejpam-5528	149	51	,	,	PUNCT
ejpam-5528	149	52	then	then	ADV
ejpam-5528	149	53	from	from	ADP
ejpam-5528	149	54	(	(	PUNCT
ejpam-5528	149	55	2.11	2.11	NUM
ejpam-5528	149	56	)	)	PUNCT
ejpam-5528	149	57	,	,	PUNCT
ejpam-5528	149	58	we	we	PRON
ejpam-5528	149	59	find	find	VERB
ejpam-5528	149	60	that	that	SCONJ
ejpam-5528	149	61	u(qq∗	u(qq∗	ADJ
ejpam-5528	149	62	−	−	PROPN
ejpam-5528	149	63	1)v	1)v	NUM
ejpam-5528	149	64	=	=	SYM
ejpam-5528	149	65	0	0	NUM
ejpam-5528	149	66	for	for	ADP
ejpam-5528	149	67	all	all	DET
ejpam-5528	149	68	u	u	NOUN
ejpam-5528	149	69	,	,	PUNCT
ejpam-5528	149	70	v	v	NOUN
ejpam-5528	149	71	∈	∈	NOUN
ejpam-5528	149	72	ℜ.	ℜ.	PROPN
ejpam-5528	149	73	consequently	consequently	ADV
ejpam-5528	149	74	,	,	PUNCT
ejpam-5528	149	75	qq∗	qq∗	ADJ
ejpam-5528	149	76	=	=	NOUN
ejpam-5528	150	1	1	1	X
ejpam-5528	150	2	.	.	X
ejpam-5528	150	3	hence	hence	ADV
ejpam-5528	150	4	we	we	PRON
ejpam-5528	150	5	assume	assume	VERB
ejpam-5528	150	6	that	that	SCONJ
ejpam-5528	150	7	q	q	PROPN
ejpam-5528	150	8	∈	∈	PROPN
ejpam-5528	150	9	c.	c.	NOUN
ejpam-5528	150	10	adding	add	VERB
ejpam-5528	150	11	(	(	PUNCT
ejpam-5528	150	12	2.11	2.11	NUM
ejpam-5528	150	13	)	)	PUNCT
ejpam-5528	150	14	and	and	CCONJ
ejpam-5528	150	15	(	(	PUNCT
ejpam-5528	150	16	2.12	2.12	NUM
ejpam-5528	150	17	)	)	PUNCT
ejpam-5528	150	18	,	,	PUNCT
ejpam-5528	150	19	we	we	PRON
ejpam-5528	150	20	obtain	obtain	VERB
ejpam-5528	150	21	qq∗uv	qq∗uv	NOUN
ejpam-5528	150	22	−	−	PROPN
ejpam-5528	150	23	q1vuq	q1vuq	PROPN
ejpam-5528	150	24	∗	∗	NOUN
ejpam-5528	150	25	1	1	NUM
ejpam-5528	150	26	=	=	SYM
ejpam-5528	150	27	uv	uv	NOUN
ejpam-5528	150	28	,	,	PUNCT
ejpam-5528	150	29	(	(	PUNCT
ejpam-5528	150	30	2.14	2.14	NUM
ejpam-5528	150	31	)	)	PUNCT
ejpam-5528	150	32	for	for	ADP
ejpam-5528	150	33	all	all	DET
ejpam-5528	150	34	u	u	NOUN
ejpam-5528	150	35	,	,	PUNCT
ejpam-5528	150	36	v	v	NOUN
ejpam-5528	150	37	∈	∈	NOUN
ejpam-5528	150	38	ℜ.	ℜ.	PROPN
ejpam-5528	150	39	putting	put	VERB
ejpam-5528	150	40	u	u	NOUN
ejpam-5528	150	41	=	=	X
ejpam-5528	150	42	v	v	NOUN
ejpam-5528	150	43	=	=	SYM
ejpam-5528	150	44	α	α	NOUN
ejpam-5528	150	45	in	in	ADP
ejpam-5528	150	46	(	(	PUNCT
ejpam-5528	150	47	2.14	2.14	NUM
ejpam-5528	150	48	)	)	PUNCT
ejpam-5528	150	49	,	,	PUNCT
ejpam-5528	150	50	we	we	PRON
ejpam-5528	150	51	find	find	VERB
ejpam-5528	150	52	that	that	SCONJ
ejpam-5528	150	53	qq∗	qq∗	ADJ
ejpam-5528	150	54	−	−	PROPN
ejpam-5528	150	55	q1q	q1q	PROPN
ejpam-5528	150	56	∗	∗	NOUN
ejpam-5528	150	57	1	1	NUM
ejpam-5528	150	58	=	=	SYM
ejpam-5528	150	59	1	1	NUM
ejpam-5528	150	60	.	.	PUNCT
ejpam-5528	150	61	(	(	PUNCT
ejpam-5528	150	62	2.15	2.15	NUM
ejpam-5528	150	63	)	)	PUNCT
ejpam-5528	150	64	hence	hence	ADV
ejpam-5528	150	65	from	from	ADP
ejpam-5528	150	66	(	(	PUNCT
ejpam-5528	150	67	2.14	2.14	NUM
ejpam-5528	150	68	)	)	PUNCT
ejpam-5528	150	69	,	,	PUNCT
ejpam-5528	150	70	we	we	PRON
ejpam-5528	150	71	have	have	VERB
ejpam-5528	150	72	q1q	q1q	PROPN
ejpam-5528	150	73	∗	∗	NOUN
ejpam-5528	150	74	1uv	1uv	NOUN
ejpam-5528	151	1	=	=	PUNCT
ejpam-5528	151	2	q1vuq	q1vuq	PROPN
ejpam-5528	151	3	∗	∗	NOUN
ejpam-5528	151	4	1	1	NUM
ejpam-5528	151	5	for	for	ADP
ejpam-5528	151	6	all	all	DET
ejpam-5528	151	7	u	u	NOUN
ejpam-5528	151	8	,	,	PUNCT
ejpam-5528	151	9	v	v	NOUN
ejpam-5528	151	10	∈	∈	NOUN
ejpam-5528	151	11	ℜ.	ℜ.	PROPN
ejpam-5528	151	12	taking	take	VERB
ejpam-5528	151	13	v	v	NOUN
ejpam-5528	151	14	=	=	SYM
ejpam-5528	151	15	α	α	NOUN
ejpam-5528	151	16	in	in	ADP
ejpam-5528	151	17	the	the	DET
ejpam-5528	151	18	last	last	ADJ
ejpam-5528	151	19	relation	relation	NOUN
ejpam-5528	151	20	,	,	PUNCT
ejpam-5528	151	21	we	we	PRON
ejpam-5528	151	22	have	have	VERB
ejpam-5528	151	23	q1[q	q1[q	NOUN
ejpam-5528	151	24	∗	∗	PROPN
ejpam-5528	151	25	1	1	NUM
ejpam-5528	151	26	,	,	PUNCT
ejpam-5528	151	27	u	u	NOUN
ejpam-5528	151	28	]	]	X
ejpam-5528	151	29	=	=	SYM
ejpam-5528	151	30	0	0	NUM
ejpam-5528	151	31	for	for	ADP
ejpam-5528	151	32	all	all	DET
ejpam-5528	151	33	u	u	NOUN
ejpam-5528	151	34	∈	∈	PROPN
ejpam-5528	151	35	ℜ.	ℜ.	PROPN
ejpam-5528	151	36	therefore	therefore	ADV
ejpam-5528	151	37	q1	q1	VERB
ejpam-5528	151	38	∈	∈	PROPN
ejpam-5528	151	39	c	c	PROPN
ejpam-5528	151	40	and	and	CCONJ
ejpam-5528	151	41	hence	hence	ADV
ejpam-5528	151	42	from	from	ADP
ejpam-5528	151	43	(	(	PUNCT
ejpam-5528	151	44	2.14	2.14	NUM
ejpam-5528	151	45	)	)	PUNCT
ejpam-5528	151	46	,	,	PUNCT
ejpam-5528	151	47	we	we	PRON
ejpam-5528	151	48	find	find	VERB
ejpam-5528	151	49	that	that	SCONJ
ejpam-5528	151	50	qq∗uv	qq∗uv	ADJ
ejpam-5528	151	51	−	−	PROPN
ejpam-5528	151	52	q1q	q1q	PROPN
ejpam-5528	151	53	∗	∗	NOUN
ejpam-5528	151	54	1vu	1vu	NOUN
ejpam-5528	152	1	=	=	SYM
ejpam-5528	152	2	uv	uv	NOUN
ejpam-5528	152	3	for	for	ADP
ejpam-5528	152	4	all	all	DET
ejpam-5528	152	5	u	u	NOUN
ejpam-5528	152	6	,	,	PUNCT
ejpam-5528	152	7	v	v	NOUN
ejpam-5528	152	8	∈	∈	NOUN
ejpam-5528	152	9	ℜ.	ℜ.	ADJ
ejpam-5528	152	10	using	use	VERB
ejpam-5528	152	11	(	(	PUNCT
ejpam-5528	152	12	2.15	2.15	NUM
ejpam-5528	152	13	)	)	PUNCT
ejpam-5528	152	14	,	,	PUNCT
ejpam-5528	152	15	we	we	PRON
ejpam-5528	152	16	get	get	VERB
ejpam-5528	152	17	q1q	q1q	PROPN
ejpam-5528	152	18	∗	∗	NOUN
ejpam-5528	152	19	1(uv	1(uv	NUM
ejpam-5528	152	20	+	+	CCONJ
ejpam-5528	152	21	vu	vu	X
ejpam-5528	152	22	)	)	PUNCT
ejpam-5528	152	23	=	=	SYM
ejpam-5528	152	24	0	0	NUM
ejpam-5528	152	25	for	for	ADP
ejpam-5528	152	26	all	all	DET
ejpam-5528	152	27	u	u	NOUN
ejpam-5528	152	28	,	,	PUNCT
ejpam-5528	152	29	v	v	NOUN
ejpam-5528	152	30	∈	∈	NOUN
ejpam-5528	152	31	ℜ.	ℜ.	PROPN
ejpam-5528	152	32	putting	put	VERB
ejpam-5528	152	33	u	u	NOUN
ejpam-5528	152	34	=	=	X
ejpam-5528	152	35	v	v	NOUN
ejpam-5528	152	36	=	=	SYM
ejpam-5528	152	37	α	α	PROPN
ejpam-5528	152	38	in	in	ADP
ejpam-5528	152	39	the	the	DET
ejpam-5528	152	40	previous	previous	ADJ
ejpam-5528	152	41	relation	relation	NOUN
ejpam-5528	152	42	,	,	PUNCT
ejpam-5528	152	43	we	we	PRON
ejpam-5528	152	44	get	get	VERB
ejpam-5528	152	45	q1q	q1q	PROPN
ejpam-5528	152	46	∗	∗	NOUN
ejpam-5528	152	47	1	1	NUM
ejpam-5528	152	48	=	=	SYM
ejpam-5528	152	49	0	0	NUM
ejpam-5528	152	50	.	.	PUNCT
ejpam-5528	153	1	since	since	SCONJ
ejpam-5528	153	2	c	c	PROPN
ejpam-5528	153	3	is	be	AUX
ejpam-5528	153	4	a	a	DET
ejpam-5528	153	5	field	field	NOUN
ejpam-5528	153	6	,	,	PUNCT
ejpam-5528	153	7	we	we	PRON
ejpam-5528	153	8	conclude	conclude	VERB
ejpam-5528	153	9	that	that	DET
ejpam-5528	153	10	q1	q1	PROPN
ejpam-5528	153	11	=	=	PUNCT
ejpam-5528	153	12	0	0	X
ejpam-5528	153	13	.	.	PUNCT
ejpam-5528	154	1	from	from	ADP
ejpam-5528	154	2	(	(	PUNCT
ejpam-5528	154	3	2.8	2.8	NUM
ejpam-5528	154	4	)	)	PUNCT
ejpam-5528	154	5	,	,	PUNCT
ejpam-5528	154	6	we	we	PRON
ejpam-5528	154	7	infer	infer	VERB
ejpam-5528	154	8	that	that	SCONJ
ejpam-5528	154	9	ω(u	ω(u	NOUN
ejpam-5528	154	10	)	)	PUNCT
ejpam-5528	155	1	=	=	SYM
ejpam-5528	155	2	uq	uq	NOUN
ejpam-5528	155	3	for	for	ADP
ejpam-5528	155	4	all	all	DET
ejpam-5528	155	5	u	u	NOUN
ejpam-5528	155	6	∈	∈	PROPN
ejpam-5528	155	7	ℜ.	ℜ.	VERB
ejpam-5528	155	8	the	the	DET
ejpam-5528	155	9	following	follow	VERB
ejpam-5528	155	10	example	example	NOUN
ejpam-5528	155	11	shows	show	VERB
ejpam-5528	155	12	that	that	SCONJ
ejpam-5528	155	13	theorem	theorem	VERB
ejpam-5528	155	14	2.1	2.1	NUM
ejpam-5528	155	15	does	do	AUX
ejpam-5528	155	16	not	not	PART
ejpam-5528	155	17	hold	hold	VERB
ejpam-5528	155	18	if	if	SCONJ
ejpam-5528	155	19	dimcℜc	dimcℜc	ADJ
ejpam-5528	155	20	=	=	SYM
ejpam-5528	155	21	4	4	NUM
ejpam-5528	155	22	and	and	CCONJ
ejpam-5528	155	23	‘	'	PUNCT
ejpam-5528	155	24	∗	∗	NOUN
ejpam-5528	155	25	’	'	PUNCT
ejpam-5528	155	26	is	be	AUX
ejpam-5528	155	27	of	of	ADP
ejpam-5528	155	28	the	the	DET
ejpam-5528	155	29	first	first	ADJ
ejpam-5528	155	30	kind	kind	NOUN
ejpam-5528	155	31	.	.	PUNCT
ejpam-5528	156	1	example	example	NOUN
ejpam-5528	156	2	2.1	2.1	NUM
ejpam-5528	156	3	.	.	PUNCT
ejpam-5528	157	1	consider	consider	VERB
ejpam-5528	157	2	the	the	DET
ejpam-5528	157	3	ring	ring	NOUN
ejpam-5528	157	4	m2(k	m2(k	PROPN
ejpam-5528	157	5	)	)	PUNCT
ejpam-5528	157	6	of	of	ADP
ejpam-5528	157	7	all	all	DET
ejpam-5528	157	8	2	2	NUM
ejpam-5528	157	9	×	×	NOUN
ejpam-5528	157	10	2	2	NUM
ejpam-5528	157	11	matrices	matrix	NOUN
ejpam-5528	157	12	over	over	ADP
ejpam-5528	157	13	any	any	DET
ejpam-5528	157	14	field	field	NOUN
ejpam-5528	157	15	k	k	X
ejpam-5528	157	16	with	with	ADP
ejpam-5528	157	17	involution	involution	NOUN
ejpam-5528	157	18	∗	∗	NOUN
ejpam-5528	157	19	as	as	ADP
ejpam-5528	157	20	the	the	DET
ejpam-5528	157	21	usual	usual	ADJ
ejpam-5528	157	22	transpose	transpose	NOUN
ejpam-5528	157	23	map	map	NOUN
ejpam-5528	157	24	.	.	PUNCT
ejpam-5528	158	1	let	let	VERB
ejpam-5528	158	2	λ	λ	X
ejpam-5528	158	3	∈	∈	PROPN
ejpam-5528	158	4	k	k	AUX
ejpam-5528	158	5	be	be	AUX
ejpam-5528	158	6	fixed	fix	VERB
ejpam-5528	158	7	such	such	ADJ
ejpam-5528	158	8	that	that	DET
ejpam-5528	158	9	λ	λ	PROPN
ejpam-5528	158	10	/∈	/∈	PUNCT
ejpam-5528	158	11	{	{	PUNCT
ejpam-5528	158	12	−1	−1	NOUN
ejpam-5528	158	13	,	,	PUNCT
ejpam-5528	158	14	0	0	NUM
ejpam-5528	158	15	,	,	PUNCT
ejpam-5528	158	16	1	1	NUM
ejpam-5528	158	17	}	}	PUNCT
ejpam-5528	158	18	.	.	PUNCT
ejpam-5528	159	1	define	define	VERB
ejpam-5528	159	2	the	the	DET
ejpam-5528	159	3	map	map	NOUN
ejpam-5528	159	4	ω	ω	NOUN
ejpam-5528	159	5	:	:	PUNCT
ejpam-5528	159	6	m2(k	m2(k	NOUN
ejpam-5528	159	7	)	)	PUNCT
ejpam-5528	159	8	→	→	SYM
ejpam-5528	159	9	m2(k	m2(k	NOUN
ejpam-5528	159	10	)	)	PUNCT
ejpam-5528	159	11	by	by	ADP
ejpam-5528	159	12	ω	ω	PROPN
ejpam-5528	159	13	(	(	PUNCT
ejpam-5528	159	14	[	[	PUNCT
ejpam-5528	159	15	a	a	PRON
ejpam-5528	159	16	b	b	NOUN
ejpam-5528	159	17	c	c	NOUN
ejpam-5528	159	18	d	d	NOUN
ejpam-5528	159	19	]	]	X
ejpam-5528	159	20	)	)	PUNCT
ejpam-5528	160	1	=	=	PUNCT
ejpam-5528	160	2	[	[	PUNCT
ejpam-5528	160	3	λa	λa	X
ejpam-5528	160	4	b	b	X
ejpam-5528	160	5	λ	λ	X
ejpam-5528	160	6	c	c	X
ejpam-5528	160	7	λ	λ	X
ejpam-5528	160	8	λd	λd	X
ejpam-5528	160	9	]	]	PUNCT
ejpam-5528	160	10	.	.	PUNCT
ejpam-5528	161	1	then	then	ADV
ejpam-5528	161	2	it	it	PRON
ejpam-5528	161	3	can	can	AUX
ejpam-5528	161	4	be	be	AUX
ejpam-5528	161	5	easily	easily	ADV
ejpam-5528	161	6	seen	see	VERB
ejpam-5528	161	7	that	that	SCONJ
ejpam-5528	161	8	ω([u	ω([u	NOUN
ejpam-5528	161	9	,	,	PUNCT
ejpam-5528	161	10	v]•	v]•	NOUN
ejpam-5528	161	11	)	)	PUNCT
ejpam-5528	161	12	=	=	PUNCT
ejpam-5528	162	1	[	[	X
ejpam-5528	162	2	u	u	NOUN
ejpam-5528	162	3	,	,	PUNCT
ejpam-5528	162	4	v]•	v]•	PROPN
ejpam-5528	162	5	holds	hold	VERB
ejpam-5528	162	6	for	for	ADP
ejpam-5528	162	7	all	all	DET
ejpam-5528	162	8	u	u	NOUN
ejpam-5528	162	9	,	,	PUNCT
ejpam-5528	162	10	v	v	NOUN
ejpam-5528	162	11	∈	∈	PROPN
ejpam-5528	162	12	m2(k	m2(k	PROPN
ejpam-5528	162	13	)	)	PUNCT
ejpam-5528	162	14	.	.	PUNCT
ejpam-5528	163	1	however	however	ADV
ejpam-5528	163	2	,	,	PUNCT
ejpam-5528	163	3	ω	ω	PROPN
ejpam-5528	163	4	is	be	AUX
ejpam-5528	163	5	not	not	PART
ejpam-5528	163	6	of	of	ADP
ejpam-5528	163	7	the	the	DET
ejpam-5528	163	8	form	form	NOUN
ejpam-5528	163	9	as	as	SCONJ
ejpam-5528	163	10	described	describe	VERB
ejpam-5528	163	11	in	in	ADP
ejpam-5528	163	12	theorem	theorem	ADJ
ejpam-5528	163	13	2.1	2.1	NUM
ejpam-5528	163	14	.	.	PUNCT
ejpam-5528	164	1	the	the	DET
ejpam-5528	164	2	following	following	ADJ
ejpam-5528	164	3	result	result	NOUN
ejpam-5528	164	4	gives	give	VERB
ejpam-5528	164	5	a	a	DET
ejpam-5528	164	6	characterization	characterization	NOUN
ejpam-5528	164	7	of	of	ADP
ejpam-5528	164	8	bi	bi	ADJ
ejpam-5528	164	9	-	-	ADJ
ejpam-5528	164	10	skew	skew	ADJ
ejpam-5528	164	11	commuting	commuting	NOUN
ejpam-5528	164	12	maps	map	NOUN
ejpam-5528	164	13	in	in	ADP
ejpam-5528	164	14	prime	prime	ADJ
ejpam-5528	164	15	rings	ring	NOUN
ejpam-5528	164	16	without	without	ADP
ejpam-5528	164	17	assuming	assume	VERB
ejpam-5528	164	18	the	the	DET
ejpam-5528	164	19	existence	existence	NOUN
ejpam-5528	164	20	of	of	ADP
ejpam-5528	164	21	the	the	DET
ejpam-5528	164	22	unity	unity	NOUN
ejpam-5528	164	23	and	and	CCONJ
ejpam-5528	164	24	a	a	DET
ejpam-5528	164	25	nontrivial	nontrivial	ADJ
ejpam-5528	164	26	symmetric	symmetric	ADJ
ejpam-5528	164	27	idempotent	idempotent	NOUN
ejpam-5528	164	28	.	.	PUNCT
ejpam-5528	165	1	theorem	theorem	VERB
ejpam-5528	165	2	2.2	2.2	NUM
ejpam-5528	165	3	.	.	PUNCT
ejpam-5528	166	1	let	let	VERB
ejpam-5528	166	2	ℜ	ℜ	PROPN
ejpam-5528	166	3	be	be	AUX
ejpam-5528	166	4	a	a	DET
ejpam-5528	166	5	prime	prime	ADJ
ejpam-5528	166	6	ring	ring	NOUN
ejpam-5528	166	7	with	with	ADP
ejpam-5528	166	8	an	an	DET
ejpam-5528	166	9	involution	involution	NOUN
ejpam-5528	166	10	‘	'	PUNCT
ejpam-5528	166	11	∗	∗	NOUN
ejpam-5528	166	12	’	'	PUNCT
ejpam-5528	166	13	of	of	ADP
ejpam-5528	166	14	order	order	NOUN
ejpam-5528	166	15	2	2	NUM
ejpam-5528	166	16	and	and	CCONJ
ejpam-5528	166	17	let	let	VERB
ejpam-5528	166	18	ω	ω	NOUN
ejpam-5528	166	19	:	:	PUNCT
ejpam-5528	166	20	ℜ	ℜ	PROPN
ejpam-5528	166	21	→	→	SYM
ejpam-5528	166	22	ℜ	ℜ	PROPN
ejpam-5528	166	23	be	be	AUX
ejpam-5528	166	24	a	a	DET
ejpam-5528	166	25	bi	bi	ADJ
ejpam-5528	166	26	-	-	ADJ
ejpam-5528	166	27	skew	skew	ADJ
ejpam-5528	166	28	commuting	commuting	NOUN
ejpam-5528	166	29	map	map	NOUN
ejpam-5528	166	30	.	.	PUNCT
ejpam-5528	167	1	then	then	ADV
ejpam-5528	167	2	there	there	PRON
ejpam-5528	167	3	exists	exist	VERB
ejpam-5528	167	4	q∗	q∗	NOUN
ejpam-5528	167	5	=	=	SYM
ejpam-5528	167	6	q	q	PUNCT
ejpam-5528	167	7	∈	∈	PROPN
ejpam-5528	167	8	qms(ℜ	qms(ℜ	PROPN
ejpam-5528	167	9	)	)	PUNCT
ejpam-5528	167	10	such	such	ADJ
ejpam-5528	167	11	that	that	DET
ejpam-5528	167	12	ω(u	ω(u	NOUN
ejpam-5528	167	13	)	)	PUNCT
ejpam-5528	167	14	=	=	SYM
ejpam-5528	167	15	uq	uq	NOUN
ejpam-5528	167	16	for	for	ADP
ejpam-5528	167	17	all	all	DET
ejpam-5528	167	18	u	u	NOUN
ejpam-5528	167	19	∈	∈	PROPN
ejpam-5528	167	20	ℜ	ℜ	PROPN
ejpam-5528	167	21	provided	provide	VERB
ejpam-5528	167	22	that	that	SCONJ
ejpam-5528	167	23	either	either	CCONJ
ejpam-5528	167	24	dimcℜc	dimcℜc	VERB
ejpam-5528	167	25	>	>	X
ejpam-5528	167	26	4	4	NUM
ejpam-5528	167	27	or	or	CCONJ
ejpam-5528	167	28	both	both	PRON
ejpam-5528	167	29	char(ℜ	char(ℜ	NOUN
ejpam-5528	167	30	)	)	PUNCT
ejpam-5528	167	31	̸=	̸=	PROPN
ejpam-5528	167	32	2	2	NUM
ejpam-5528	167	33	and	and	CCONJ
ejpam-5528	167	34	’	'	PUNCT
ejpam-5528	167	35	∗	∗	NOUN
ejpam-5528	167	36	‘	'	PUNCT
ejpam-5528	167	37	is	be	AUX
ejpam-5528	167	38	of	of	ADP
ejpam-5528	167	39	the	the	DET
ejpam-5528	167	40	second	second	ADJ
ejpam-5528	167	41	kind	kind	NOUN
ejpam-5528	167	42	.	.	PUNCT
ejpam-5528	168	1	proof	proof	NOUN
ejpam-5528	168	2	.	.	PUNCT
ejpam-5528	169	1	according	accord	VERB
ejpam-5528	169	2	to	to	ADP
ejpam-5528	169	3	the	the	DET
ejpam-5528	169	4	given	give	VERB
ejpam-5528	169	5	hypothesis	hypothesis	NOUN
ejpam-5528	169	6	[	[	X
ejpam-5528	169	7	ω(u	ω(u	NOUN
ejpam-5528	169	8	)	)	PUNCT
ejpam-5528	169	9	,	,	PUNCT
ejpam-5528	169	10	v]•	v]•	X
ejpam-5528	169	11	=	=	PUNCT
ejpam-5528	170	1	[	[	X
ejpam-5528	170	2	u	u	NOUN
ejpam-5528	170	3	,	,	PUNCT
ejpam-5528	170	4	ω(v)]•	ω(v)]•	PUNCT
ejpam-5528	170	5	(	(	PUNCT
ejpam-5528	170	6	2.16	2.16	NUM
ejpam-5528	170	7	)	)	PUNCT
ejpam-5528	170	8	for	for	ADP
ejpam-5528	170	9	all	all	DET
ejpam-5528	170	10	u	u	NOUN
ejpam-5528	170	11	,	,	PUNCT
ejpam-5528	170	12	v	v	NOUN
ejpam-5528	170	13	∈	∈	NOUN
ejpam-5528	170	14	ℜ.	ℜ.	PROPN
ejpam-5528	170	15	first	first	ADV
ejpam-5528	170	16	we	we	PRON
ejpam-5528	170	17	show	show	VERB
ejpam-5528	170	18	ω	ω	PROPN
ejpam-5528	170	19	is	be	AUX
ejpam-5528	170	20	additive	additive	ADJ
ejpam-5528	170	21	.	.	PUNCT
ejpam-5528	171	1	for	for	ADP
ejpam-5528	171	2	every	every	DET
ejpam-5528	171	3	u	u	NOUN
ejpam-5528	171	4	,	,	PUNCT
ejpam-5528	171	5	v	v	NOUN
ejpam-5528	171	6	,	,	PUNCT
ejpam-5528	171	7	w	w	PROPN
ejpam-5528	171	8	∈	∈	PROPN
ejpam-5528	171	9	ℜ	ℜ	PROPN
ejpam-5528	171	10	,	,	PUNCT
ejpam-5528	171	11	we	we	PRON
ejpam-5528	171	12	have	have	VERB
ejpam-5528	171	13	[	[	X
ejpam-5528	171	14	ω(u+	ω(u+	X
ejpam-5528	171	15	w)−	w)−	PROPN
ejpam-5528	171	16	ω(u)−	ω(u)−	NOUN
ejpam-5528	171	17	ω(w	ω(w	NUM
ejpam-5528	171	18	)	)	PUNCT
ejpam-5528	171	19	,	,	PUNCT
ejpam-5528	171	20	v]•	v]•	X
ejpam-5528	172	1	=	=	PUNCT
ejpam-5528	173	1	[	[	X
ejpam-5528	173	2	ω(u+	ω(u+	X
ejpam-5528	173	3	w	w	NOUN
ejpam-5528	173	4	)	)	PUNCT
ejpam-5528	173	5	,	,	PUNCT
ejpam-5528	173	6	v]•	v]•	PROPN
ejpam-5528	174	1	−	−	PROPN
ejpam-5528	175	1	[	[	X
ejpam-5528	175	2	ω(u	ω(u	NUM
ejpam-5528	175	3	)	)	PUNCT
ejpam-5528	175	4	,	,	PUNCT
ejpam-5528	175	5	v]•	v]•	PROPN
ejpam-5528	175	6	−	−	PROPN
ejpam-5528	176	1	[	[	X
ejpam-5528	176	2	ω(w	ω(w	NOUN
ejpam-5528	176	3	)	)	PUNCT
ejpam-5528	176	4	,	,	PUNCT
ejpam-5528	176	5	v]•	v]•	PROPN
ejpam-5528	176	6	moin	moin	PROPN
ejpam-5528	176	7	a.	a.	PROPN
ejpam-5528	176	8	ansari	ansari	PROPN
ejpam-5528	176	9	et	et	PROPN
ejpam-5528	176	10	al	al	PROPN
ejpam-5528	176	11	.	.	PUNCT
ejpam-5528	176	12	/	/	SYM
ejpam-5528	176	13	eur	eur	PROPN
ejpam-5528	176	14	.	.	PUNCT
ejpam-5528	177	1	j.	j.	PROPN
ejpam-5528	177	2	pure	pure	PROPN
ejpam-5528	177	3	appl	appl	PROPN
ejpam-5528	177	4	.	.	PROPN
ejpam-5528	177	5	math	math	PROPN
ejpam-5528	177	6	,	,	PUNCT
ejpam-5528	177	7	18	18	NUM
ejpam-5528	177	8	(	(	PUNCT
ejpam-5528	177	9	2	2	NUM
ejpam-5528	177	10	)	)	PUNCT
ejpam-5528	177	11	(	(	PUNCT
ejpam-5528	177	12	2025	2025	NUM
ejpam-5528	177	13	)	)	PUNCT
ejpam-5528	177	14	,	,	PUNCT
ejpam-5528	177	15	5528	5528	NUM
ejpam-5528	177	16	7	7	NUM
ejpam-5528	177	17	of	of	ADP
ejpam-5528	177	18	14	14	NUM
ejpam-5528	177	19	=	=	SYM
ejpam-5528	178	1	[	[	X
ejpam-5528	178	2	u+	u+	X
ejpam-5528	178	3	w	w	NOUN
ejpam-5528	178	4	,	,	PUNCT
ejpam-5528	178	5	ω(v)]•	ω(v)]•	NUM
ejpam-5528	178	6	−	−	PUNCT
ejpam-5528	178	7	[	[	X
ejpam-5528	178	8	u	u	NOUN
ejpam-5528	178	9	,	,	PUNCT
ejpam-5528	178	10	ω(v)]•	ω(v)]•	NUM
ejpam-5528	178	11	−	−	PUNCT
ejpam-5528	179	1	[	[	X
ejpam-5528	179	2	w	w	NOUN
ejpam-5528	179	3	,	,	PUNCT
ejpam-5528	179	4	ω(v)]•	ω(v)]•	ADP
ejpam-5528	179	5	=	=	SYM
ejpam-5528	179	6	0	0	NUM
ejpam-5528	179	7	applying	apply	VERB
ejpam-5528	179	8	lemma	lemma	PROPN
ejpam-5528	179	9	2.1	2.1	NUM
ejpam-5528	179	10	,	,	PUNCT
ejpam-5528	179	11	we	we	PRON
ejpam-5528	179	12	infer	infer	VERB
ejpam-5528	179	13	that	that	SCONJ
ejpam-5528	179	14	ω(u+	ω(u+	NUM
ejpam-5528	179	15	v	v	NOUN
ejpam-5528	179	16	)	)	PUNCT
ejpam-5528	179	17	=	=	SYM
ejpam-5528	179	18	ω(u	ω(u	PROPN
ejpam-5528	179	19	)	)	PUNCT
ejpam-5528	179	20	+	+	CCONJ
ejpam-5528	179	21	ω(v	ω(v	NOUN
ejpam-5528	179	22	)	)	PUNCT
ejpam-5528	179	23	for	for	ADP
ejpam-5528	179	24	all	all	DET
ejpam-5528	179	25	a	a	DET
ejpam-5528	179	26	,	,	PUNCT
ejpam-5528	179	27	b	b	X
ejpam-5528	179	28	∈	∈	PROPN
ejpam-5528	179	29	ℜ	ℜ	PROPN
ejpam-5528	179	30	,	,	PUNCT
ejpam-5528	179	31	that	that	ADV
ejpam-5528	179	32	is	is	ADV
ejpam-5528	179	33	,	,	PUNCT
ejpam-5528	179	34	ω	ω	PROPN
ejpam-5528	179	35	is	be	AUX
ejpam-5528	179	36	additive	additive	ADJ
ejpam-5528	179	37	.	.	PUNCT
ejpam-5528	180	1	now	now	ADV
ejpam-5528	180	2	(	(	PUNCT
ejpam-5528	180	3	2.16	2.16	NUM
ejpam-5528	180	4	)	)	PUNCT
ejpam-5528	180	5	,	,	PUNCT
ejpam-5528	180	6	can	can	AUX
ejpam-5528	180	7	be	be	AUX
ejpam-5528	180	8	rewritten	rewrite	VERB
ejpam-5528	180	9	as	as	ADP
ejpam-5528	180	10	uω(v)∗	uω(v)∗	PROPN
ejpam-5528	180	11	+	+	NUM
ejpam-5528	180	12	vω(u)∗	vω(u)∗	NOUN
ejpam-5528	180	13	−	−	NOUN
ejpam-5528	180	14	ω(u)v∗	ω(u)v∗	PROPN
ejpam-5528	180	15	−	−	PROPN
ejpam-5528	180	16	ω(v)u∗	ω(v)u∗	NUM
ejpam-5528	180	17	=	=	SYM
ejpam-5528	180	18	0	0	NUM
ejpam-5528	180	19	(	(	PUNCT
ejpam-5528	180	20	2.17	2.17	NUM
ejpam-5528	180	21	)	)	PUNCT
ejpam-5528	180	22	for	for	ADP
ejpam-5528	180	23	all	all	DET
ejpam-5528	180	24	u	u	NOUN
ejpam-5528	180	25	,	,	PUNCT
ejpam-5528	180	26	v	v	NOUN
ejpam-5528	180	27	∈	∈	NOUN
ejpam-5528	180	28	ℜ.	ℜ.	ADV
ejpam-5528	180	29	now	now	ADV
ejpam-5528	180	30	we	we	PRON
ejpam-5528	180	31	proceed	proceed	VERB
ejpam-5528	180	32	by	by	ADP
ejpam-5528	180	33	considering	consider	VERB
ejpam-5528	180	34	the	the	DET
ejpam-5528	180	35	following	follow	VERB
ejpam-5528	180	36	two	two	NUM
ejpam-5528	180	37	cases	case	NOUN
ejpam-5528	180	38	:	:	PUNCT
ejpam-5528	180	39	case	case	NOUN
ejpam-5528	180	40	1	1	NUM
ejpam-5528	180	41	:	:	PUNCT
ejpam-5528	180	42	dim(ℜc	dim(ℜc	NOUN
ejpam-5528	180	43	)	)	PUNCT
ejpam-5528	180	44	>	>	X
ejpam-5528	180	45	4	4	X
ejpam-5528	180	46	.	.	PUNCT
ejpam-5528	180	47	according	accord	VERB
ejpam-5528	180	48	to	to	ADP
ejpam-5528	180	49	[	[	X
ejpam-5528	180	50	27	27	NUM
ejpam-5528	180	51	,	,	PUNCT
ejpam-5528	180	52	theorem	theorem	VERB
ejpam-5528	180	53	3.5	3.5	NUM
ejpam-5528	180	54	]	]	PUNCT
ejpam-5528	180	55	there	there	PRON
ejpam-5528	180	56	exists	exist	VERB
ejpam-5528	180	57	q	q	PROPN
ejpam-5528	180	58	∈	∈	PROPN
ejpam-5528	180	59	qml(ℜ	qml(ℜ	NOUN
ejpam-5528	180	60	)	)	PUNCT
ejpam-5528	180	61	such	such	ADJ
ejpam-5528	180	62	that	that	DET
ejpam-5528	180	63	ω(u	ω(u	NOUN
ejpam-5528	180	64	)	)	PUNCT
ejpam-5528	181	1	=	=	SYM
ejpam-5528	181	2	uq	uq	NOUN
ejpam-5528	181	3	for	for	ADP
ejpam-5528	181	4	all	all	DET
ejpam-5528	181	5	u	u	PRON
ejpam-5528	181	6	∈	∈	PROPN
ejpam-5528	181	7	ℜ	ℜ	PROPN
ejpam-5528	181	8	(	(	PUNCT
ejpam-5528	181	9	2.18	2.18	NUM
ejpam-5528	181	10	)	)	PUNCT
ejpam-5528	181	11	and	and	CCONJ
ejpam-5528	181	12	ω(v)∗	ω(v)∗	NOUN
ejpam-5528	181	13	=	=	PUNCT
ejpam-5528	181	14	qv∗	qv∗	ADJ
ejpam-5528	181	15	for	for	ADP
ejpam-5528	181	16	all	all	PRON
ejpam-5528	181	17	v	v	NOUN
ejpam-5528	181	18	∈	∈	NOUN
ejpam-5528	181	19	ℜ.	ℜ.	PROPN
ejpam-5528	181	20	(	(	PUNCT
ejpam-5528	181	21	2.19	2.19	NUM
ejpam-5528	181	22	)	)	PUNCT
ejpam-5528	181	23	since	since	SCONJ
ejpam-5528	181	24	qv∗	qv∗	ADJ
ejpam-5528	181	25	=	=	SYM
ejpam-5528	181	26	ω(v)∗	ω(v)∗	NOUN
ejpam-5528	181	27	∈	∈	PROPN
ejpam-5528	181	28	ℜ	ℜ	PROPN
ejpam-5528	181	29	for	for	ADP
ejpam-5528	181	30	all	all	PRON
ejpam-5528	181	31	v	v	NOUN
ejpam-5528	181	32	∈	∈	NOUN
ejpam-5528	181	33	ℜ.	ℜ.	PROPN
ejpam-5528	181	34	therefore	therefore	ADV
ejpam-5528	181	35	qℜ	qℜ	NOUN
ejpam-5528	181	36	⊆	⊆	NUM
ejpam-5528	181	37	ℜ	ℜ	NOUN
ejpam-5528	181	38	and	and	CCONJ
ejpam-5528	181	39	hence	hence	ADV
ejpam-5528	181	40	q	q	X
ejpam-5528	181	41	∈	∈	PROPN
ejpam-5528	181	42	qmr(ℜ	qmr(ℜ	PROPN
ejpam-5528	181	43	)	)	PUNCT
ejpam-5528	181	44	.	.	PUNCT
ejpam-5528	182	1	consequently	consequently	ADV
ejpam-5528	182	2	,	,	PUNCT
ejpam-5528	182	3	q	q	PROPN
ejpam-5528	182	4	∈	∈	PROPN
ejpam-5528	182	5	qms(ℜ	qms(ℜ	PROPN
ejpam-5528	182	6	)	)	PUNCT
ejpam-5528	182	7	.	.	PUNCT
ejpam-5528	183	1	thus	thus	ADV
ejpam-5528	183	2	from	from	ADP
ejpam-5528	183	3	(	(	PUNCT
ejpam-5528	183	4	2.19	2.19	NUM
ejpam-5528	183	5	)	)	PUNCT
ejpam-5528	183	6	,	,	PUNCT
ejpam-5528	183	7	we	we	PRON
ejpam-5528	183	8	find	find	VERB
ejpam-5528	183	9	that	that	SCONJ
ejpam-5528	183	10	ω(u	ω(u	NOUN
ejpam-5528	183	11	)	)	PUNCT
ejpam-5528	183	12	=	=	SYM
ejpam-5528	183	13	uq∗	uq∗	ADJ
ejpam-5528	183	14	for	for	ADP
ejpam-5528	183	15	all	all	DET
ejpam-5528	183	16	u	u	PRON
ejpam-5528	183	17	∈	∈	PROPN
ejpam-5528	183	18	ℜ.	ℜ.	PROPN
ejpam-5528	183	19	(	(	PUNCT
ejpam-5528	183	20	2.20	2.20	NUM
ejpam-5528	183	21	)	)	PUNCT
ejpam-5528	183	22	from	from	ADP
ejpam-5528	183	23	(	(	PUNCT
ejpam-5528	183	24	2.18	2.18	NUM
ejpam-5528	183	25	)	)	PUNCT
ejpam-5528	183	26	and	and	CCONJ
ejpam-5528	183	27	(	(	PUNCT
ejpam-5528	183	28	2.20	2.20	NUM
ejpam-5528	183	29	)	)	PUNCT
ejpam-5528	183	30	,	,	PUNCT
ejpam-5528	183	31	we	we	PRON
ejpam-5528	183	32	have	have	VERB
ejpam-5528	183	33	uq	uq	NOUN
ejpam-5528	183	34	=	=	PUNCT
ejpam-5528	183	35	uq∗	uq∗	PROPN
ejpam-5528	183	36	for	for	ADP
ejpam-5528	183	37	all	all	DET
ejpam-5528	183	38	u	u	NOUN
ejpam-5528	183	39	∈	∈	NOUN
ejpam-5528	183	40	ℜ.	ℜ.	PROPN
ejpam-5528	183	41	hence	hence	ADV
ejpam-5528	183	42	q∗	q∗	NOUN
ejpam-5528	183	43	=	=	SYM
ejpam-5528	183	44	q.	q.	NOUN
ejpam-5528	183	45	case	case	NOUN
ejpam-5528	183	46	ii	ii	PROPN
ejpam-5528	183	47	:	:	PUNCT
ejpam-5528	183	48	dim(ℜ	dim(ℜ	PROPN
ejpam-5528	183	49	)	)	PUNCT
ejpam-5528	183	50	≤	≤	NUM
ejpam-5528	183	51	4	4	NUM
ejpam-5528	183	52	.	.	PUNCT
ejpam-5528	184	1	in	in	ADP
ejpam-5528	184	2	this	this	DET
ejpam-5528	184	3	case	case	NOUN
ejpam-5528	184	4	by	by	ADP
ejpam-5528	184	5	[	[	X
ejpam-5528	184	6	26	26	NUM
ejpam-5528	184	7	,	,	PUNCT
ejpam-5528	184	8	theorem	theorem	VERB
ejpam-5528	184	9	2	2	NUM
ejpam-5528	184	10	]	]	PUNCT
ejpam-5528	184	11	,	,	PUNCT
ejpam-5528	184	12	z(a	z(a	NOUN
ejpam-5528	184	13	)	)	PUNCT
ejpam-5528	184	14	̸=	̸=	PROPN
ejpam-5528	184	15	{	{	PUNCT
ejpam-5528	184	16	0	0	NUM
ejpam-5528	184	17	}	}	PUNCT
ejpam-5528	184	18	.	.	PUNCT
ejpam-5528	185	1	also	also	ADV
ejpam-5528	185	2	,	,	PUNCT
ejpam-5528	185	3	by	by	ADP
ejpam-5528	185	4	the	the	DET
ejpam-5528	185	5	given	give	VERB
ejpam-5528	185	6	hypothesis	hypothesis	NOUN
ejpam-5528	185	7	char(ℜ	char(ℜ	PART
ejpam-5528	185	8	)	)	PUNCT
ejpam-5528	185	9	̸=	̸=	PROPN
ejpam-5528	185	10	2	2	NUM
ejpam-5528	185	11	and	and	CCONJ
ejpam-5528	185	12	ζ∗	ζ∗	PROPN
ejpam-5528	185	13	̸=	̸=	PROPN
ejpam-5528	185	14	ζ	ζ	NOUN
ejpam-5528	185	15	for	for	ADP
ejpam-5528	185	16	some	some	DET
ejpam-5528	185	17	ζ	ζ	NOUN
ejpam-5528	185	18	∈	∈	NOUN
ejpam-5528	185	19	z(a	z(a	NOUN
ejpam-5528	185	20	)	)	PUNCT
ejpam-5528	185	21	.	.	PUNCT
ejpam-5528	186	1	let	let	VERB
ejpam-5528	186	2	α	α	NOUN
ejpam-5528	186	3	=	=	SYM
ejpam-5528	186	4	ζ∗	ζ∗	ADJ
ejpam-5528	186	5	−	−	PROPN
ejpam-5528	186	6	ζ	ζ	NOUN
ejpam-5528	186	7	and	and	CCONJ
ejpam-5528	186	8	β	β	X
ejpam-5528	186	9	=	=	PUNCT
ejpam-5528	186	10	α2	α2	PROPN
ejpam-5528	186	11	.	.	PUNCT
ejpam-5528	187	1	then	then	ADV
ejpam-5528	187	2	α∗	α∗	VERB
ejpam-5528	187	3	=	=	PUNCT
ejpam-5528	187	4	−α	−α	NOUN
ejpam-5528	187	5	and	and	CCONJ
ejpam-5528	187	6	β∗	β∗	NOUN
ejpam-5528	187	7	=	=	SYM
ejpam-5528	188	1	β	β	X
ejpam-5528	188	2	.	.	PUNCT
ejpam-5528	189	1	setting	set	VERB
ejpam-5528	189	2	v	v	NOUN
ejpam-5528	189	3	=	=	SYM
ejpam-5528	189	4	α	α	NOUN
ejpam-5528	189	5	in	in	ADP
ejpam-5528	189	6	(	(	PUNCT
ejpam-5528	189	7	2.17	2.17	NUM
ejpam-5528	189	8	)	)	PUNCT
ejpam-5528	189	9	,	,	PUNCT
ejpam-5528	189	10	we	we	PRON
ejpam-5528	189	11	get	get	VERB
ejpam-5528	189	12	α(ω(u	α(ω(u	NOUN
ejpam-5528	189	13	)	)	PUNCT
ejpam-5528	190	1	+	+	NUM
ejpam-5528	190	2	ω(u)∗	ω(u)∗	X
ejpam-5528	190	3	)	)	PUNCT
ejpam-5528	190	4	=	=	SYM
ejpam-5528	190	5	ω(α)u∗	ω(α)u∗	NUM
ejpam-5528	190	6	−	−	PROPN
ejpam-5528	190	7	uω(α)∗	uω(α)∗	PROPN
ejpam-5528	190	8	,	,	PUNCT
ejpam-5528	190	9	(	(	PUNCT
ejpam-5528	190	10	2.21	2.21	NUM
ejpam-5528	190	11	)	)	PUNCT
ejpam-5528	190	12	for	for	ADP
ejpam-5528	190	13	all	all	DET
ejpam-5528	190	14	u	u	NOUN
ejpam-5528	190	15	∈	∈	PROPN
ejpam-5528	190	16	ℜ.	ℜ.	PROPN
ejpam-5528	190	17	also	also	ADV
ejpam-5528	190	18	taking	take	VERB
ejpam-5528	190	19	v	v	NOUN
ejpam-5528	190	20	=	=	PRON
ejpam-5528	190	21	β	β	X
ejpam-5528	190	22	in	in	ADP
ejpam-5528	190	23	(	(	PUNCT
ejpam-5528	190	24	2.17	2.17	NUM
ejpam-5528	190	25	)	)	PUNCT
ejpam-5528	190	26	,	,	PUNCT
ejpam-5528	190	27	we	we	PRON
ejpam-5528	190	28	get	get	VERB
ejpam-5528	190	29	β(ω(u)−	β(ω(u)−	PUNCT
ejpam-5528	190	30	ω(u)∗	ω(u)∗	X
ejpam-5528	190	31	)	)	PUNCT
ejpam-5528	191	1	=	=	PUNCT
ejpam-5528	191	2	uω(β)∗	uω(β)∗	PROPN
ejpam-5528	191	3	−	−	PROPN
ejpam-5528	191	4	ω(β)u∗	ω(β)u∗	PROPN
ejpam-5528	191	5	(	(	PUNCT
ejpam-5528	191	6	2.22	2.22	NUM
ejpam-5528	191	7	)	)	PUNCT
ejpam-5528	191	8	for	for	ADP
ejpam-5528	191	9	all	all	DET
ejpam-5528	191	10	u	u	PRON
ejpam-5528	191	11	∈	∈	PROPN
ejpam-5528	191	12	ℜ.	ℜ.	PROPN
ejpam-5528	191	13	multiplying	multiply	VERB
ejpam-5528	191	14	both	both	DET
ejpam-5528	191	15	sides	side	NOUN
ejpam-5528	191	16	of	of	ADP
ejpam-5528	191	17	(	(	PUNCT
ejpam-5528	191	18	2.21	2.21	NUM
ejpam-5528	191	19	)	)	PUNCT
ejpam-5528	191	20	by	by	ADP
ejpam-5528	191	21	β	β	X
ejpam-5528	191	22	and	and	CCONJ
ejpam-5528	191	23	(	(	PUNCT
ejpam-5528	191	24	2.22	2.22	NUM
ejpam-5528	191	25	)	)	PUNCT
ejpam-5528	191	26	by	by	ADP
ejpam-5528	191	27	α	α	X
ejpam-5528	191	28	,	,	PUNCT
ejpam-5528	191	29	we	we	PRON
ejpam-5528	191	30	get	get	VERB
ejpam-5528	191	31	αβ(ω(u	αβ(ω(u	NOUN
ejpam-5528	191	32	)	)	PUNCT
ejpam-5528	192	1	+	+	CCONJ
ejpam-5528	192	2	ω(u)∗	ω(u)∗	X
ejpam-5528	192	3	)	)	PUNCT
ejpam-5528	192	4	=	=	SYM
ejpam-5528	192	5	βω(α)u∗	βω(α)u∗	NOUN
ejpam-5528	192	6	−	−	NOUN
ejpam-5528	192	7	βuω(α)∗	βuω(α)∗	NOUN
ejpam-5528	192	8	,	,	PUNCT
ejpam-5528	192	9	(	(	PUNCT
ejpam-5528	192	10	2.23	2.23	NUM
ejpam-5528	192	11	)	)	PUNCT
ejpam-5528	192	12	and	and	CCONJ
ejpam-5528	192	13	αβ(ω(u)−	αβ(ω(u)−	NUM
ejpam-5528	192	14	ω(u)∗	ω(u)∗	NOUN
ejpam-5528	192	15	)	)	PUNCT
ejpam-5528	193	1	=	=	SYM
ejpam-5528	193	2	αuω(β)∗	αuω(β)∗	PROPN
ejpam-5528	193	3	−	−	PROPN
ejpam-5528	193	4	αω(β)u∗	αω(β)u∗	NOUN
ejpam-5528	193	5	(	(	PUNCT
ejpam-5528	193	6	2.24	2.24	NUM
ejpam-5528	193	7	)	)	PUNCT
ejpam-5528	193	8	for	for	ADP
ejpam-5528	193	9	all	all	DET
ejpam-5528	193	10	u	u	PRON
ejpam-5528	193	11	∈	∈	PROPN
ejpam-5528	193	12	ℜ	ℜ	PROPN
ejpam-5528	193	13	,	,	PUNCT
ejpam-5528	193	14	respectively	respectively	ADV
ejpam-5528	193	15	.	.	PUNCT
ejpam-5528	194	1	adding	add	VERB
ejpam-5528	194	2	(	(	PUNCT
ejpam-5528	194	3	2.23	2.23	NUM
ejpam-5528	194	4	)	)	PUNCT
ejpam-5528	194	5	and	and	CCONJ
ejpam-5528	194	6	(	(	PUNCT
ejpam-5528	194	7	2.24	2.24	NUM
ejpam-5528	194	8	)	)	PUNCT
ejpam-5528	194	9	,	,	PUNCT
ejpam-5528	194	10	we	we	PRON
ejpam-5528	194	11	find	find	VERB
ejpam-5528	194	12	that	that	SCONJ
ejpam-5528	194	13	ω(u	ω(u	NOUN
ejpam-5528	194	14	)	)	PUNCT
ejpam-5528	195	1	=	=	PUNCT
ejpam-5528	195	2	uq	uq	NOUN
ejpam-5528	195	3	+	+	PUNCT
ejpam-5528	195	4	q1u	q1u	NOUN
ejpam-5528	195	5	∗	∗	NOUN
ejpam-5528	195	6	,	,	PUNCT
ejpam-5528	195	7	(	(	PUNCT
ejpam-5528	195	8	2.25	2.25	NUM
ejpam-5528	195	9	)	)	PUNCT
ejpam-5528	195	10	for	for	ADP
ejpam-5528	195	11	all	all	DET
ejpam-5528	195	12	u	u	PRON
ejpam-5528	195	13	∈	∈	PROPN
ejpam-5528	195	14	ℜ	ℜ	PROPN
ejpam-5528	195	15	,	,	PUNCT
ejpam-5528	195	16	where	where	SCONJ
ejpam-5528	195	17	q	q	NOUN
ejpam-5528	195	18	=	=	X
ejpam-5528	195	19	(	(	PUNCT
ejpam-5528	195	20	2αβ)−1(αω(β)∗	2αβ)−1(αω(β)∗	NUM
ejpam-5528	195	21	−	−	NUM
ejpam-5528	195	22	βω(α)∗	βω(α)∗	NOUN
ejpam-5528	195	23	)	)	PUNCT
ejpam-5528	195	24	∈	∈	PROPN
ejpam-5528	195	25	ℜc	ℜc	PROPN
ejpam-5528	195	26	and	and	CCONJ
ejpam-5528	195	27	q1	q1	PROPN
ejpam-5528	195	28	=	=	SYM
ejpam-5528	195	29	(	(	PUNCT
ejpam-5528	195	30	2αβ)−1(βω(α	2αβ)−1(βω(α	NUM
ejpam-5528	195	31	)	)	PUNCT
ejpam-5528	195	32	−	−	NOUN
ejpam-5528	195	33	αω(β	αω(β	NUM
ejpam-5528	195	34	)	)	PUNCT
ejpam-5528	195	35	)	)	PUNCT
ejpam-5528	196	1	∈	∈	PROPN
ejpam-5528	196	2	ℜc	ℜc	PROPN
ejpam-5528	196	3	.	.	PUNCT
ejpam-5528	196	4	using	use	VERB
ejpam-5528	196	5	this	this	PRON
ejpam-5528	196	6	in	in	ADP
ejpam-5528	196	7	(	(	PUNCT
ejpam-5528	196	8	2.17	2.17	NUM
ejpam-5528	196	9	)	)	PUNCT
ejpam-5528	196	10	,	,	PUNCT
ejpam-5528	196	11	we	we	PRON
ejpam-5528	196	12	have	have	VERB
ejpam-5528	196	13	u(vq∗1	u(vq∗1	ADJ
ejpam-5528	196	14	+	+	NUM
ejpam-5528	196	15	q∗v∗	q∗v∗	NOUN
ejpam-5528	196	16	)	)	PUNCT
ejpam-5528	197	1	+	+	CCONJ
ejpam-5528	197	2	v(uq∗1	v(uq∗1	NOUN
ejpam-5528	197	3	+	+	CCONJ
ejpam-5528	197	4	q∗u∗)−	q∗u∗)−	X
ejpam-5528	197	5	(	(	PUNCT
ejpam-5528	197	6	uq	uq	NOUN
ejpam-5528	197	7	+	+	ADJ
ejpam-5528	197	8	q1u	q1u	NOUN
ejpam-5528	197	9	∗)v∗	∗)v∗	NOUN
ejpam-5528	197	10	−	−	PROPN
ejpam-5528	197	11	(	(	PUNCT
ejpam-5528	197	12	vq	vq	PROPN
ejpam-5528	197	13	+	+	CCONJ
ejpam-5528	197	14	q1v	q1v	PROPN
ejpam-5528	197	15	∗)u∗	∗)u∗	NOUN
ejpam-5528	197	16	=	=	SYM
ejpam-5528	197	17	0	0	NUM
ejpam-5528	197	18	(	(	PUNCT
ejpam-5528	197	19	2.26	2.26	NUM
ejpam-5528	197	20	)	)	PUNCT
ejpam-5528	197	21	moin	moin	NOUN
ejpam-5528	197	22	a.	a.	NOUN
ejpam-5528	197	23	ansari	ansari	PROPN
ejpam-5528	197	24	et	et	PROPN
ejpam-5528	197	25	al	al	PROPN
ejpam-5528	197	26	.	.	PUNCT
ejpam-5528	197	27	/	/	SYM
ejpam-5528	197	28	eur	eur	PROPN
ejpam-5528	197	29	.	.	PUNCT
ejpam-5528	198	1	j.	j.	PROPN
ejpam-5528	198	2	pure	pure	PROPN
ejpam-5528	198	3	appl	appl	PROPN
ejpam-5528	198	4	.	.	PROPN
ejpam-5528	198	5	math	math	PROPN
ejpam-5528	198	6	,	,	PUNCT
ejpam-5528	198	7	18	18	NUM
ejpam-5528	198	8	(	(	PUNCT
ejpam-5528	198	9	2	2	NUM
ejpam-5528	198	10	)	)	PUNCT
ejpam-5528	198	11	(	(	PUNCT
ejpam-5528	198	12	2025	2025	NUM
ejpam-5528	198	13	)	)	PUNCT
ejpam-5528	198	14	,	,	PUNCT
ejpam-5528	198	15	5528	5528	NUM
ejpam-5528	198	16	8	8	NUM
ejpam-5528	198	17	of	of	ADP
ejpam-5528	198	18	14	14	NUM
ejpam-5528	198	19	for	for	ADP
ejpam-5528	198	20	all	all	DET
ejpam-5528	198	21	u	u	NOUN
ejpam-5528	198	22	,	,	PUNCT
ejpam-5528	198	23	v	v	NOUN
ejpam-5528	198	24	∈	∈	PROPN
ejpam-5528	198	25	ℜ.alter	ℜ.alter	ADP
ejpam-5528	198	26	v	v	NUM
ejpam-5528	198	27	by	by	ADP
ejpam-5528	198	28	αv	αv	NOUN
ejpam-5528	198	29	in	in	ADP
ejpam-5528	198	30	(	(	PUNCT
ejpam-5528	198	31	2.26	2.26	NUM
ejpam-5528	198	32	)	)	PUNCT
ejpam-5528	199	1	,	,	PUNCT
ejpam-5528	199	2	we	we	PRON
ejpam-5528	199	3	get	get	VERB
ejpam-5528	199	4	u(vq∗1	u(vq∗1	ADJ
ejpam-5528	199	5	−	−	NOUN
ejpam-5528	199	6	q∗v∗	q∗v∗	NOUN
ejpam-5528	199	7	)	)	PUNCT
ejpam-5528	199	8	+	+	CCONJ
ejpam-5528	199	9	v(uq∗1	v(uq∗1	ADJ
ejpam-5528	199	10	+	+	CCONJ
ejpam-5528	199	11	q∗u∗	q∗u∗	ADJ
ejpam-5528	199	12	)	)	PUNCT
ejpam-5528	200	1	+	+	CCONJ
ejpam-5528	200	2	(	(	PUNCT
ejpam-5528	200	3	uq	uq	NOUN
ejpam-5528	200	4	+	+	ADJ
ejpam-5528	200	5	q1u	q1u	NOUN
ejpam-5528	200	6	∗)v∗	∗)v∗	NOUN
ejpam-5528	200	7	−	−	PROPN
ejpam-5528	200	8	(	(	PUNCT
ejpam-5528	200	9	vq	vq	PROPN
ejpam-5528	200	10	−	−	PROPN
ejpam-5528	200	11	q1v	q1v	NOUN
ejpam-5528	200	12	∗)u∗	∗)u∗	NOUN
ejpam-5528	200	13	=	=	SYM
ejpam-5528	200	14	0	0	NUM
ejpam-5528	200	15	(	(	PUNCT
ejpam-5528	200	16	2.27	2.27	NUM
ejpam-5528	200	17	)	)	PUNCT
ejpam-5528	200	18	for	for	ADP
ejpam-5528	200	19	all	all	DET
ejpam-5528	200	20	u	u	NOUN
ejpam-5528	200	21	,	,	PUNCT
ejpam-5528	200	22	v	v	NOUN
ejpam-5528	200	23	∈	∈	NOUN
ejpam-5528	200	24	ℜ.	ℜ.	PROPN
ejpam-5528	200	25	adding	add	VERB
ejpam-5528	200	26	(	(	PUNCT
ejpam-5528	200	27	2.26	2.26	NUM
ejpam-5528	200	28	)	)	PUNCT
ejpam-5528	200	29	and	and	CCONJ
ejpam-5528	200	30	(	(	PUNCT
ejpam-5528	200	31	2.27	2.27	NUM
ejpam-5528	200	32	)	)	PUNCT
ejpam-5528	200	33	,	,	PUNCT
ejpam-5528	200	34	we	we	PRON
ejpam-5528	200	35	find	find	VERB
ejpam-5528	200	36	that	that	SCONJ
ejpam-5528	200	37	uvq∗1	uvq∗1	ADJ
ejpam-5528	200	38	+	+	CCONJ
ejpam-5528	200	39	v(uq∗1	v(uq∗1	ADJ
ejpam-5528	200	40	+	+	CCONJ
ejpam-5528	200	41	q∗u∗)−	q∗u∗)−	NUM
ejpam-5528	200	42	vqu∗	vqu∗	NOUN
ejpam-5528	200	43	=	=	SYM
ejpam-5528	200	44	0	0	NUM
ejpam-5528	200	45	(	(	PUNCT
ejpam-5528	200	46	2.28	2.28	NUM
ejpam-5528	200	47	)	)	PUNCT
ejpam-5528	200	48	for	for	ADP
ejpam-5528	200	49	all	all	DET
ejpam-5528	200	50	u	u	NOUN
ejpam-5528	200	51	,	,	PUNCT
ejpam-5528	200	52	v	v	NOUN
ejpam-5528	200	53	∈	∈	PROPN
ejpam-5528	200	54	ℜ.alter	ℜ.alter	NOUN
ejpam-5528	200	55	u	u	NOUN
ejpam-5528	200	56	by	by	ADP
ejpam-5528	200	57	αu	αu	PRON
ejpam-5528	200	58	in	in	ADP
ejpam-5528	200	59	(	(	PUNCT
ejpam-5528	200	60	2.28	2.28	NUM
ejpam-5528	200	61	)	)	PUNCT
ejpam-5528	200	62	,	,	PUNCT
ejpam-5528	200	63	we	we	PRON
ejpam-5528	200	64	get	get	VERB
ejpam-5528	200	65	uvq∗1	uvq∗1	ADJ
ejpam-5528	200	66	+	+	NOUN
ejpam-5528	200	67	v(uq∗1	v(uq∗1	ADJ
ejpam-5528	200	68	−	−	NOUN
ejpam-5528	200	69	q∗u∗	q∗u∗	ADJ
ejpam-5528	200	70	)	)	PUNCT
ejpam-5528	201	1	+	+	NUM
ejpam-5528	201	2	vqu∗	vqu∗	NOUN
ejpam-5528	201	3	=	=	SYM
ejpam-5528	201	4	0	0	NUM
ejpam-5528	201	5	(	(	PUNCT
ejpam-5528	201	6	2.29	2.29	NUM
ejpam-5528	201	7	)	)	PUNCT
ejpam-5528	201	8	for	for	ADP
ejpam-5528	201	9	all	all	DET
ejpam-5528	201	10	u	u	NOUN
ejpam-5528	201	11	,	,	PUNCT
ejpam-5528	201	12	v	v	NOUN
ejpam-5528	201	13	∈	∈	NOUN
ejpam-5528	201	14	ℜ.	ℜ.	PROPN
ejpam-5528	201	15	adding	add	VERB
ejpam-5528	201	16	(	(	PUNCT
ejpam-5528	201	17	2.28	2.28	NUM
ejpam-5528	201	18	)	)	PUNCT
ejpam-5528	201	19	and	and	CCONJ
ejpam-5528	201	20	(	(	PUNCT
ejpam-5528	201	21	2.29	2.29	NUM
ejpam-5528	201	22	)	)	PUNCT
ejpam-5528	201	23	,	,	PUNCT
ejpam-5528	201	24	we	we	PRON
ejpam-5528	201	25	get	get	VERB
ejpam-5528	201	26	(	(	PUNCT
ejpam-5528	201	27	uv	uv	NOUN
ejpam-5528	201	28	+	+	NOUN
ejpam-5528	201	29	vu)q∗1	vu)q∗1	PUNCT
ejpam-5528	202	1	=	=	NOUN
ejpam-5528	202	2	0	0	NUM
ejpam-5528	202	3	for	for	ADP
ejpam-5528	202	4	all	all	DET
ejpam-5528	202	5	u	u	NOUN
ejpam-5528	202	6	,	,	PUNCT
ejpam-5528	202	7	v	v	NOUN
ejpam-5528	202	8	∈	∈	NOUN
ejpam-5528	202	9	ℜ.	ℜ.	PROPN
ejpam-5528	202	10	consequently	consequently	ADV
ejpam-5528	202	11	,	,	PUNCT
ejpam-5528	202	12	q1	q1	PROPN
ejpam-5528	202	13	=	=	SYM
ejpam-5528	202	14	0	0	PUNCT
ejpam-5528	202	15	and	and	CCONJ
ejpam-5528	202	16	hence	hence	ADV
ejpam-5528	202	17	from	from	ADP
ejpam-5528	202	18	(	(	PUNCT
ejpam-5528	202	19	2.28	2.28	NUM
ejpam-5528	202	20	)	)	PUNCT
ejpam-5528	202	21	,	,	PUNCT
ejpam-5528	202	22	we	we	PRON
ejpam-5528	202	23	see	see	VERB
ejpam-5528	202	24	that	that	PRON
ejpam-5528	202	25	vq∗u	vq∗u	PRON
ejpam-5528	202	26	=	=	PUNCT
ejpam-5528	202	27	vqu	vqu	NOUN
ejpam-5528	202	28	for	for	ADP
ejpam-5528	202	29	all	all	DET
ejpam-5528	202	30	u	u	NOUN
ejpam-5528	202	31	,	,	PUNCT
ejpam-5528	202	32	v	v	NOUN
ejpam-5528	202	33	∈	∈	NOUN
ejpam-5528	202	34	ℜ.	ℜ.	PROPN
ejpam-5528	202	35	thus	thus	ADV
ejpam-5528	202	36	q∗	q∗	NOUN
ejpam-5528	202	37	=	=	SYM
ejpam-5528	202	38	q.	q.	NOUN
ejpam-5528	202	39	hence	hence	ADV
ejpam-5528	202	40	ω(u	ω(u	NUM
ejpam-5528	202	41	)	)	PUNCT
ejpam-5528	203	1	=	=	SYM
ejpam-5528	203	2	qu	qu	PROPN
ejpam-5528	203	3	for	for	ADP
ejpam-5528	203	4	all	all	DET
ejpam-5528	203	5	u	u	PROPN
ejpam-5528	203	6	∈	∈	PROPN
ejpam-5528	203	7	ℜ	ℜ	PROPN
ejpam-5528	203	8	,	,	PUNCT
ejpam-5528	203	9	where	where	SCONJ
ejpam-5528	203	10	q∗	q∗	NOUN
ejpam-5528	203	11	=	=	PUNCT
ejpam-5528	203	12	q	q	X
ejpam-5528	203	13	∈	∈	PROPN
ejpam-5528	203	14	ℜc	ℜc	PROPN
ejpam-5528	203	15	.	.	PUNCT
ejpam-5528	204	1	the	the	DET
ejpam-5528	204	2	following	follow	VERB
ejpam-5528	204	3	example	example	NOUN
ejpam-5528	204	4	shows	show	VERB
ejpam-5528	204	5	that	that	SCONJ
ejpam-5528	204	6	theorem	theorem	VERB
ejpam-5528	204	7	2.2	2.2	NUM
ejpam-5528	204	8	does	do	AUX
ejpam-5528	204	9	not	not	PART
ejpam-5528	204	10	hold	hold	VERB
ejpam-5528	204	11	if	if	SCONJ
ejpam-5528	204	12	dimcℜc	dimcℜc	ADJ
ejpam-5528	204	13	=	=	SYM
ejpam-5528	204	14	4	4	NUM
ejpam-5528	204	15	and	and	CCONJ
ejpam-5528	204	16	‘	'	PUNCT
ejpam-5528	204	17	∗	∗	NOUN
ejpam-5528	204	18	’	'	PUNCT
ejpam-5528	204	19	is	be	AUX
ejpam-5528	204	20	of	of	ADP
ejpam-5528	204	21	the	the	DET
ejpam-5528	204	22	first	first	ADJ
ejpam-5528	204	23	kind	kind	NOUN
ejpam-5528	204	24	.	.	PUNCT
ejpam-5528	205	1	example	example	NOUN
ejpam-5528	205	2	2.2	2.2	NUM
ejpam-5528	205	3	.	.	PUNCT
ejpam-5528	206	1	let	let	AUX
ejpam-5528	206	2	m2(k	m2(k	NOUN
ejpam-5528	206	3	)	)	PUNCT
ejpam-5528	206	4	be	be	VERB
ejpam-5528	206	5	the	the	DET
ejpam-5528	206	6	ring	ring	NOUN
ejpam-5528	206	7	of	of	ADP
ejpam-5528	206	8	all	all	DET
ejpam-5528	206	9	square	square	ADJ
ejpam-5528	206	10	matrices	matrix	NOUN
ejpam-5528	206	11	of	of	ADP
ejpam-5528	206	12	order	order	NOUN
ejpam-5528	206	13	2	2	NUM
ejpam-5528	206	14	over	over	ADP
ejpam-5528	206	15	any	any	DET
ejpam-5528	206	16	field	field	NOUN
ejpam-5528	206	17	k	k	X
ejpam-5528	206	18	with	with	ADP
ejpam-5528	206	19	involution	involution	NOUN
ejpam-5528	206	20	‘	'	PUNCT
ejpam-5528	206	21	∗	∗	NOUN
ejpam-5528	206	22	’	'	PUNCT
ejpam-5528	206	23	as	as	ADP
ejpam-5528	206	24	the	the	DET
ejpam-5528	206	25	usual	usual	ADJ
ejpam-5528	206	26	transpose	transpose	NOUN
ejpam-5528	206	27	.	.	PUNCT
ejpam-5528	207	1	define	define	VERB
ejpam-5528	207	2	the	the	DET
ejpam-5528	207	3	map	map	NOUN
ejpam-5528	207	4	ω	ω	NOUN
ejpam-5528	207	5	:	:	PUNCT
ejpam-5528	207	6	m2(k	m2(k	NOUN
ejpam-5528	207	7	)	)	PUNCT
ejpam-5528	207	8	→	→	SYM
ejpam-5528	207	9	m2(k	m2(k	NOUN
ejpam-5528	207	10	)	)	PUNCT
ejpam-5528	207	11	by	by	ADP
ejpam-5528	207	12	ω	ω	PROPN
ejpam-5528	207	13	(	(	PUNCT
ejpam-5528	207	14	[	[	PUNCT
ejpam-5528	207	15	ζ1	ζ1	NOUN
ejpam-5528	207	16	ζ2	ζ2	NOUN
ejpam-5528	207	17	ζ3	ζ3	NOUN
ejpam-5528	207	18	ζ4	ζ4	NOUN
ejpam-5528	207	19	]	]	PUNCT
ejpam-5528	207	20	)	)	PUNCT
ejpam-5528	208	1	=	=	SYM
ejpam-5528	208	2	[	[	PUNCT
ejpam-5528	208	3	ζ1	ζ1	NOUN
ejpam-5528	208	4	−	−	PROPN
ejpam-5528	208	5	ζ4	ζ4	ADJ
ejpam-5528	208	6	ζ2	ζ2	NOUN
ejpam-5528	208	7	−	−	NOUN
ejpam-5528	208	8	ζ3	ζ3	NOUN
ejpam-5528	208	9	ζ2	ζ2	NOUN
ejpam-5528	208	10	−	−	NOUN
ejpam-5528	208	11	ζ3	ζ3	NOUN
ejpam-5528	208	12	ζ1	ζ1	NOUN
ejpam-5528	208	13	−	−	PROPN
ejpam-5528	208	14	ζ4	ζ4	PROPN
ejpam-5528	208	15	]	]	PUNCT
ejpam-5528	208	16	.	.	PUNCT
ejpam-5528	209	1	then	then	ADV
ejpam-5528	209	2	it	it	PRON
ejpam-5528	209	3	can	can	AUX
ejpam-5528	209	4	be	be	AUX
ejpam-5528	209	5	easily	easily	ADV
ejpam-5528	209	6	seen	see	VERB
ejpam-5528	209	7	that	that	SCONJ
ejpam-5528	209	8	[	[	X
ejpam-5528	209	9	ω(a	ω(a	NOUN
ejpam-5528	209	10	)	)	PUNCT
ejpam-5528	209	11	,	,	PUNCT
ejpam-5528	209	12	b]•	b]•	PROPN
ejpam-5528	210	1	=	=	X
ejpam-5528	211	1	[	[	X
ejpam-5528	211	2	a	a	DET
ejpam-5528	211	3	,	,	PUNCT
ejpam-5528	211	4	ω(b)]•	ω(b)]•	NUM
ejpam-5528	211	5	for	for	ADP
ejpam-5528	211	6	all	all	DET
ejpam-5528	211	7	a	a	PRON
ejpam-5528	211	8	,	,	PUNCT
ejpam-5528	211	9	b	b	X
ejpam-5528	211	10	∈	∈	PROPN
ejpam-5528	211	11	ℜ.	ℜ.	PROPN
ejpam-5528	211	12	however	however	ADV
ejpam-5528	211	13	,	,	PUNCT
ejpam-5528	211	14	ω	ω	PROPN
ejpam-5528	211	15	is	be	AUX
ejpam-5528	211	16	not	not	PART
ejpam-5528	211	17	of	of	ADP
ejpam-5528	211	18	the	the	DET
ejpam-5528	211	19	form	form	NOUN
ejpam-5528	211	20	as	as	SCONJ
ejpam-5528	211	21	described	describe	VERB
ejpam-5528	211	22	in	in	ADP
ejpam-5528	211	23	theorem	theorem	ADJ
ejpam-5528	211	24	2.2	2.2	NUM
ejpam-5528	211	25	.	.	PUNCT
ejpam-5528	212	1	3	3	X
ejpam-5528	212	2	.	.	X
ejpam-5528	212	3	generalized	generalize	VERB
ejpam-5528	212	4	bi	bi	ADJ
ejpam-5528	212	5	-	-	ADJ
ejpam-5528	212	6	skew	skew	ADJ
ejpam-5528	212	7	jordan	jordan	PROPN
ejpam-5528	212	8	derivations	derivation	NOUN
ejpam-5528	212	9	in	in	ADP
ejpam-5528	212	10	prime	prime	ADJ
ejpam-5528	212	11	rings	ring	NOUN
ejpam-5528	212	12	the	the	DET
ejpam-5528	212	13	following	following	ADJ
ejpam-5528	212	14	result	result	NOUN
ejpam-5528	212	15	gives	give	VERB
ejpam-5528	212	16	a	a	DET
ejpam-5528	212	17	characterization	characterization	NOUN
ejpam-5528	212	18	of	of	ADP
ejpam-5528	212	19	additive	additive	ADJ
ejpam-5528	212	20	bi	bi	ADJ
ejpam-5528	212	21	-	-	ADJ
ejpam-5528	212	22	skew	skew	ADJ
ejpam-5528	212	23	jordan	jordan	PROPN
ejpam-5528	212	24	derivations	derivation	NOUN
ejpam-5528	212	25	in	in	ADP
ejpam-5528	212	26	prime	prime	ADJ
ejpam-5528	212	27	rings	ring	NOUN
ejpam-5528	212	28	without	without	ADP
ejpam-5528	212	29	assuming	assume	VERB
ejpam-5528	212	30	the	the	DET
ejpam-5528	212	31	existence	existence	NOUN
ejpam-5528	212	32	of	of	ADP
ejpam-5528	212	33	a	a	DET
ejpam-5528	212	34	nontrivial	nontrivial	ADJ
ejpam-5528	212	35	symmetric	symmetric	ADJ
ejpam-5528	212	36	idempotent	idempotent	NOUN
ejpam-5528	212	37	.	.	PUNCT
ejpam-5528	213	1	theorem	theorem	VERB
ejpam-5528	213	2	3.1	3.1	NUM
ejpam-5528	213	3	.	.	PUNCT
ejpam-5528	214	1	let	let	VERB
ejpam-5528	214	2	ℜ	ℜ	PROPN
ejpam-5528	214	3	be	be	AUX
ejpam-5528	214	4	a	a	DET
ejpam-5528	214	5	noncommutative	noncommutative	ADJ
ejpam-5528	214	6	prime	prime	ADJ
ejpam-5528	214	7	ring	ring	NOUN
ejpam-5528	214	8	with	with	ADP
ejpam-5528	214	9	an	an	DET
ejpam-5528	214	10	involution	involution	NOUN
ejpam-5528	214	11	‘	'	PUNCT
ejpam-5528	214	12	∗	∗	NOUN
ejpam-5528	214	13	’	'	PUNCT
ejpam-5528	214	14	and	and	CCONJ
ejpam-5528	214	15	let	let	VERB
ejpam-5528	214	16	ω	ω	NOUN
ejpam-5528	214	17	:	:	PUNCT
ejpam-5528	214	18	ℜ	ℜ	PROPN
ejpam-5528	214	19	→	→	SYM
ejpam-5528	214	20	qms(ℜ	qms(ℜ	PROPN
ejpam-5528	214	21	)	)	PUNCT
ejpam-5528	214	22	be	be	VERB
ejpam-5528	214	23	an	an	DET
ejpam-5528	214	24	additive	additive	ADJ
ejpam-5528	214	25	bi	bi	ADJ
ejpam-5528	214	26	-	-	ADJ
ejpam-5528	214	27	skew	skew	ADJ
ejpam-5528	214	28	jordan	jordan	PROPN
ejpam-5528	214	29	derivation	derivation	PROPN
ejpam-5528	214	30	.	.	PUNCT
ejpam-5528	215	1	suppose	suppose	VERB
ejpam-5528	215	2	that	that	SCONJ
ejpam-5528	215	3	either	either	CCONJ
ejpam-5528	215	4	dimcℜc	dimcℜc	VERB
ejpam-5528	215	5	>	>	X
ejpam-5528	215	6	4	4	NUM
ejpam-5528	215	7	or	or	CCONJ
ejpam-5528	215	8	ℜ	ℜ	NOUN
ejpam-5528	215	9	is	be	AUX
ejpam-5528	215	10	unital	unital	ADJ
ejpam-5528	215	11	.	.	PUNCT
ejpam-5528	216	1	then	then	ADV
ejpam-5528	216	2	ω	ω	PROPN
ejpam-5528	216	3	is	be	AUX
ejpam-5528	216	4	a	a	DET
ejpam-5528	216	5	∗-derivation	∗-derivation	NOUN
ejpam-5528	216	6	unless	unless	SCONJ
ejpam-5528	216	7	dimcℜc	dimcℜc	ADJ
ejpam-5528	216	8	=	=	NOUN
ejpam-5528	216	9	4	4	NUM
ejpam-5528	216	10	and	and	CCONJ
ejpam-5528	216	11	char(ℜ	char(ℜ	PROPN
ejpam-5528	216	12	)	)	PUNCT
ejpam-5528	216	13	=	=	SYM
ejpam-5528	216	14	2	2	X
ejpam-5528	216	15	.	.	X
ejpam-5528	216	16	proof	proof	NOUN
ejpam-5528	216	17	.	.	PUNCT
ejpam-5528	217	1	since	since	SCONJ
ejpam-5528	217	2	ω	ω	NOUN
ejpam-5528	217	3	:	:	PUNCT
ejpam-5528	217	4	ℜ	ℜ	PROPN
ejpam-5528	217	5	→	→	SYM
ejpam-5528	217	6	qms(ℜ	qms(ℜ	NUM
ejpam-5528	217	7	)	)	PUNCT
ejpam-5528	217	8	is	be	AUX
ejpam-5528	217	9	an	an	DET
ejpam-5528	217	10	additive	additive	ADJ
ejpam-5528	217	11	bi	bi	ADJ
ejpam-5528	217	12	-	-	ADJ
ejpam-5528	217	13	skew	skew	ADJ
ejpam-5528	217	14	jordan	jordan	PROPN
ejpam-5528	217	15	derivation	derivation	PROPN
ejpam-5528	217	16	,	,	PUNCT
ejpam-5528	217	17	therefore	therefore	ADV
ejpam-5528	217	18	ω(u	ω(u	PROPN
ejpam-5528	217	19	•	•	NOUN
ejpam-5528	217	20	v	v	NOUN
ejpam-5528	217	21	)	)	PUNCT
ejpam-5528	217	22	=	=	SYM
ejpam-5528	217	23	ω(u	ω(u	PROPN
ejpam-5528	217	24	)	)	PUNCT
ejpam-5528	217	25	•	•	NUM
ejpam-5528	217	26	v	v	NOUN
ejpam-5528	217	27	+	+	NUM
ejpam-5528	217	28	u	u	NOUN
ejpam-5528	217	29	•	•	NOUN
ejpam-5528	217	30	ω(v	ω(v	NOUN
ejpam-5528	217	31	)	)	PUNCT
ejpam-5528	217	32	for	for	ADP
ejpam-5528	217	33	all	all	DET
ejpam-5528	217	34	u	u	NOUN
ejpam-5528	217	35	,	,	PUNCT
ejpam-5528	217	36	v	v	NOUN
ejpam-5528	217	37	∈	∈	NOUN
ejpam-5528	217	38	ℜ.	ℜ.	VERB
ejpam-5528	217	39	now	now	ADV
ejpam-5528	217	40	a	a	DET
ejpam-5528	217	41	•	•	NOUN
ejpam-5528	217	42	b	b	X
ejpam-5528	217	43	=	=	SYM
ejpam-5528	217	44	b	b	PROPN
ejpam-5528	217	45	•	•	NUM
ejpam-5528	217	46	a	a	PRON
ejpam-5528	217	47	for	for	ADP
ejpam-5528	217	48	any	any	DET
ejpam-5528	217	49	a	a	PRON
ejpam-5528	217	50	,	,	PUNCT
ejpam-5528	217	51	b	b	X
ejpam-5528	217	52	∈	∈	PROPN
ejpam-5528	217	53	ℜ.	ℜ.	PROPN
ejpam-5528	217	54	hence	hence	ADV
ejpam-5528	217	55	if	if	SCONJ
ejpam-5528	217	56	ℜ	ℜ	ADJ
ejpam-5528	217	57	is	be	AUX
ejpam-5528	217	58	2	2	NUM
ejpam-5528	217	59	-	-	PUNCT
ejpam-5528	217	60	torsion	torsion	NOUN
ejpam-5528	217	61	free	free	ADJ
ejpam-5528	217	62	,	,	PUNCT
ejpam-5528	217	63	then	then	ADV
ejpam-5528	217	64	replacing	replace	VERB
ejpam-5528	217	65	v	v	NOUN
ejpam-5528	217	66	by	by	ADP
ejpam-5528	217	67	u	u	NOUN
ejpam-5528	217	68	in	in	ADP
ejpam-5528	217	69	the	the	DET
ejpam-5528	217	70	previous	previous	ADJ
ejpam-5528	217	71	expression	expression	NOUN
ejpam-5528	217	72	,	,	PUNCT
ejpam-5528	217	73	we	we	PRON
ejpam-5528	217	74	have	have	VERB
ejpam-5528	217	75	ω(uu∗	ω(uu∗	NOUN
ejpam-5528	217	76	)	)	PUNCT
ejpam-5528	217	77	=	=	SYM
ejpam-5528	217	78	ω(u	ω(u	PROPN
ejpam-5528	217	79	)	)	PUNCT
ejpam-5528	218	1	•	•	NUM
ejpam-5528	218	2	u	u	NOUN
ejpam-5528	218	3	for	for	ADP
ejpam-5528	218	4	all	all	DET
ejpam-5528	218	5	u	u	NOUN
ejpam-5528	218	6	∈	∈	NOUN
ejpam-5528	218	7	ℜ.	ℜ.	PROPN
ejpam-5528	218	8	also	also	ADV
ejpam-5528	218	9	if	if	SCONJ
ejpam-5528	218	10	ω	ω	PRON
ejpam-5528	218	11	:	:	PUNCT
ejpam-5528	218	12	ℜ	ℜ	PROPN
ejpam-5528	218	13	→	→	SYM
ejpam-5528	218	14	qms(ℜ	qms(ℜ	NUM
ejpam-5528	218	15	)	)	PUNCT
ejpam-5528	218	16	is	be	AUX
ejpam-5528	218	17	an	an	DET
ejpam-5528	218	18	additive	additive	ADJ
ejpam-5528	218	19	map	map	NOUN
ejpam-5528	218	20	satisfying	satisfy	VERB
ejpam-5528	218	21	ω(uu∗	ω(uu∗	NOUN
ejpam-5528	218	22	)	)	PUNCT
ejpam-5528	218	23	=	=	SYM
ejpam-5528	218	24	ω(u	ω(u	PROPN
ejpam-5528	218	25	)	)	PUNCT
ejpam-5528	218	26	•	•	NUM
ejpam-5528	218	27	u	u	NOUN
ejpam-5528	218	28	for	for	ADP
ejpam-5528	218	29	all	all	DET
ejpam-5528	218	30	u	u	PRON
ejpam-5528	218	31	∈	∈	PROPN
ejpam-5528	218	32	ℜ	ℜ	PROPN
ejpam-5528	218	33	,	,	PUNCT
ejpam-5528	218	34	then	then	ADV
ejpam-5528	218	35	replacing	replace	VERB
ejpam-5528	218	36	u	u	NOUN
ejpam-5528	218	37	by	by	ADP
ejpam-5528	218	38	u+	u+	NUM
ejpam-5528	218	39	v	v	NOUN
ejpam-5528	218	40	in	in	ADP
ejpam-5528	218	41	the	the	DET
ejpam-5528	218	42	last	last	ADJ
ejpam-5528	218	43	expression	expression	NOUN
ejpam-5528	218	44	,	,	PUNCT
ejpam-5528	218	45	we	we	PRON
ejpam-5528	218	46	find	find	VERB
ejpam-5528	218	47	that	that	SCONJ
ejpam-5528	218	48	ω(u	ω(u	PROPN
ejpam-5528	218	49	•	•	NUM
ejpam-5528	218	50	v	v	NOUN
ejpam-5528	218	51	)	)	PUNCT
ejpam-5528	218	52	=	=	SYM
ejpam-5528	218	53	ω(u	ω(u	PROPN
ejpam-5528	218	54	)	)	PUNCT
ejpam-5528	218	55	•	•	NUM
ejpam-5528	218	56	v	v	NOUN
ejpam-5528	218	57	+	+	NUM
ejpam-5528	218	58	u	u	NOUN
ejpam-5528	218	59	•	•	NOUN
ejpam-5528	218	60	ω(v	ω(v	NOUN
ejpam-5528	218	61	)	)	PUNCT
ejpam-5528	218	62	for	for	ADP
ejpam-5528	218	63	all	all	DET
ejpam-5528	218	64	u	u	NOUN
ejpam-5528	218	65	,	,	PUNCT
ejpam-5528	218	66	v	v	NOUN
ejpam-5528	218	67	∈	∈	NOUN
ejpam-5528	218	68	ℜ.	ℜ.	PROPN
ejpam-5528	218	69	thus	thus	ADV
ejpam-5528	218	70	if	if	SCONJ
ejpam-5528	218	71	ℜ	ℜ	PROPN
ejpam-5528	218	72	is	be	AUX
ejpam-5528	218	73	a	a	DET
ejpam-5528	218	74	2	2	NUM
ejpam-5528	218	75	-	-	PUNCT
ejpam-5528	218	76	torsion	torsion	NOUN
ejpam-5528	218	77	free	free	ADJ
ejpam-5528	218	78	prime	prime	ADJ
ejpam-5528	218	79	ring	ring	NOUN
ejpam-5528	218	80	with	with	ADP
ejpam-5528	218	81	an	an	DET
ejpam-5528	218	82	involution	involution	NOUN
ejpam-5528	218	83	‘	'	PUNCT
ejpam-5528	218	84	∗	∗	NOUN
ejpam-5528	218	85	’	'	PUNCT
ejpam-5528	218	86	,	,	PUNCT
ejpam-5528	218	87	then	then	ADV
ejpam-5528	218	88	an	an	DET
ejpam-5528	218	89	additive	additive	ADJ
ejpam-5528	218	90	map	map	NOUN
ejpam-5528	218	91	ω	ω	NOUN
ejpam-5528	218	92	:	:	PUNCT
ejpam-5528	218	93	ℜ	ℜ	PROPN
ejpam-5528	218	94	→	→	SYM
ejpam-5528	218	95	qms(ℜ	qms(ℜ	NUM
ejpam-5528	218	96	)	)	PUNCT
ejpam-5528	218	97	is	be	AUX
ejpam-5528	218	98	a	a	DET
ejpam-5528	218	99	bi	bi	ADJ
ejpam-5528	218	100	-	-	ADJ
ejpam-5528	218	101	skew	skew	ADJ
ejpam-5528	218	102	jordan	jordan	PROPN
ejpam-5528	218	103	derivation	derivation	PROPN
ejpam-5528	219	1	if	if	SCONJ
ejpam-5528	219	2	and	and	CCONJ
ejpam-5528	219	3	only	only	ADV
ejpam-5528	219	4	if	if	SCONJ
ejpam-5528	219	5	ω(uu∗	ω(uu∗	NOUN
ejpam-5528	219	6	)	)	PUNCT
ejpam-5528	219	7	=	=	SYM
ejpam-5528	219	8	ω(u)•u	ω(u)•u	NUM
ejpam-5528	219	9	for	for	ADP
ejpam-5528	219	10	all	all	DET
ejpam-5528	219	11	u	u	NOUN
ejpam-5528	219	12	∈	∈	NOUN
ejpam-5528	219	13	ℜ.	ℜ.	PROPN
ejpam-5528	219	14	therefore	therefore	ADV
ejpam-5528	219	15	in	in	ADP
ejpam-5528	219	16	view	view	NOUN
ejpam-5528	219	17	of	of	ADP
ejpam-5528	219	18	theorem	theorem	ADJ
ejpam-5528	219	19	2.1	2.1	NUM
ejpam-5528	219	20	of	of	ADP
ejpam-5528	219	21	[	[	X
ejpam-5528	219	22	20	20	NUM
ejpam-5528	219	23	]	]	PUNCT
ejpam-5528	219	24	and	and	CCONJ
ejpam-5528	219	25	the	the	DET
ejpam-5528	219	26	arguments	argument	NOUN
ejpam-5528	219	27	given	give	VERB
ejpam-5528	219	28	in	in	ADP
ejpam-5528	219	29	case	case	NOUN
ejpam-5528	219	30	i	i	PRON
ejpam-5528	219	31	of	of	ADP
ejpam-5528	219	32	its	its	PRON
ejpam-5528	219	33	proof	proof	NOUN
ejpam-5528	219	34	,	,	PUNCT
ejpam-5528	219	35	we	we	PRON
ejpam-5528	219	36	conclude	conclude	VERB
ejpam-5528	219	37	that	that	SCONJ
ejpam-5528	219	38	ω	ω	PROPN
ejpam-5528	219	39	is	be	AUX
ejpam-5528	219	40	a	a	DET
ejpam-5528	219	41	∗-derivation	∗-derivation	NOUN
ejpam-5528	219	42	unless	unless	SCONJ
ejpam-5528	219	43	dimcℜc	dimcℜc	ADJ
ejpam-5528	219	44	=	=	NOUN
ejpam-5528	219	45	4	4	NUM
ejpam-5528	219	46	and	and	CCONJ
ejpam-5528	219	47	char(ℜ	char(ℜ	PROPN
ejpam-5528	219	48	)	)	PUNCT
ejpam-5528	219	49	=	=	SYM
ejpam-5528	219	50	2	2	X
ejpam-5528	219	51	.	.	X
ejpam-5528	219	52	proposition	proposition	NOUN
ejpam-5528	219	53	3.1	3.1	NUM
ejpam-5528	219	54	.	.	PUNCT
ejpam-5528	220	1	let	let	VERB
ejpam-5528	220	2	ℜ	ℜ	PROPN
ejpam-5528	220	3	be	be	AUX
ejpam-5528	220	4	a	a	DET
ejpam-5528	220	5	noncommutative	noncommutative	ADJ
ejpam-5528	220	6	prime	prime	ADJ
ejpam-5528	220	7	ring	ring	NOUN
ejpam-5528	220	8	with	with	ADP
ejpam-5528	220	9	an	an	DET
ejpam-5528	220	10	involution	involution	NOUN
ejpam-5528	220	11	‘	'	PUNCT
ejpam-5528	220	12	∗	∗	NOUN
ejpam-5528	220	13	’	'	PUNCT
ejpam-5528	220	14	and	and	CCONJ
ejpam-5528	220	15	let	let	VERB
ejpam-5528	220	16	ω	ω	NOUN
ejpam-5528	220	17	:	:	PUNCT
ejpam-5528	220	18	ℜ	ℜ	PROPN
ejpam-5528	220	19	→	→	SYM
ejpam-5528	220	20	qms(ℜ	qms(ℜ	PROPN
ejpam-5528	220	21	)	)	PUNCT
ejpam-5528	220	22	be	be	AUX
ejpam-5528	220	23	a	a	DET
ejpam-5528	220	24	left	left	ADJ
ejpam-5528	220	25	(	(	PUNCT
ejpam-5528	220	26	right	right	ADJ
ejpam-5528	220	27	)	)	PUNCT
ejpam-5528	220	28	bi	bi	ADJ
ejpam-5528	220	29	-	-	ADJ
ejpam-5528	220	30	skew	skew	ADJ
ejpam-5528	220	31	jordan	jordan	PROPN
ejpam-5528	220	32	centralizer	centralizer	PROPN
ejpam-5528	220	33	.	.	PUNCT
ejpam-5528	221	1	then	then	ADV
ejpam-5528	221	2	there	there	PRON
ejpam-5528	221	3	exists	exist	VERB
ejpam-5528	221	4	λ∗	λ∗	NOUN
ejpam-5528	222	1	=	=	PUNCT
ejpam-5528	222	2	λ	λ	X
ejpam-5528	222	3	∈	∈	PROPN
ejpam-5528	222	4	c	c	NOUN
ejpam-5528	222	5	such	such	ADJ
ejpam-5528	222	6	that	that	DET
ejpam-5528	222	7	ω(u	ω(u	NOUN
ejpam-5528	222	8	)	)	PUNCT
ejpam-5528	223	1	=	=	SYM
ejpam-5528	223	2	λu	λu	X
ejpam-5528	223	3	for	for	ADP
ejpam-5528	223	4	all	all	DET
ejpam-5528	223	5	u	u	PROPN
ejpam-5528	223	6	∈	∈	PROPN
ejpam-5528	223	7	ℜ.	ℜ.	PROPN
ejpam-5528	223	8	moin	moin	PROPN
ejpam-5528	223	9	a.	a.	NOUN
ejpam-5528	223	10	ansari	ansari	PROPN
ejpam-5528	223	11	et	et	PROPN
ejpam-5528	223	12	al	al	PROPN
ejpam-5528	223	13	.	.	PUNCT
ejpam-5528	223	14	/	/	SYM
ejpam-5528	223	15	eur	eur	PROPN
ejpam-5528	223	16	.	.	PUNCT
ejpam-5528	224	1	j.	j.	PROPN
ejpam-5528	224	2	pure	pure	PROPN
ejpam-5528	224	3	appl	appl	PROPN
ejpam-5528	224	4	.	.	PROPN
ejpam-5528	224	5	math	math	PROPN
ejpam-5528	224	6	,	,	PUNCT
ejpam-5528	224	7	18	18	NUM
ejpam-5528	224	8	(	(	PUNCT
ejpam-5528	224	9	2	2	NUM
ejpam-5528	224	10	)	)	PUNCT
ejpam-5528	224	11	(	(	PUNCT
ejpam-5528	224	12	2025	2025	NUM
ejpam-5528	224	13	)	)	PUNCT
ejpam-5528	224	14	,	,	PUNCT
ejpam-5528	224	15	5528	5528	NUM
ejpam-5528	224	16	9	9	NUM
ejpam-5528	224	17	of	of	ADP
ejpam-5528	224	18	14	14	NUM
ejpam-5528	224	19	proof	proof	NOUN
ejpam-5528	224	20	.	.	PUNCT
ejpam-5528	225	1	we	we	PRON
ejpam-5528	225	2	give	give	VERB
ejpam-5528	225	3	the	the	DET
ejpam-5528	225	4	details	detail	NOUN
ejpam-5528	225	5	of	of	ADP
ejpam-5528	225	6	the	the	DET
ejpam-5528	225	7	proof	proof	NOUN
ejpam-5528	225	8	only	only	ADV
ejpam-5528	225	9	when	when	SCONJ
ejpam-5528	225	10	ω	ω	PROPN
ejpam-5528	225	11	is	be	AUX
ejpam-5528	225	12	a	a	DET
ejpam-5528	225	13	left	left	ADJ
ejpam-5528	225	14	bi	bi	NOUN
ejpam-5528	225	15	-	-	ADJ
ejpam-5528	225	16	skew	skew	ADJ
ejpam-5528	225	17	jordan	jordan	PROPN
ejpam-5528	225	18	centralizer	centralizer	PROPN
ejpam-5528	225	19	.	.	PUNCT
ejpam-5528	226	1	the	the	DET
ejpam-5528	226	2	case	case	NOUN
ejpam-5528	226	3	when	when	SCONJ
ejpam-5528	226	4	ω	ω	PROPN
ejpam-5528	226	5	is	be	AUX
ejpam-5528	226	6	a	a	DET
ejpam-5528	226	7	right	right	ADJ
ejpam-5528	226	8	bi	bi	ADJ
ejpam-5528	226	9	-	-	ADJ
ejpam-5528	226	10	skew	skew	ADJ
ejpam-5528	226	11	jordan	jordan	PROPN
ejpam-5528	226	12	centralizer	centralizer	NOUN
ejpam-5528	226	13	can	can	AUX
ejpam-5528	226	14	be	be	AUX
ejpam-5528	226	15	proved	prove	VERB
ejpam-5528	226	16	by	by	ADP
ejpam-5528	226	17	using	use	VERB
ejpam-5528	226	18	similar	similar	ADJ
ejpam-5528	226	19	arguments	argument	NOUN
ejpam-5528	226	20	.	.	PUNCT
ejpam-5528	227	1	suppose	suppose	VERB
ejpam-5528	227	2	ω(u	ω(u	PROPN
ejpam-5528	227	3	•	•	NUM
ejpam-5528	227	4	v	v	NOUN
ejpam-5528	227	5	)	)	PUNCT
ejpam-5528	227	6	=	=	SYM
ejpam-5528	227	7	ω(u	ω(u	PROPN
ejpam-5528	227	8	)	)	PUNCT
ejpam-5528	227	9	•	•	NUM
ejpam-5528	227	10	v	v	NOUN
ejpam-5528	227	11	(	(	PUNCT
ejpam-5528	227	12	3.1	3.1	NUM
ejpam-5528	227	13	)	)	PUNCT
ejpam-5528	227	14	for	for	ADP
ejpam-5528	227	15	all	all	DET
ejpam-5528	227	16	u	u	NOUN
ejpam-5528	227	17	,	,	PUNCT
ejpam-5528	227	18	v	v	NOUN
ejpam-5528	227	19	∈	∈	PROPN
ejpam-5528	227	20	ℜ.	ℜ.	PROPN
ejpam-5528	227	21	alter	alter	NOUN
ejpam-5528	227	22	v	v	NOUN
ejpam-5528	227	23	by	by	ADP
ejpam-5528	227	24	v	v	PRON
ejpam-5528	227	25	+	+	CCONJ
ejpam-5528	227	26	w	w	NOUN
ejpam-5528	227	27	in	in	ADP
ejpam-5528	227	28	(	(	PUNCT
ejpam-5528	227	29	3.1	3.1	NUM
ejpam-5528	227	30	)	)	PUNCT
ejpam-5528	227	31	,	,	PUNCT
ejpam-5528	227	32	we	we	PRON
ejpam-5528	227	33	have	have	VERB
ejpam-5528	227	34	ω(u	ω(u	PROPN
ejpam-5528	227	35	•	•	NOUN
ejpam-5528	227	36	v	v	NOUN
ejpam-5528	227	37	+	+	NUM
ejpam-5528	227	38	u	u	NOUN
ejpam-5528	227	39	•	•	PROPN
ejpam-5528	227	40	w	w	NOUN
ejpam-5528	227	41	)	)	PUNCT
ejpam-5528	227	42	=	=	SYM
ejpam-5528	227	43	ω(u	ω(u	PROPN
ejpam-5528	227	44	)	)	PUNCT
ejpam-5528	228	1	•	•	NOUN
ejpam-5528	228	2	v	v	ADP
ejpam-5528	228	3	+	+	NOUN
ejpam-5528	228	4	ω(u	ω(u	NOUN
ejpam-5528	228	5	)	)	PUNCT
ejpam-5528	228	6	•	•	NUM
ejpam-5528	228	7	w	w	PROPN
ejpam-5528	228	8	(	(	PUNCT
ejpam-5528	228	9	3.2	3.2	NUM
ejpam-5528	228	10	)	)	PUNCT
ejpam-5528	228	11	for	for	ADP
ejpam-5528	228	12	all	all	DET
ejpam-5528	228	13	u	u	NOUN
ejpam-5528	228	14	,	,	PUNCT
ejpam-5528	228	15	v	v	NOUN
ejpam-5528	228	16	,	,	PUNCT
ejpam-5528	228	17	w	w	PROPN
ejpam-5528	228	18	∈	∈	PROPN
ejpam-5528	228	19	ℜ.	ℜ.	PROPN
ejpam-5528	228	20	that	that	PRON
ejpam-5528	228	21	is	be	AUX
ejpam-5528	228	22	,	,	PUNCT
ejpam-5528	228	23	ω(v	ω(v	PROPN
ejpam-5528	228	24	•	•	NUM
ejpam-5528	228	25	u+	u+	NUM
ejpam-5528	228	26	v	v	NUM
ejpam-5528	228	27	•	•	NUM
ejpam-5528	228	28	w	w	NOUN
ejpam-5528	228	29	)	)	PUNCT
ejpam-5528	228	30	=	=	SYM
ejpam-5528	228	31	ω(v	ω(v	NOUN
ejpam-5528	228	32	)	)	PUNCT
ejpam-5528	228	33	•	•	NOUN
ejpam-5528	228	34	u+ω(v	u+ω(v	NUM
ejpam-5528	228	35	)	)	PUNCT
ejpam-5528	228	36	•	•	PROPN
ejpam-5528	228	37	w	w	PROPN
ejpam-5528	228	38	(	(	PUNCT
ejpam-5528	228	39	3.3	3.3	NUM
ejpam-5528	228	40	)	)	PUNCT
ejpam-5528	228	41	for	for	ADP
ejpam-5528	228	42	all	all	DET
ejpam-5528	228	43	u	u	NOUN
ejpam-5528	228	44	,	,	PUNCT
ejpam-5528	228	45	v	v	NOUN
ejpam-5528	228	46	,	,	PUNCT
ejpam-5528	228	47	w	w	PROPN
ejpam-5528	228	48	∈	∈	PROPN
ejpam-5528	228	49	ℜ.	ℜ.	PROPN
ejpam-5528	228	50	also	also	ADV
ejpam-5528	228	51	alter	alter	VERB
ejpam-5528	228	52	u	u	NOUN
ejpam-5528	228	53	by	by	ADP
ejpam-5528	228	54	u+	u+	NOUN
ejpam-5528	228	55	w	w	NOUN
ejpam-5528	228	56	in	in	ADP
ejpam-5528	228	57	(	(	PUNCT
ejpam-5528	228	58	3.1	3.1	NUM
ejpam-5528	228	59	)	)	PUNCT
ejpam-5528	228	60	,	,	PUNCT
ejpam-5528	228	61	we	we	PRON
ejpam-5528	228	62	have	have	VERB
ejpam-5528	228	63	ω(u	ω(u	PROPN
ejpam-5528	228	64	•	•	NOUN
ejpam-5528	228	65	v	v	ADP
ejpam-5528	228	66	+	+	CCONJ
ejpam-5528	228	67	w	w	NOUN
ejpam-5528	228	68	•	•	NUM
ejpam-5528	228	69	v	v	NOUN
ejpam-5528	228	70	)	)	PUNCT
ejpam-5528	228	71	=	=	NOUN
ejpam-5528	228	72	ω(u+	ω(u+	NUM
ejpam-5528	228	73	w	w	NOUN
ejpam-5528	228	74	)	)	PUNCT
ejpam-5528	228	75	•	•	NUM
ejpam-5528	228	76	v	v	NOUN
ejpam-5528	228	77	(	(	PUNCT
ejpam-5528	228	78	3.4	3.4	NUM
ejpam-5528	228	79	)	)	PUNCT
ejpam-5528	228	80	for	for	ADP
ejpam-5528	228	81	all	all	DET
ejpam-5528	228	82	u	u	NOUN
ejpam-5528	228	83	,	,	PUNCT
ejpam-5528	228	84	v	v	NOUN
ejpam-5528	228	85	,	,	PUNCT
ejpam-5528	228	86	w	w	PROPN
ejpam-5528	228	87	∈	∈	PROPN
ejpam-5528	228	88	ℜ.	ℜ.	PROPN
ejpam-5528	228	89	comparing	compare	VERB
ejpam-5528	228	90	(	(	PUNCT
ejpam-5528	228	91	3.3	3.3	NUM
ejpam-5528	228	92	)	)	PUNCT
ejpam-5528	228	93	and	and	CCONJ
ejpam-5528	228	94	(	(	PUNCT
ejpam-5528	228	95	3.4	3.4	NUM
ejpam-5528	228	96	)	)	PUNCT
ejpam-5528	228	97	,	,	PUNCT
ejpam-5528	228	98	we	we	PRON
ejpam-5528	228	99	find	find	VERB
ejpam-5528	228	100	that	that	SCONJ
ejpam-5528	228	101	ω(u+	ω(u+	NUM
ejpam-5528	229	1	w	w	X
ejpam-5528	229	2	)	)	PUNCT
ejpam-5528	229	3	•	•	NUM
ejpam-5528	229	4	v	v	NOUN
ejpam-5528	229	5	=	=	SYM
ejpam-5528	229	6	ω(v	ω(v	NOUN
ejpam-5528	229	7	)	)	PUNCT
ejpam-5528	229	8	•	•	NOUN
ejpam-5528	229	9	u+ω(v	u+ω(v	NUM
ejpam-5528	229	10	)	)	PUNCT
ejpam-5528	229	11	•	•	PROPN
ejpam-5528	229	12	w	w	PROPN
ejpam-5528	229	13	(	(	PUNCT
ejpam-5528	229	14	3.5	3.5	NUM
ejpam-5528	229	15	)	)	PUNCT
ejpam-5528	229	16	for	for	ADP
ejpam-5528	229	17	all	all	DET
ejpam-5528	229	18	u	u	NOUN
ejpam-5528	229	19	,	,	PUNCT
ejpam-5528	229	20	v	v	NOUN
ejpam-5528	229	21	,	,	PUNCT
ejpam-5528	229	22	w	w	PROPN
ejpam-5528	229	23	∈	∈	PROPN
ejpam-5528	229	24	ℜ.	ℜ.	PROPN
ejpam-5528	229	25	putting	put	VERB
ejpam-5528	229	26	w	w	NOUN
ejpam-5528	229	27	=	=	NOUN
ejpam-5528	229	28	0	0	NUM
ejpam-5528	229	29	in	in	ADP
ejpam-5528	229	30	(	(	PUNCT
ejpam-5528	229	31	3.5	3.5	NUM
ejpam-5528	229	32	)	)	PUNCT
ejpam-5528	229	33	,	,	PUNCT
ejpam-5528	229	34	we	we	PRON
ejpam-5528	229	35	get	get	VERB
ejpam-5528	229	36	ω(u	ω(u	NUM
ejpam-5528	229	37	)	)	PUNCT
ejpam-5528	230	1	•	•	NUM
ejpam-5528	230	2	v	v	NOUN
ejpam-5528	230	3	=	=	SYM
ejpam-5528	230	4	ω(v	ω(v	NOUN
ejpam-5528	230	5	)	)	PUNCT
ejpam-5528	230	6	•	•	NUM
ejpam-5528	230	7	u	u	NOUN
ejpam-5528	230	8	(	(	PUNCT
ejpam-5528	230	9	3.6	3.6	NUM
ejpam-5528	230	10	)	)	PUNCT
ejpam-5528	230	11	for	for	ADP
ejpam-5528	230	12	all	all	DET
ejpam-5528	230	13	u	u	NOUN
ejpam-5528	230	14	,	,	PUNCT
ejpam-5528	230	15	v	v	NOUN
ejpam-5528	230	16	∈	∈	NOUN
ejpam-5528	230	17	ℜ.	ℜ.	PROPN
ejpam-5528	230	18	therefore	therefore	ADV
ejpam-5528	230	19	from	from	ADP
ejpam-5528	230	20	(	(	PUNCT
ejpam-5528	230	21	3.5	3.5	NUM
ejpam-5528	230	22	)	)	PUNCT
ejpam-5528	230	23	,	,	PUNCT
ejpam-5528	230	24	we	we	PRON
ejpam-5528	230	25	find	find	VERB
ejpam-5528	230	26	that	that	SCONJ
ejpam-5528	230	27	(	(	PUNCT
ejpam-5528	230	28	ω(u+	ω(u+	PUNCT
ejpam-5528	230	29	w)−	w)−	PROPN
ejpam-5528	230	30	ω(u)−	ω(u)−	NOUN
ejpam-5528	230	31	ω(w	ω(w	NUM
ejpam-5528	230	32	)	)	PUNCT
ejpam-5528	230	33	)	)	PUNCT
ejpam-5528	230	34	•	•	NUM
ejpam-5528	230	35	v	v	X
ejpam-5528	230	36	=	=	SYM
ejpam-5528	230	37	0	0	NUM
ejpam-5528	230	38	(	(	PUNCT
ejpam-5528	230	39	3.7	3.7	NUM
ejpam-5528	230	40	)	)	PUNCT
ejpam-5528	230	41	for	for	ADP
ejpam-5528	230	42	all	all	DET
ejpam-5528	230	43	u	u	NOUN
ejpam-5528	230	44	,	,	PUNCT
ejpam-5528	230	45	v	v	NOUN
ejpam-5528	230	46	,	,	PUNCT
ejpam-5528	230	47	w	w	PROPN
ejpam-5528	230	48	∈	∈	PROPN
ejpam-5528	230	49	ℜ.	ℜ.	PROPN
ejpam-5528	230	50	in	in	ADP
ejpam-5528	230	51	view	view	NOUN
ejpam-5528	230	52	of	of	ADP
ejpam-5528	230	53	lemma	lemma	PROPN
ejpam-5528	230	54	2.1	2.1	NUM
ejpam-5528	230	55	,	,	PUNCT
ejpam-5528	230	56	it	it	PRON
ejpam-5528	230	57	follows	follow	VERB
ejpam-5528	230	58	that	that	SCONJ
ejpam-5528	230	59	ω(u+	ω(u+	NUM
ejpam-5528	230	60	w	w	X
ejpam-5528	230	61	)	)	PUNCT
ejpam-5528	230	62	=	=	SYM
ejpam-5528	230	63	ω(u	ω(u	PROPN
ejpam-5528	230	64	)	)	PUNCT
ejpam-5528	230	65	+	+	NUM
ejpam-5528	230	66	ω(w	ω(w	NUM
ejpam-5528	230	67	)	)	PUNCT
ejpam-5528	230	68	for	for	ADP
ejpam-5528	230	69	all	all	DET
ejpam-5528	230	70	u	u	NOUN
ejpam-5528	230	71	,	,	PUNCT
ejpam-5528	230	72	v	v	NOUN
ejpam-5528	230	73	∈	∈	NOUN
ejpam-5528	230	74	ℜ.	ℜ.	PROPN
ejpam-5528	230	75	thus	thus	ADV
ejpam-5528	230	76	ω	ω	NOUN
ejpam-5528	230	77	is	be	AUX
ejpam-5528	230	78	additive	additive	ADJ
ejpam-5528	230	79	.	.	PUNCT
ejpam-5528	231	1	now	now	ADV
ejpam-5528	231	2	(	(	PUNCT
ejpam-5528	231	3	3.1	3.1	NUM
ejpam-5528	231	4	)	)	PUNCT
ejpam-5528	231	5	can	can	AUX
ejpam-5528	231	6	be	be	AUX
ejpam-5528	231	7	rewritten	rewrite	VERB
ejpam-5528	231	8	as	as	ADP
ejpam-5528	231	9	ω(uv∗	ω(uv∗	ADJ
ejpam-5528	231	10	+	+	CCONJ
ejpam-5528	231	11	vu∗	vu∗	NOUN
ejpam-5528	231	12	)	)	PUNCT
ejpam-5528	231	13	=	=	SYM
ejpam-5528	232	1	ω(u)v∗	ω(u)v∗	PROPN
ejpam-5528	232	2	+	+	NUM
ejpam-5528	232	3	vω(u)∗	vω(u)∗	NOUN
ejpam-5528	232	4	(	(	PUNCT
ejpam-5528	232	5	3.8	3.8	NUM
ejpam-5528	232	6	)	)	PUNCT
ejpam-5528	232	7	for	for	ADP
ejpam-5528	232	8	all	all	DET
ejpam-5528	232	9	u	u	NOUN
ejpam-5528	232	10	,	,	PUNCT
ejpam-5528	232	11	v	v	NOUN
ejpam-5528	232	12	∈	∈	NOUN
ejpam-5528	232	13	ℜ.	ℜ.	PROPN
ejpam-5528	232	14	consider	consider	VERB
ejpam-5528	232	15	the	the	DET
ejpam-5528	232	16	map	map	NOUN
ejpam-5528	232	17	φ	φ	NOUN
ejpam-5528	232	18	:	:	PUNCT
ejpam-5528	232	19	ℜ2	ℜ2	PROPN
ejpam-5528	232	20	→	→	SYM
ejpam-5528	232	21	qms(ℜ	qms(ℜ	NUM
ejpam-5528	232	22	)	)	PUNCT
ejpam-5528	232	23	given	give	VERB
ejpam-5528	232	24	by	by	ADP
ejpam-5528	232	25	φ(u	φ(u	NOUN
ejpam-5528	232	26	,	,	PUNCT
ejpam-5528	232	27	v	v	NOUN
ejpam-5528	232	28	)	)	PUNCT
ejpam-5528	232	29	=	=	PUNCT
ejpam-5528	232	30	ω(uv∗	ω(uv∗	X
ejpam-5528	232	31	)	)	PUNCT
ejpam-5528	232	32	+	+	NUM
ejpam-5528	232	33	ω(vu∗	ω(vu∗	NUM
ejpam-5528	232	34	)	)	PUNCT
ejpam-5528	232	35	.	.	PUNCT
ejpam-5528	233	1	in	in	ADP
ejpam-5528	233	2	view	view	NOUN
ejpam-5528	233	3	of	of	ADP
ejpam-5528	233	4	lemma	lemma	PROPN
ejpam-5528	233	5	2.3	2.3	NUM
ejpam-5528	233	6	,	,	PUNCT
ejpam-5528	233	7	it	it	PRON
ejpam-5528	233	8	follows	follow	VERB
ejpam-5528	233	9	that	that	SCONJ
ejpam-5528	233	10	φ	φ	PROPN
ejpam-5528	233	11	satisfies	satisfy	VERB
ejpam-5528	233	12	the	the	DET
ejpam-5528	233	13	following	follow	VERB
ejpam-5528	233	14	relation	relation	NOUN
ejpam-5528	233	15	φ(uw	φ(uw	NOUN
ejpam-5528	233	16	,	,	PUNCT
ejpam-5528	233	17	v	v	NOUN
ejpam-5528	233	18	)	)	PUNCT
ejpam-5528	233	19	=	=	PUNCT
ejpam-5528	233	20	φ(u	φ(u	NOUN
ejpam-5528	233	21	,	,	PUNCT
ejpam-5528	233	22	vw∗	vw∗	NOUN
ejpam-5528	233	23	)	)	PUNCT
ejpam-5528	233	24	for	for	ADP
ejpam-5528	233	25	all	all	DET
ejpam-5528	233	26	u	u	NOUN
ejpam-5528	233	27	,	,	PUNCT
ejpam-5528	233	28	v	v	NOUN
ejpam-5528	233	29	,	,	PUNCT
ejpam-5528	233	30	w	w	PROPN
ejpam-5528	233	31	∈	∈	PROPN
ejpam-5528	233	32	ℜ.	ℜ.	PROPN
ejpam-5528	233	33	using	use	VERB
ejpam-5528	233	34	(	(	PUNCT
ejpam-5528	233	35	3.8	3.8	NUM
ejpam-5528	233	36	)	)	PUNCT
ejpam-5528	233	37	,	,	PUNCT
ejpam-5528	233	38	we	we	PRON
ejpam-5528	233	39	obtain	obtain	VERB
ejpam-5528	233	40	(	(	PUNCT
ejpam-5528	233	41	ω(uw)−	ω(uw)−	X
ejpam-5528	233	42	ω(u)w)v∗	ω(u)w)v∗	NUM
ejpam-5528	233	43	+	+	NUM
ejpam-5528	233	44	v(ω(uw)∗	v(ω(uw)∗	NUM
ejpam-5528	233	45	−	−	ADP
ejpam-5528	233	46	w∗ω(u)∗	w∗ω(u)∗	NOUN
ejpam-5528	233	47	)	)	PUNCT
ejpam-5528	233	48	=	=	SYM
ejpam-5528	233	49	0	0	NUM
ejpam-5528	234	1	(	(	PUNCT
ejpam-5528	234	2	3.9	3.9	NUM
ejpam-5528	234	3	)	)	PUNCT
ejpam-5528	234	4	moin	moin	NOUN
ejpam-5528	234	5	a.	a.	NOUN
ejpam-5528	234	6	ansari	ansari	PROPN
ejpam-5528	234	7	et	et	PROPN
ejpam-5528	234	8	al	al	PROPN
ejpam-5528	234	9	.	.	PUNCT
ejpam-5528	234	10	/	/	SYM
ejpam-5528	234	11	eur	eur	PROPN
ejpam-5528	234	12	.	.	PUNCT
ejpam-5528	235	1	j.	j.	PROPN
ejpam-5528	235	2	pure	pure	PROPN
ejpam-5528	235	3	appl	appl	PROPN
ejpam-5528	235	4	.	.	PROPN
ejpam-5528	235	5	math	math	PROPN
ejpam-5528	235	6	,	,	PUNCT
ejpam-5528	235	7	18	18	NUM
ejpam-5528	235	8	(	(	PUNCT
ejpam-5528	235	9	2	2	NUM
ejpam-5528	235	10	)	)	PUNCT
ejpam-5528	235	11	(	(	PUNCT
ejpam-5528	235	12	2025	2025	NUM
ejpam-5528	235	13	)	)	PUNCT
ejpam-5528	235	14	,	,	PUNCT
ejpam-5528	235	15	5528	5528	NUM
ejpam-5528	235	16	10	10	NUM
ejpam-5528	235	17	of	of	ADP
ejpam-5528	235	18	14	14	NUM
ejpam-5528	235	19	for	for	ADP
ejpam-5528	235	20	all	all	DET
ejpam-5528	235	21	u	u	NOUN
ejpam-5528	235	22	,	,	PUNCT
ejpam-5528	235	23	v	v	NOUN
ejpam-5528	235	24	,	,	PUNCT
ejpam-5528	235	25	w	w	PROPN
ejpam-5528	235	26	∈	∈	PROPN
ejpam-5528	235	27	ℜ.	ℜ.	PROPN
ejpam-5528	235	28	applying	apply	VERB
ejpam-5528	235	29	lemma	lemma	PROPN
ejpam-5528	235	30	2.1	2.1	NUM
ejpam-5528	235	31	,	,	PUNCT
ejpam-5528	235	32	we	we	PRON
ejpam-5528	235	33	deduce	deduce	VERB
ejpam-5528	235	34	that	that	SCONJ
ejpam-5528	235	35	ω(uw	ω(uw	NOUN
ejpam-5528	235	36	)	)	PUNCT
ejpam-5528	235	37	=	=	PUNCT
ejpam-5528	236	1	ω(u)w	ω(u)w	PROPN
ejpam-5528	236	2	for	for	ADP
ejpam-5528	236	3	all	all	DET
ejpam-5528	236	4	u	u	NOUN
ejpam-5528	236	5	,	,	PUNCT
ejpam-5528	236	6	w	w	PROPN
ejpam-5528	236	7	∈	∈	NOUN
ejpam-5528	236	8	ℜ.	ℜ.	PROPN
ejpam-5528	236	9	by	by	ADP
ejpam-5528	236	10	[	[	X
ejpam-5528	236	11	23	23	NUM
ejpam-5528	236	12	,	,	PUNCT
ejpam-5528	236	13	lemma	lemma	PROPN
ejpam-5528	236	14	2.1	2.1	NUM
ejpam-5528	236	15	]	]	PUNCT
ejpam-5528	236	16	there	there	PRON
ejpam-5528	236	17	exists	exist	VERB
ejpam-5528	236	18	q	q	PROPN
ejpam-5528	236	19	∈	∈	PROPN
ejpam-5528	236	20	qmr(ℜ	qmr(ℜ	PROPN
ejpam-5528	236	21	)	)	PUNCT
ejpam-5528	236	22	such	such	ADJ
ejpam-5528	236	23	that	that	DET
ejpam-5528	236	24	ω(u	ω(u	NOUN
ejpam-5528	236	25	)	)	PUNCT
ejpam-5528	236	26	=	=	SYM
ejpam-5528	236	27	qu	qu	PROPN
ejpam-5528	236	28	for	for	ADP
ejpam-5528	236	29	all	all	DET
ejpam-5528	236	30	u	u	NOUN
ejpam-5528	236	31	∈	∈	NOUN
ejpam-5528	236	32	ℜ.	ℜ.	PROPN
ejpam-5528	236	33	now	now	ADV
ejpam-5528	236	34	in	in	ADP
ejpam-5528	236	35	view	view	NOUN
ejpam-5528	236	36	of	of	ADP
ejpam-5528	236	37	[	[	X
ejpam-5528	236	38	1	1	NUM
ejpam-5528	236	39	,	,	PUNCT
ejpam-5528	236	40	proposition	proposition	NOUN
ejpam-5528	236	41	2.1.7	2.1.7	NUM
ejpam-5528	236	42	]	]	PUNCT
ejpam-5528	236	43	,	,	PUNCT
ejpam-5528	236	44	it	it	PRON
ejpam-5528	236	45	follows	follow	VERB
ejpam-5528	236	46	that	that	SCONJ
ejpam-5528	236	47	there	there	PRON
ejpam-5528	236	48	exists	exist	VERB
ejpam-5528	236	49	a	a	DET
ejpam-5528	236	50	nonzero	nonzero	ADJ
ejpam-5528	236	51	dense	dense	ADJ
ejpam-5528	236	52	right	right	ADJ
ejpam-5528	236	53	ideal	ideal	NOUN
ejpam-5528	236	54	k	k	PROPN
ejpam-5528	236	55	of	of	ADP
ejpam-5528	236	56	ℜ	ℜ	PROPN
ejpam-5528	236	57	such	such	ADJ
ejpam-5528	236	58	that	that	SCONJ
ejpam-5528	236	59	kq	kq	PROPN
ejpam-5528	236	60	⊆	⊆	NUM
ejpam-5528	236	61	ℜ.	ℜ.	PROPN
ejpam-5528	236	62	hence	hence	ADV
ejpam-5528	236	63	from	from	ADP
ejpam-5528	236	64	(	(	PUNCT
ejpam-5528	236	65	3.8	3.8	NUM
ejpam-5528	236	66	)	)	PUNCT
ejpam-5528	236	67	,	,	PUNCT
ejpam-5528	236	68	we	we	PRON
ejpam-5528	236	69	have	have	VERB
ejpam-5528	236	70	qvu∗	qvu∗	NOUN
ejpam-5528	236	71	=	=	NOUN
ejpam-5528	236	72	v(qu)∗	v(qu)∗	NOUN
ejpam-5528	236	73	for	for	ADP
ejpam-5528	236	74	all	all	DET
ejpam-5528	236	75	u	u	NOUN
ejpam-5528	236	76	∈	∈	PROPN
ejpam-5528	236	77	k	k	NOUN
ejpam-5528	236	78	and	and	CCONJ
ejpam-5528	236	79	v	v	ADP
ejpam-5528	236	80	∈	∈	NOUN
ejpam-5528	236	81	ℜ.	ℜ.	PROPN
ejpam-5528	236	82	(	(	PUNCT
ejpam-5528	236	83	3.10	3.10	NUM
ejpam-5528	236	84	)	)	PUNCT
ejpam-5528	236	85	for	for	ADP
ejpam-5528	236	86	each	each	DET
ejpam-5528	236	87	fixed	fix	VERB
ejpam-5528	236	88	u	u	NOUN
ejpam-5528	236	89	this	this	PRON
ejpam-5528	236	90	is	be	AUX
ejpam-5528	236	91	a	a	DET
ejpam-5528	236	92	gpi	gpi	NOUN
ejpam-5528	236	93	.	.	PUNCT
ejpam-5528	237	1	hence	hence	ADV
ejpam-5528	237	2	by	by	ADP
ejpam-5528	237	3	[	[	X
ejpam-5528	237	4	1	1	NUM
ejpam-5528	237	5	,	,	PUNCT
ejpam-5528	237	6	theorem	theorem	VERB
ejpam-5528	237	7	6.4.4	6.4.4	NUM
ejpam-5528	237	8	]	]	PUNCT
ejpam-5528	237	9	qvu∗	qvu∗	NOUN
ejpam-5528	237	10	=	=	NOUN
ejpam-5528	237	11	v(qu)∗	v(qu)∗	NOUN
ejpam-5528	237	12	for	for	ADP
ejpam-5528	237	13	all	all	PRON
ejpam-5528	237	14	v	v	ADP
ejpam-5528	237	15	∈	∈	NOUN
ejpam-5528	237	16	qmr(ℜ	qmr(ℜ	NOUN
ejpam-5528	237	17	)	)	PUNCT
ejpam-5528	237	18	.	.	PUNCT
ejpam-5528	238	1	therefore	therefore	ADV
ejpam-5528	238	2	putting	put	VERB
ejpam-5528	238	3	v	v	NOUN
ejpam-5528	238	4	=	=	SYM
ejpam-5528	238	5	1	1	NUM
ejpam-5528	238	6	,	,	PUNCT
ejpam-5528	238	7	we	we	PRON
ejpam-5528	238	8	find	find	VERB
ejpam-5528	238	9	that	that	DET
ejpam-5528	238	10	qu∗	qu∗	NOUN
ejpam-5528	238	11	=	=	SYM
ejpam-5528	238	12	(	(	PUNCT
ejpam-5528	238	13	qu)∗	qu)∗	NOUN
ejpam-5528	238	14	for	for	ADP
ejpam-5528	238	15	all	all	DET
ejpam-5528	238	16	u	u	PROPN
ejpam-5528	238	17	∈	∈	PROPN
ejpam-5528	238	18	k.	k.	NOUN
ejpam-5528	239	1	thus	thus	ADV
ejpam-5528	239	2	from	from	ADP
ejpam-5528	239	3	(	(	PUNCT
ejpam-5528	239	4	3.10	3.10	NUM
ejpam-5528	239	5	)	)	PUNCT
ejpam-5528	239	6	,	,	PUNCT
ejpam-5528	239	7	we	we	PRON
ejpam-5528	239	8	have	have	AUX
ejpam-5528	239	9	qvu∗	qvu∗	NOUN
ejpam-5528	239	10	=	=	NOUN
ejpam-5528	239	11	vqu∗	vqu∗	NOUN
ejpam-5528	239	12	for	for	ADP
ejpam-5528	239	13	all	all	DET
ejpam-5528	239	14	v	v	ADP
ejpam-5528	239	15	∈	∈	PROPN
ejpam-5528	239	16	ℜ	ℜ	PROPN
ejpam-5528	239	17	and	and	CCONJ
ejpam-5528	239	18	u	u	PROPN
ejpam-5528	239	19	∈	∈	PROPN
ejpam-5528	239	20	k.	k.	PROPN
ejpam-5528	240	1	consequently	consequently	ADV
ejpam-5528	240	2	,	,	PUNCT
ejpam-5528	240	3	q	q	PROPN
ejpam-5528	240	4	∈	∈	PROPN
ejpam-5528	240	5	c.	c.	NOUN
ejpam-5528	240	6	now	now	ADV
ejpam-5528	240	7	from	from	ADP
ejpam-5528	240	8	(	(	PUNCT
ejpam-5528	240	9	3.10	3.10	NUM
ejpam-5528	240	10	)	)	PUNCT
ejpam-5528	240	11	it	it	PRON
ejpam-5528	240	12	can	can	AUX
ejpam-5528	240	13	be	be	AUX
ejpam-5528	240	14	easily	easily	ADV
ejpam-5528	240	15	seen	see	VERB
ejpam-5528	240	16	that	that	DET
ejpam-5528	240	17	q∗	q∗	NOUN
ejpam-5528	240	18	=	=	PUNCT
ejpam-5528	240	19	q.	q.	NOUN
ejpam-5528	240	20	this	this	PRON
ejpam-5528	240	21	completes	complete	VERB
ejpam-5528	240	22	the	the	DET
ejpam-5528	240	23	proof	proof	NOUN
ejpam-5528	240	24	.	.	PUNCT
ejpam-5528	241	1	now	now	ADV
ejpam-5528	241	2	we	we	PRON
ejpam-5528	241	3	are	be	AUX
ejpam-5528	241	4	ready	ready	ADJ
ejpam-5528	241	5	to	to	PART
ejpam-5528	241	6	provide	provide	VERB
ejpam-5528	241	7	a	a	DET
ejpam-5528	241	8	characterization	characterization	NOUN
ejpam-5528	241	9	of	of	ADP
ejpam-5528	241	10	generalized	generalized	ADJ
ejpam-5528	241	11	bi	bi	ADJ
ejpam-5528	241	12	-	-	ADJ
ejpam-5528	241	13	skew	skew	ADJ
ejpam-5528	241	14	jordan	jordan	PROPN
ejpam-5528	241	15	derivations	derivation	NOUN
ejpam-5528	241	16	in	in	ADP
ejpam-5528	241	17	prime	prime	ADJ
ejpam-5528	241	18	rings	ring	NOUN
ejpam-5528	241	19	.	.	PUNCT
ejpam-5528	242	1	theorem	theorem	VERB
ejpam-5528	242	2	3.2	3.2	NUM
ejpam-5528	242	3	.	.	PUNCT
ejpam-5528	243	1	let	let	VERB
ejpam-5528	243	2	ℜ	ℜ	PROPN
ejpam-5528	243	3	be	be	AUX
ejpam-5528	243	4	a	a	DET
ejpam-5528	243	5	unital	unital	ADJ
ejpam-5528	243	6	prime	prime	NOUN
ejpam-5528	243	7	∗-ring	∗-ring	NOUN
ejpam-5528	243	8	containing	contain	VERB
ejpam-5528	243	9	a	a	DET
ejpam-5528	243	10	nontrivial	nontrivial	ADJ
ejpam-5528	243	11	symmetric	symmetric	ADJ
ejpam-5528	243	12	idempotent	idempotent	NOUN
ejpam-5528	243	13	.	.	PUNCT
ejpam-5528	244	1	suppose	suppose	VERB
ejpam-5528	244	2	that	that	SCONJ
ejpam-5528	244	3	φ	φ	PROPN
ejpam-5528	244	4	:	:	PUNCT
ejpam-5528	244	5	ℜ	ℜ	PROPN
ejpam-5528	244	6	→	→	SYM
ejpam-5528	244	7	qms(ℜ	qms(ℜ	NUM
ejpam-5528	244	8	)	)	PUNCT
ejpam-5528	244	9	is	be	AUX
ejpam-5528	244	10	a	a	DET
ejpam-5528	244	11	generalized	generalized	ADJ
ejpam-5528	244	12	bi	bi	ADJ
ejpam-5528	244	13	-	-	ADJ
ejpam-5528	244	14	skew	skew	ADJ
ejpam-5528	244	15	jordan	jordan	PROPN
ejpam-5528	244	16	derivation	derivation	PROPN
ejpam-5528	244	17	with	with	ADP
ejpam-5528	244	18	ω	ω	NUM
ejpam-5528	244	19	:	:	PUNCT
ejpam-5528	244	20	ℜ	ℜ	PROPN
ejpam-5528	244	21	→	→	SYM
ejpam-5528	244	22	qms(ℜ	qms(ℜ	NUM
ejpam-5528	244	23	)	)	PUNCT
ejpam-5528	244	24	as	as	ADP
ejpam-5528	244	25	associated	associated	ADJ
ejpam-5528	244	26	bi	bi	ADJ
ejpam-5528	244	27	-	-	ADJ
ejpam-5528	244	28	skew	skew	ADJ
ejpam-5528	244	29	jordan	jordan	PROPN
ejpam-5528	244	30	derivation	derivation	PROPN
ejpam-5528	244	31	.	.	PUNCT
ejpam-5528	245	1	then	then	ADV
ejpam-5528	245	2	ω	ω	PROPN
ejpam-5528	245	3	is	be	AUX
ejpam-5528	245	4	an	an	DET
ejpam-5528	245	5	additive	additive	ADJ
ejpam-5528	245	6	∗derivation	∗derivation	NOUN
ejpam-5528	245	7	and	and	CCONJ
ejpam-5528	245	8	there	there	PRON
ejpam-5528	245	9	exists	exist	VERB
ejpam-5528	245	10	λ∗	λ∗	NOUN
ejpam-5528	246	1	=	=	PUNCT
ejpam-5528	246	2	λ	λ	X
ejpam-5528	246	3	∈	∈	PROPN
ejpam-5528	246	4	c	c	NOUN
ejpam-5528	246	5	such	such	ADJ
ejpam-5528	246	6	that	that	SCONJ
ejpam-5528	246	7	φ(u	φ(u	NOUN
ejpam-5528	246	8	)	)	PUNCT
ejpam-5528	246	9	=	=	SYM
ejpam-5528	246	10	λu	λu	X
ejpam-5528	246	11	+	+	CCONJ
ejpam-5528	246	12	ω(u	ω(u	PROPN
ejpam-5528	246	13	)	)	PUNCT
ejpam-5528	246	14	unless	unless	SCONJ
ejpam-5528	246	15	dimcℜc	dimcℜc	ADJ
ejpam-5528	246	16	=	=	NOUN
ejpam-5528	246	17	4	4	NUM
ejpam-5528	246	18	and	and	CCONJ
ejpam-5528	246	19	char(ℜ	char(ℜ	PROPN
ejpam-5528	246	20	)	)	PUNCT
ejpam-5528	246	21	=	=	SYM
ejpam-5528	246	22	2	2	X
ejpam-5528	246	23	.	.	PUNCT
ejpam-5528	246	24	proof	proof	NOUN
ejpam-5528	246	25	.	.	PUNCT
ejpam-5528	247	1	by	by	ADP
ejpam-5528	247	2	the	the	DET
ejpam-5528	247	3	given	give	VERB
ejpam-5528	247	4	hypothesis	hypothesis	NOUN
ejpam-5528	247	5	φ(u	φ(u	NOUN
ejpam-5528	247	6	•	•	NOUN
ejpam-5528	247	7	v	v	NOUN
ejpam-5528	247	8	)	)	PUNCT
ejpam-5528	247	9	=	=	SYM
ejpam-5528	247	10	φ(u	φ(u	NOUN
ejpam-5528	247	11	)	)	PUNCT
ejpam-5528	247	12	•	•	NUM
ejpam-5528	247	13	v	v	NOUN
ejpam-5528	247	14	+	+	NUM
ejpam-5528	247	15	u	u	NOUN
ejpam-5528	247	16	•	•	NOUN
ejpam-5528	247	17	ω(v	ω(v	NOUN
ejpam-5528	247	18	)	)	PUNCT
ejpam-5528	247	19	and	and	CCONJ
ejpam-5528	247	20	ω(u	ω(u	PROPN
ejpam-5528	247	21	•	•	NOUN
ejpam-5528	247	22	v	v	NOUN
ejpam-5528	247	23	)	)	PUNCT
ejpam-5528	247	24	=	=	SYM
ejpam-5528	247	25	ω(u	ω(u	PROPN
ejpam-5528	247	26	)	)	PUNCT
ejpam-5528	247	27	•	•	NUM
ejpam-5528	247	28	v	v	NOUN
ejpam-5528	247	29	+	+	NUM
ejpam-5528	247	30	u	u	NOUN
ejpam-5528	247	31	•	•	NOUN
ejpam-5528	247	32	ω(v	ω(v	NOUN
ejpam-5528	247	33	)	)	PUNCT
ejpam-5528	247	34	for	for	ADP
ejpam-5528	247	35	all	all	DET
ejpam-5528	247	36	u	u	NOUN
ejpam-5528	247	37	,	,	PUNCT
ejpam-5528	247	38	v	v	NOUN
ejpam-5528	247	39	∈	∈	NOUN
ejpam-5528	247	40	ℜ.	ℜ.	PROPN
ejpam-5528	247	41	therefore	therefore	ADV
ejpam-5528	247	42	,	,	PUNCT
ejpam-5528	247	43	ψ(u	ψ(u	PROPN
ejpam-5528	247	44	•	•	NOUN
ejpam-5528	247	45	v	v	NOUN
ejpam-5528	247	46	)	)	PUNCT
ejpam-5528	247	47	=	=	PUNCT
ejpam-5528	247	48	ψ(u	ψ(u	PROPN
ejpam-5528	247	49	)	)	PUNCT
ejpam-5528	247	50	•	•	NUM
ejpam-5528	247	51	v	v	NOUN
ejpam-5528	247	52	for	for	ADP
ejpam-5528	247	53	all	all	DET
ejpam-5528	247	54	u	u	NOUN
ejpam-5528	247	55	,	,	PUNCT
ejpam-5528	247	56	v	v	NOUN
ejpam-5528	247	57	∈	∈	PROPN
ejpam-5528	247	58	ℜ	ℜ	PROPN
ejpam-5528	247	59	,	,	PUNCT
ejpam-5528	247	60	where	where	SCONJ
ejpam-5528	247	61	ψ	ψ	X
ejpam-5528	247	62	:	:	PUNCT
ejpam-5528	247	63	ℜ	ℜ	PROPN
ejpam-5528	247	64	→	→	SYM
ejpam-5528	247	65	qms(ℜ	qms(ℜ	NUM
ejpam-5528	247	66	)	)	PUNCT
ejpam-5528	247	67	is	be	AUX
ejpam-5528	247	68	a	a	DET
ejpam-5528	247	69	map	map	NOUN
ejpam-5528	247	70	given	give	VERB
ejpam-5528	247	71	by	by	ADP
ejpam-5528	247	72	ψ(u	ψ(u	PROPN
ejpam-5528	247	73	)	)	PUNCT
ejpam-5528	247	74	=	=	PUNCT
ejpam-5528	247	75	(	(	PUNCT
ejpam-5528	247	76	φ	φ	PROPN
ejpam-5528	247	77	−	−	PROPN
ejpam-5528	247	78	ω)(u	ω)(u	NOUN
ejpam-5528	247	79	)	)	PUNCT
ejpam-5528	247	80	.	.	PUNCT
ejpam-5528	248	1	in	in	ADP
ejpam-5528	248	2	view	view	NOUN
ejpam-5528	248	3	of	of	ADP
ejpam-5528	248	4	proposition	proposition	NOUN
ejpam-5528	248	5	3.1	3.1	NUM
ejpam-5528	248	6	,	,	PUNCT
ejpam-5528	248	7	it	it	PRON
ejpam-5528	248	8	follows	follow	VERB
ejpam-5528	248	9	that	that	SCONJ
ejpam-5528	248	10	there	there	PRON
ejpam-5528	248	11	exists	exist	VERB
ejpam-5528	248	12	λ∗	λ∗	NOUN
ejpam-5528	249	1	=	=	PUNCT
ejpam-5528	249	2	λ	λ	X
ejpam-5528	249	3	∈	∈	PROPN
ejpam-5528	249	4	c	c	NOUN
ejpam-5528	249	5	such	such	ADJ
ejpam-5528	249	6	that	that	DET
ejpam-5528	249	7	ψ(u	ψ(u	PROPN
ejpam-5528	249	8	)	)	PUNCT
ejpam-5528	249	9	=	=	PUNCT
ejpam-5528	250	1	λu	λu	PROPN
ejpam-5528	250	2	for	for	ADP
ejpam-5528	250	3	all	all	DET
ejpam-5528	250	4	u	u	NOUN
ejpam-5528	250	5	∈	∈	NOUN
ejpam-5528	250	6	ℜ.	ℜ.	PROPN
ejpam-5528	250	7	consequently	consequently	ADV
ejpam-5528	250	8	,	,	PUNCT
ejpam-5528	250	9	φ(u	φ(u	PROPN
ejpam-5528	250	10	)	)	PUNCT
ejpam-5528	250	11	=	=	SYM
ejpam-5528	250	12	λu	λu	X
ejpam-5528	250	13	+	+	CCONJ
ejpam-5528	250	14	ω(u	ω(u	PROPN
ejpam-5528	250	15	)	)	PUNCT
ejpam-5528	250	16	for	for	ADP
ejpam-5528	250	17	all	all	DET
ejpam-5528	250	18	u	u	PROPN
ejpam-5528	250	19	∈	∈	PROPN
ejpam-5528	250	20	ℜ.	ℜ.	PROPN
ejpam-5528	250	21	finally	finally	ADV
ejpam-5528	250	22	,	,	PUNCT
ejpam-5528	250	23	by	by	ADP
ejpam-5528	250	24	[	[	X
ejpam-5528	250	25	20	20	NUM
ejpam-5528	250	26	]	]	PUNCT
ejpam-5528	250	27	,	,	PUNCT
ejpam-5528	250	28	ω	ω	PROPN
ejpam-5528	250	29	is	be	AUX
ejpam-5528	250	30	an	an	DET
ejpam-5528	250	31	additive	additive	ADJ
ejpam-5528	250	32	∗-derivation	∗-derivation	NOUN
ejpam-5528	250	33	.	.	PUNCT
ejpam-5528	251	1	this	this	PRON
ejpam-5528	251	2	completes	complete	VERB
ejpam-5528	251	3	the	the	DET
ejpam-5528	251	4	proof	proof	NOUN
ejpam-5528	251	5	.	.	PUNCT
ejpam-5528	252	1	the	the	DET
ejpam-5528	252	2	following	following	ADJ
ejpam-5528	252	3	result	result	NOUN
ejpam-5528	252	4	gives	give	VERB
ejpam-5528	252	5	a	a	DET
ejpam-5528	252	6	characterization	characterization	NOUN
ejpam-5528	252	7	of	of	ADP
ejpam-5528	252	8	generalized	generalized	ADJ
ejpam-5528	252	9	additive	additive	ADJ
ejpam-5528	252	10	bi	bi	ADJ
ejpam-5528	252	11	-	-	ADJ
ejpam-5528	252	12	skew	skew	ADJ
ejpam-5528	252	13	jordan	jordan	PROPN
ejpam-5528	252	14	derivations	derivation	NOUN
ejpam-5528	252	15	in	in	ADP
ejpam-5528	252	16	prime	prime	ADJ
ejpam-5528	252	17	rings	ring	NOUN
ejpam-5528	252	18	without	without	ADP
ejpam-5528	252	19	assuming	assume	VERB
ejpam-5528	252	20	the	the	DET
ejpam-5528	252	21	existence	existence	NOUN
ejpam-5528	252	22	of	of	ADP
ejpam-5528	252	23	a	a	DET
ejpam-5528	252	24	nontrivial	nontrivial	ADJ
ejpam-5528	252	25	symmetric	symmetric	ADJ
ejpam-5528	252	26	idempotent	idempotent	NOUN
ejpam-5528	252	27	.	.	PUNCT
ejpam-5528	253	1	theorem	theorem	VERB
ejpam-5528	253	2	3.3	3.3	NUM
ejpam-5528	253	3	.	.	PUNCT
ejpam-5528	254	1	let	let	VERB
ejpam-5528	254	2	ℜ	ℜ	PROPN
ejpam-5528	254	3	be	be	AUX
ejpam-5528	254	4	a	a	DET
ejpam-5528	254	5	noncommutative	noncommutative	ADJ
ejpam-5528	254	6	prime	prime	ADJ
ejpam-5528	254	7	ring	ring	NOUN
ejpam-5528	254	8	with	with	ADP
ejpam-5528	254	9	an	an	DET
ejpam-5528	254	10	involution	involution	NOUN
ejpam-5528	254	11	‘	'	PUNCT
ejpam-5528	254	12	∗	∗	NOUN
ejpam-5528	254	13	’	'	PUNCT
ejpam-5528	254	14	and	and	CCONJ
ejpam-5528	254	15	let	let	VERB
ejpam-5528	254	16	φ	φ	NOUN
ejpam-5528	254	17	:	:	PUNCT
ejpam-5528	254	18	ℜ	ℜ	PROPN
ejpam-5528	254	19	→	→	SYM
ejpam-5528	254	20	qms(ℜ	qms(ℜ	PROPN
ejpam-5528	254	21	)	)	PUNCT
ejpam-5528	254	22	be	be	VERB
ejpam-5528	254	23	a	a	DET
ejpam-5528	254	24	generalized	generalized	ADJ
ejpam-5528	254	25	bi	bi	ADJ
ejpam-5528	254	26	-	-	ADJ
ejpam-5528	254	27	skew	skew	ADJ
ejpam-5528	254	28	jordan	jordan	PROPN
ejpam-5528	254	29	derivation	derivation	PROPN
ejpam-5528	254	30	with	with	ADP
ejpam-5528	254	31	ω	ω	NUM
ejpam-5528	254	32	:	:	PUNCT
ejpam-5528	254	33	ℜ	ℜ	PROPN
ejpam-5528	254	34	→	→	SYM
ejpam-5528	254	35	qms(ℜ	qms(ℜ	NUM
ejpam-5528	254	36	)	)	PUNCT
ejpam-5528	254	37	as	as	SCONJ
ejpam-5528	254	38	associated	associated	ADJ
ejpam-5528	254	39	bi	bi	ADJ
ejpam-5528	254	40	-	-	ADJ
ejpam-5528	254	41	skew	skew	ADJ
ejpam-5528	254	42	jordan	jordan	PROPN
ejpam-5528	254	43	derivation	derivation	PROPN
ejpam-5528	254	44	such	such	ADJ
ejpam-5528	254	45	that	that	SCONJ
ejpam-5528	254	46	both	both	DET
ejpam-5528	254	47	φ	φ	PROPN
ejpam-5528	254	48	and	and	CCONJ
ejpam-5528	254	49	ω	ω	PROPN
ejpam-5528	254	50	are	be	AUX
ejpam-5528	254	51	additive	additive	ADJ
ejpam-5528	254	52	.	.	PUNCT
ejpam-5528	255	1	suppose	suppose	VERB
ejpam-5528	255	2	that	that	SCONJ
ejpam-5528	255	3	either	either	CCONJ
ejpam-5528	255	4	dimcℜc	dimcℜc	VERB
ejpam-5528	255	5	>	>	X
ejpam-5528	255	6	4	4	NUM
ejpam-5528	255	7	or	or	CCONJ
ejpam-5528	255	8	ℜ	ℜ	NOUN
ejpam-5528	255	9	is	be	AUX
ejpam-5528	255	10	unital	unital	ADJ
ejpam-5528	255	11	.	.	PUNCT
ejpam-5528	256	1	then	then	ADV
ejpam-5528	256	2	ω	ω	PROPN
ejpam-5528	256	3	is	be	AUX
ejpam-5528	256	4	a	a	DET
ejpam-5528	256	5	∗-derivation	∗-derivation	NOUN
ejpam-5528	256	6	and	and	CCONJ
ejpam-5528	256	7	there	there	PRON
ejpam-5528	256	8	exists	exist	VERB
ejpam-5528	256	9	λ∗	λ∗	NOUN
ejpam-5528	257	1	=	=	PUNCT
ejpam-5528	257	2	λ	λ	X
ejpam-5528	257	3	∈	∈	PROPN
ejpam-5528	257	4	c	c	NOUN
ejpam-5528	257	5	such	such	ADJ
ejpam-5528	257	6	that	that	SCONJ
ejpam-5528	257	7	φ(u	φ(u	NOUN
ejpam-5528	257	8	)	)	PUNCT
ejpam-5528	257	9	=	=	SYM
ejpam-5528	257	10	λu+ω(u	λu+ω(u	PROPN
ejpam-5528	257	11	)	)	PUNCT
ejpam-5528	257	12	unless	unless	SCONJ
ejpam-5528	257	13	dimcℜc	dimcℜc	ADJ
ejpam-5528	257	14	=	=	NOUN
ejpam-5528	257	15	4	4	NUM
ejpam-5528	257	16	and	and	CCONJ
ejpam-5528	257	17	char(ℜ	char(ℜ	PROPN
ejpam-5528	257	18	)	)	PUNCT
ejpam-5528	257	19	=	=	SYM
ejpam-5528	258	1	2	2	X
ejpam-5528	258	2	.	.	PUNCT
ejpam-5528	258	3	moin	moin	PROPN
ejpam-5528	258	4	a.	a.	PROPN
ejpam-5528	258	5	ansari	ansari	PROPN
ejpam-5528	258	6	et	et	PROPN
ejpam-5528	258	7	al	al	PROPN
ejpam-5528	258	8	.	.	PUNCT
ejpam-5528	258	9	/	/	SYM
ejpam-5528	258	10	eur	eur	PROPN
ejpam-5528	258	11	.	.	PUNCT
ejpam-5528	259	1	j.	j.	PROPN
ejpam-5528	259	2	pure	pure	PROPN
ejpam-5528	259	3	appl	appl	PROPN
ejpam-5528	259	4	.	.	PROPN
ejpam-5528	259	5	math	math	PROPN
ejpam-5528	259	6	,	,	PUNCT
ejpam-5528	259	7	18	18	NUM
ejpam-5528	259	8	(	(	PUNCT
ejpam-5528	259	9	2	2	NUM
ejpam-5528	259	10	)	)	PUNCT
ejpam-5528	259	11	(	(	PUNCT
ejpam-5528	259	12	2025	2025	NUM
ejpam-5528	259	13	)	)	PUNCT
ejpam-5528	259	14	,	,	PUNCT
ejpam-5528	259	15	5528	5528	NUM
ejpam-5528	259	16	11	11	NUM
ejpam-5528	259	17	of	of	ADP
ejpam-5528	259	18	14	14	NUM
ejpam-5528	259	19	proof	proof	NOUN
ejpam-5528	259	20	.	.	PUNCT
ejpam-5528	260	1	by	by	ADP
ejpam-5528	260	2	the	the	DET
ejpam-5528	260	3	given	give	VERB
ejpam-5528	260	4	hypothesis	hypothesis	NOUN
ejpam-5528	260	5	φ(u	φ(u	NOUN
ejpam-5528	260	6	•	•	NOUN
ejpam-5528	260	7	v	v	NOUN
ejpam-5528	260	8	)	)	PUNCT
ejpam-5528	260	9	=	=	SYM
ejpam-5528	260	10	φ(u	φ(u	NOUN
ejpam-5528	260	11	)	)	PUNCT
ejpam-5528	260	12	•	•	NUM
ejpam-5528	260	13	v	v	NOUN
ejpam-5528	260	14	+	+	NUM
ejpam-5528	260	15	u	u	NOUN
ejpam-5528	260	16	•	•	NOUN
ejpam-5528	260	17	ω(v	ω(v	NOUN
ejpam-5528	260	18	)	)	PUNCT
ejpam-5528	260	19	and	and	CCONJ
ejpam-5528	260	20	ω(u	ω(u	PROPN
ejpam-5528	260	21	•	•	NOUN
ejpam-5528	260	22	v	v	NOUN
ejpam-5528	260	23	)	)	PUNCT
ejpam-5528	260	24	=	=	SYM
ejpam-5528	260	25	ω(u	ω(u	PROPN
ejpam-5528	260	26	)	)	PUNCT
ejpam-5528	260	27	•	•	NUM
ejpam-5528	260	28	v	v	NOUN
ejpam-5528	260	29	+	+	NUM
ejpam-5528	260	30	u	u	NOUN
ejpam-5528	260	31	•	•	NOUN
ejpam-5528	260	32	ω(v	ω(v	NOUN
ejpam-5528	260	33	)	)	PUNCT
ejpam-5528	260	34	for	for	ADP
ejpam-5528	260	35	all	all	DET
ejpam-5528	260	36	u	u	NOUN
ejpam-5528	260	37	,	,	PUNCT
ejpam-5528	260	38	v	v	NOUN
ejpam-5528	260	39	∈	∈	NOUN
ejpam-5528	260	40	ℜ.	ℜ.	PROPN
ejpam-5528	260	41	therefore	therefore	ADV
ejpam-5528	260	42	,	,	PUNCT
ejpam-5528	260	43	ψ(u	ψ(u	PROPN
ejpam-5528	260	44	•	•	NOUN
ejpam-5528	260	45	v	v	NOUN
ejpam-5528	260	46	)	)	PUNCT
ejpam-5528	260	47	=	=	PUNCT
ejpam-5528	260	48	ψ(u	ψ(u	PROPN
ejpam-5528	260	49	)	)	PUNCT
ejpam-5528	260	50	•	•	NUM
ejpam-5528	260	51	v	v	NOUN
ejpam-5528	260	52	for	for	ADP
ejpam-5528	260	53	all	all	DET
ejpam-5528	260	54	u	u	NOUN
ejpam-5528	260	55	,	,	PUNCT
ejpam-5528	260	56	v	v	NOUN
ejpam-5528	260	57	∈	∈	PROPN
ejpam-5528	260	58	ℜ	ℜ	PROPN
ejpam-5528	260	59	,	,	PUNCT
ejpam-5528	260	60	where	where	SCONJ
ejpam-5528	260	61	ψ	ψ	X
ejpam-5528	260	62	:	:	PUNCT
ejpam-5528	260	63	ℜ	ℜ	PROPN
ejpam-5528	260	64	→	→	SYM
ejpam-5528	260	65	qms(ℜ	qms(ℜ	NUM
ejpam-5528	260	66	)	)	PUNCT
ejpam-5528	260	67	is	be	AUX
ejpam-5528	260	68	a	a	DET
ejpam-5528	260	69	map	map	NOUN
ejpam-5528	260	70	given	give	VERB
ejpam-5528	260	71	by	by	ADP
ejpam-5528	260	72	ψ(u	ψ(u	PROPN
ejpam-5528	260	73	)	)	PUNCT
ejpam-5528	260	74	=	=	PUNCT
ejpam-5528	261	1	(	(	PUNCT
ejpam-5528	261	2	φ	φ	PROPN
ejpam-5528	261	3	−	−	PROPN
ejpam-5528	261	4	ω)(u	ω)(u	NOUN
ejpam-5528	261	5	)	)	PUNCT
ejpam-5528	261	6	.	.	PUNCT
ejpam-5528	262	1	in	in	ADP
ejpam-5528	262	2	view	view	NOUN
ejpam-5528	262	3	of	of	ADP
ejpam-5528	262	4	proposition	proposition	NOUN
ejpam-5528	262	5	3.1	3.1	NUM
ejpam-5528	262	6	,	,	PUNCT
ejpam-5528	262	7	it	it	PRON
ejpam-5528	262	8	follows	follow	VERB
ejpam-5528	262	9	that	that	SCONJ
ejpam-5528	262	10	there	there	PRON
ejpam-5528	262	11	exists	exist	VERB
ejpam-5528	262	12	λ∗	λ∗	NOUN
ejpam-5528	263	1	=	=	PUNCT
ejpam-5528	263	2	λ	λ	X
ejpam-5528	263	3	∈	∈	PROPN
ejpam-5528	263	4	c	c	NOUN
ejpam-5528	263	5	such	such	ADJ
ejpam-5528	263	6	that	that	DET
ejpam-5528	263	7	ψ(u	ψ(u	PROPN
ejpam-5528	263	8	)	)	PUNCT
ejpam-5528	263	9	=	=	PUNCT
ejpam-5528	264	1	λu	λu	PROPN
ejpam-5528	264	2	for	for	ADP
ejpam-5528	264	3	all	all	DET
ejpam-5528	264	4	u	u	NOUN
ejpam-5528	264	5	∈	∈	NOUN
ejpam-5528	264	6	ℜ.	ℜ.	PROPN
ejpam-5528	264	7	consequently	consequently	ADV
ejpam-5528	264	8	,	,	PUNCT
ejpam-5528	264	9	φ(u	φ(u	PROPN
ejpam-5528	264	10	)	)	PUNCT
ejpam-5528	264	11	=	=	SYM
ejpam-5528	264	12	λu	λu	X
ejpam-5528	264	13	+	+	CCONJ
ejpam-5528	264	14	ω(u	ω(u	PROPN
ejpam-5528	264	15	)	)	PUNCT
ejpam-5528	264	16	for	for	ADP
ejpam-5528	264	17	all	all	DET
ejpam-5528	264	18	u	u	PROPN
ejpam-5528	264	19	∈	∈	PROPN
ejpam-5528	264	20	ℜ.	ℜ.	PROPN
ejpam-5528	264	21	finally	finally	ADV
ejpam-5528	264	22	,	,	PUNCT
ejpam-5528	264	23	by	by	ADP
ejpam-5528	264	24	theorem	theorem	NOUN
ejpam-5528	264	25	3.1	3.1	NUM
ejpam-5528	264	26	,	,	PUNCT
ejpam-5528	264	27	ω	ω	PROPN
ejpam-5528	264	28	is	be	AUX
ejpam-5528	264	29	an	an	DET
ejpam-5528	264	30	∗-derivation	∗-derivation	NOUN
ejpam-5528	264	31	.	.	PUNCT
ejpam-5528	265	1	this	this	PRON
ejpam-5528	265	2	completes	complete	VERB
ejpam-5528	265	3	the	the	DET
ejpam-5528	265	4	proof	proof	NOUN
ejpam-5528	265	5	.	.	PUNCT
ejpam-5528	266	1	4	4	X
ejpam-5528	266	2	.	.	X
ejpam-5528	266	3	applications	application	NOUN
ejpam-5528	266	4	to	to	ADP
ejpam-5528	266	5	some	some	DET
ejpam-5528	266	6	operator	operator	NOUN
ejpam-5528	266	7	algebras	algebra	NOUN
ejpam-5528	266	8	as	as	ADP
ejpam-5528	266	9	applications	application	NOUN
ejpam-5528	266	10	of	of	ADP
ejpam-5528	266	11	the	the	DET
ejpam-5528	266	12	outcomes	outcome	NOUN
ejpam-5528	266	13	presented	present	VERB
ejpam-5528	266	14	in	in	ADP
ejpam-5528	266	15	the	the	DET
ejpam-5528	266	16	preceding	precede	VERB
ejpam-5528	266	17	sections	section	NOUN
ejpam-5528	266	18	,	,	PUNCT
ejpam-5528	266	19	we	we	PRON
ejpam-5528	266	20	aim	aim	VERB
ejpam-5528	266	21	to	to	PART
ejpam-5528	266	22	delineate	delineate	VERB
ejpam-5528	266	23	strong	strong	ADJ
ejpam-5528	266	24	biskew	biskew	NOUN
ejpam-5528	266	25	commutativity	commutativity	NOUN
ejpam-5528	266	26	-	-	PUNCT
ejpam-5528	266	27	preserving	preserve	VERB
ejpam-5528	266	28	maps	map	NOUN
ejpam-5528	266	29	,	,	PUNCT
ejpam-5528	266	30	bi	bi	ADJ
ejpam-5528	266	31	-	-	ADJ
ejpam-5528	266	32	skew	skew	ADJ
ejpam-5528	266	33	commuting	commuting	NOUN
ejpam-5528	266	34	maps	map	NOUN
ejpam-5528	266	35	,	,	PUNCT
ejpam-5528	266	36	and	and	CCONJ
ejpam-5528	266	37	generalized	generalized	ADJ
ejpam-5528	266	38	bi	bi	ADJ
ejpam-5528	266	39	-	-	ADJ
ejpam-5528	266	40	skew	skew	ADJ
ejpam-5528	266	41	jordan	jordan	PROPN
ejpam-5528	266	42	derivations	derivation	NOUN
ejpam-5528	266	43	within	within	ADP
ejpam-5528	266	44	standard	standard	ADJ
ejpam-5528	266	45	operator	operator	NOUN
ejpam-5528	266	46	algebras	algebra	NOUN
ejpam-5528	266	47	and	and	CCONJ
ejpam-5528	266	48	factor	factor	NOUN
ejpam-5528	266	49	von	von	PROPN
ejpam-5528	266	50	neumann	neumann	PROPN
ejpam-5528	266	51	algebras	algebras	PROPN
ejpam-5528	266	52	.	.	PUNCT
ejpam-5528	267	1	throughout	throughout	ADP
ejpam-5528	267	2	this	this	DET
ejpam-5528	267	3	section	section	NOUN
ejpam-5528	267	4	,	,	PUNCT
ejpam-5528	267	5	all	all	DET
ejpam-5528	267	6	vector	vector	NOUN
ejpam-5528	267	7	spaces	space	NOUN
ejpam-5528	267	8	and	and	CCONJ
ejpam-5528	267	9	algebras	algebra	NOUN
ejpam-5528	267	10	are	be	AUX
ejpam-5528	267	11	defined	define	VERB
ejpam-5528	267	12	over	over	ADP
ejpam-5528	267	13	the	the	DET
ejpam-5528	267	14	field	field	NOUN
ejpam-5528	267	15	c	c	NOUN
ejpam-5528	267	16	of	of	ADP
ejpam-5528	267	17	complex	complex	ADJ
ejpam-5528	267	18	numbers	number	NOUN
ejpam-5528	267	19	.	.	PUNCT
ejpam-5528	268	1	suppose	suppose	VERB
ejpam-5528	268	2	h	h	NOUN
ejpam-5528	268	3	represents	represent	VERB
ejpam-5528	268	4	a	a	DET
ejpam-5528	268	5	hilbert	hilbert	NOUN
ejpam-5528	268	6	space	space	NOUN
ejpam-5528	268	7	,	,	PUNCT
ejpam-5528	268	8	with	with	ADP
ejpam-5528	268	9	b(h	b(h	NOUN
ejpam-5528	268	10	)	)	PUNCT
ejpam-5528	268	11	denoting	denote	VERB
ejpam-5528	268	12	the	the	DET
ejpam-5528	268	13	algebra	algebra	NOUN
ejpam-5528	268	14	comprising	comprise	VERB
ejpam-5528	268	15	all	all	DET
ejpam-5528	268	16	bounded	bounded	ADJ
ejpam-5528	268	17	linear	linear	PROPN
ejpam-5528	268	18	operators	operator	NOUN
ejpam-5528	268	19	on	on	ADP
ejpam-5528	268	20	h	h	NOUN
ejpam-5528	268	21	,	,	PUNCT
ejpam-5528	268	22	and	and	CCONJ
ejpam-5528	268	23	f(h	f(h	PROPN
ejpam-5528	268	24	)	)	PUNCT
ejpam-5528	268	25	representing	represent	VERB
ejpam-5528	268	26	the	the	DET
ejpam-5528	268	27	ideal	ideal	NOUN
ejpam-5528	268	28	consisting	consist	VERB
ejpam-5528	268	29	of	of	ADP
ejpam-5528	268	30	all	all	DET
ejpam-5528	268	31	finite	finite	PROPN
ejpam-5528	268	32	rank	rank	NOUN
ejpam-5528	268	33	operators	operator	NOUN
ejpam-5528	268	34	within	within	ADP
ejpam-5528	268	35	b(h	b(h	PROPN
ejpam-5528	268	36	)	)	PUNCT
ejpam-5528	268	37	.	.	PUNCT
ejpam-5528	269	1	the	the	DET
ejpam-5528	269	2	map	map	NOUN
ejpam-5528	269	3	t	t	PROPN
ejpam-5528	269	4	7→	7→	NUM
ejpam-5528	269	5	t	t	NOUN
ejpam-5528	269	6	∗	∗	NOUN
ejpam-5528	269	7	,	,	PUNCT
ejpam-5528	269	8	which	which	PRON
ejpam-5528	269	9	takes	take	VERB
ejpam-5528	269	10	an	an	DET
ejpam-5528	269	11	operator	operator	NOUN
ejpam-5528	269	12	to	to	ADP
ejpam-5528	269	13	its	its	PRON
ejpam-5528	269	14	hilbert	hilbert	PROPN
ejpam-5528	269	15	adjoint	adjoint	NOUN
ejpam-5528	269	16	operator	operator	NOUN
ejpam-5528	269	17	,	,	PUNCT
ejpam-5528	269	18	is	be	AUX
ejpam-5528	269	19	an	an	DET
ejpam-5528	269	20	involution	involution	NOUN
ejpam-5528	269	21	on	on	ADP
ejpam-5528	269	22	b(h	b(h	PROPN
ejpam-5528	269	23	)	)	PUNCT
ejpam-5528	269	24	.	.	PUNCT
ejpam-5528	270	1	here	here	ADV
ejpam-5528	270	2	c	c	X
ejpam-5528	270	3	,	,	PUNCT
ejpam-5528	270	4	the	the	DET
ejpam-5528	270	5	field	field	NOUN
ejpam-5528	270	6	of	of	ADP
ejpam-5528	270	7	complex	complex	ADJ
ejpam-5528	270	8	numbers	number	NOUN
ejpam-5528	270	9	,	,	PUNCT
ejpam-5528	270	10	is	be	AUX
ejpam-5528	270	11	equipped	equip	VERB
ejpam-5528	270	12	with	with	ADP
ejpam-5528	270	13	the	the	DET
ejpam-5528	270	14	conjugate	conjugate	ADJ
ejpam-5528	270	15	involution	involution	NOUN
ejpam-5528	270	16	and	and	CCONJ
ejpam-5528	270	17	b(h	b(h	NOUN
ejpam-5528	270	18	)	)	PUNCT
ejpam-5528	270	19	forms	form	VERB
ejpam-5528	270	20	a	a	DET
ejpam-5528	270	21	∗-algebra	∗-algebra	NOUN
ejpam-5528	270	22	.	.	PUNCT
ejpam-5528	271	1	therefore	therefore	ADV
ejpam-5528	271	2	b(h	b(h	PROPN
ejpam-5528	271	3	)	)	PUNCT
ejpam-5528	271	4	is	be	AUX
ejpam-5528	271	5	an	an	DET
ejpam-5528	271	6	algebra	algebra	NOUN
ejpam-5528	271	7	of	of	ADP
ejpam-5528	271	8	characteristic	characteristic	ADJ
ejpam-5528	271	9	zero	zero	NUM
ejpam-5528	271	10	and	and	CCONJ
ejpam-5528	271	11	the	the	DET
ejpam-5528	271	12	map	map	NOUN
ejpam-5528	271	13	t	t	PROPN
ejpam-5528	271	14	7→	7→	NUM
ejpam-5528	271	15	t	t	NOUN
ejpam-5528	271	16	∗	∗	NOUN
ejpam-5528	271	17	,	,	PUNCT
ejpam-5528	271	18	where	where	SCONJ
ejpam-5528	271	19	t	t	PROPN
ejpam-5528	271	20	∗	∗	NOUN
ejpam-5528	271	21	denotes	denote	VERB
ejpam-5528	271	22	the	the	DET
ejpam-5528	271	23	hilbert	hilbert	PROPN
ejpam-5528	271	24	adjoint	adjoint	PROPN
ejpam-5528	271	25	operator	operator	NOUN
ejpam-5528	271	26	of	of	ADP
ejpam-5528	271	27	t	t	PROPN
ejpam-5528	271	28	,	,	PUNCT
ejpam-5528	271	29	is	be	AUX
ejpam-5528	271	30	an	an	DET
ejpam-5528	271	31	involution	involution	NOUN
ejpam-5528	271	32	of	of	ADP
ejpam-5528	271	33	the	the	DET
ejpam-5528	271	34	second	second	ADJ
ejpam-5528	271	35	kind	kind	NOUN
ejpam-5528	271	36	on	on	ADP
ejpam-5528	271	37	z(b(h	z(b(h	NUM
ejpam-5528	271	38	)	)	PUNCT
ejpam-5528	271	39	)	)	PUNCT
ejpam-5528	271	40	.	.	PUNCT
ejpam-5528	272	1	a	a	DET
ejpam-5528	272	2	subset	subset	NOUN
ejpam-5528	272	3	m	m	NOUN
ejpam-5528	272	4	of	of	ADP
ejpam-5528	272	5	b(h	b(h	PROPN
ejpam-5528	272	6	)	)	PUNCT
ejpam-5528	272	7	is	be	AUX
ejpam-5528	272	8	said	say	VERB
ejpam-5528	272	9	to	to	PART
ejpam-5528	272	10	be	be	AUX
ejpam-5528	272	11	closed	close	VERB
ejpam-5528	272	12	under	under	ADP
ejpam-5528	272	13	adjoint	adjoint	NOUN
ejpam-5528	272	14	operation	operation	NOUN
ejpam-5528	272	15	if	if	SCONJ
ejpam-5528	272	16	u	u	PROPN
ejpam-5528	272	17	∈	∈	PROPN
ejpam-5528	272	18	m	m	VERB
ejpam-5528	272	19	implies	imply	VERB
ejpam-5528	272	20	that	that	SCONJ
ejpam-5528	272	21	u∗	u∗	PROPN
ejpam-5528	272	22	∈	∈	PROPN
ejpam-5528	272	23	m	m	NOUN
ejpam-5528	272	24	,	,	PUNCT
ejpam-5528	272	25	that	that	ADV
ejpam-5528	272	26	is	is	ADV
ejpam-5528	272	27	,	,	PUNCT
ejpam-5528	272	28	m∗	m∗	VERB
ejpam-5528	272	29	⊆	⊆	NUM
ejpam-5528	272	30	m.	m.	NOUN
ejpam-5528	272	31	standard	standard	ADJ
ejpam-5528	272	32	operator	operator	NOUN
ejpam-5528	272	33	algebras	algebra	VERB
ejpam-5528	272	34	:	:	PUNCT
ejpam-5528	272	35	a	a	DET
ejpam-5528	272	36	subalgebra	subalgebra	NOUN
ejpam-5528	272	37	s	s	NOUN
ejpam-5528	272	38	of	of	ADP
ejpam-5528	272	39	b(h	b(h	PROPN
ejpam-5528	272	40	)	)	PUNCT
ejpam-5528	272	41	earns	earn	VERB
ejpam-5528	272	42	the	the	DET
ejpam-5528	272	43	label	label	NOUN
ejpam-5528	272	44	of	of	ADP
ejpam-5528	272	45	a	a	DET
ejpam-5528	272	46	standard	standard	ADJ
ejpam-5528	272	47	operator	operator	NOUN
ejpam-5528	272	48	algebra	algebra	NOUN
ejpam-5528	272	49	if	if	SCONJ
ejpam-5528	272	50	it	it	PRON
ejpam-5528	272	51	includes	include	VERB
ejpam-5528	272	52	the	the	DET
ejpam-5528	272	53	identity	identity	NOUN
ejpam-5528	272	54	operator	operator	NOUN
ejpam-5528	272	55	and	and	CCONJ
ejpam-5528	272	56	encompasses	encompass	VERB
ejpam-5528	272	57	f(h	f(h	PROPN
ejpam-5528	272	58	)	)	PUNCT
ejpam-5528	272	59	.	.	PUNCT
ejpam-5528	273	1	it	it	PRON
ejpam-5528	273	2	’s	’	VERB
ejpam-5528	273	3	evident	evident	ADJ
ejpam-5528	273	4	that	that	SCONJ
ejpam-5528	273	5	b(h	b(h	NOUN
ejpam-5528	273	6	)	)	PUNCT
ejpam-5528	273	7	itself	itself	PRON
ejpam-5528	273	8	is	be	AUX
ejpam-5528	273	9	a	a	DET
ejpam-5528	273	10	standard	standard	ADJ
ejpam-5528	273	11	operator	operator	NOUN
ejpam-5528	273	12	algebra	algebra	NOUN
ejpam-5528	273	13	.	.	PUNCT
ejpam-5528	274	1	furthermore	furthermore	ADV
ejpam-5528	274	2	,	,	PUNCT
ejpam-5528	274	3	every	every	DET
ejpam-5528	274	4	standard	standard	ADJ
ejpam-5528	274	5	operator	operator	NOUN
ejpam-5528	274	6	algebra	algebra	NOUN
ejpam-5528	274	7	qualifies	qualify	VERB
ejpam-5528	274	8	as	as	ADP
ejpam-5528	274	9	a	a	DET
ejpam-5528	274	10	prime	prime	ADJ
ejpam-5528	274	11	algebra	algebra	NOUN
ejpam-5528	274	12	.	.	PUNCT
ejpam-5528	275	1	moreover	moreover	ADV
ejpam-5528	275	2	,	,	PUNCT
ejpam-5528	275	3	for	for	ADP
ejpam-5528	275	4	any	any	DET
ejpam-5528	275	5	standard	standard	ADJ
ejpam-5528	275	6	operator	operator	NOUN
ejpam-5528	275	7	algebra	algebra	NOUN
ejpam-5528	275	8	s	s	PART
ejpam-5528	275	9	,	,	PUNCT
ejpam-5528	275	10	its	its	PRON
ejpam-5528	275	11	center	center	NOUN
ejpam-5528	275	12	z(s	z(s	PROPN
ejpam-5528	275	13	)	)	PUNCT
ejpam-5528	275	14	is	be	AUX
ejpam-5528	275	15	ci	ci	NOUN
ejpam-5528	275	16	.	.	PUNCT
ejpam-5528	276	1	a	a	DET
ejpam-5528	276	2	self	self	NOUN
ejpam-5528	276	3	-	-	PUNCT
ejpam-5528	276	4	adjoint	adjoint	NOUN
ejpam-5528	276	5	standard	standard	ADJ
ejpam-5528	276	6	operator	operator	NOUN
ejpam-5528	276	7	algebra	algebra	NOUN
ejpam-5528	276	8	s	s	PART
ejpam-5528	276	9	represents	represent	VERB
ejpam-5528	276	10	an	an	DET
ejpam-5528	276	11	algebra	algebra	NOUN
ejpam-5528	276	12	of	of	ADP
ejpam-5528	276	13	characteristic	characteristic	ADJ
ejpam-5528	276	14	zero	zero	NUM
ejpam-5528	276	15	,	,	PUNCT
ejpam-5528	276	16	and	and	CCONJ
ejpam-5528	276	17	a	a	DET
ejpam-5528	276	18	mapping	mapping	NOUN
ejpam-5528	276	19	t	t	PROPN
ejpam-5528	276	20	7→	7→	NUM
ejpam-5528	276	21	t	t	NOUN
ejpam-5528	276	22	∗	∗	NOUN
ejpam-5528	276	23	,	,	PUNCT
ejpam-5528	276	24	where	where	SCONJ
ejpam-5528	276	25	t	t	PROPN
ejpam-5528	276	26	∗	∗	NOUN
ejpam-5528	276	27	denotes	denote	VERB
ejpam-5528	276	28	the	the	DET
ejpam-5528	276	29	hilbert	hilbert	PROPN
ejpam-5528	276	30	adjoint	adjoint	PROPN
ejpam-5528	276	31	operator	operator	NOUN
ejpam-5528	276	32	of	of	ADP
ejpam-5528	276	33	t	t	PROPN
ejpam-5528	276	34	,	,	PUNCT
ejpam-5528	276	35	serves	serve	VERB
ejpam-5528	276	36	as	as	ADP
ejpam-5528	276	37	an	an	DET
ejpam-5528	276	38	involution	involution	NOUN
ejpam-5528	276	39	of	of	ADP
ejpam-5528	276	40	the	the	DET
ejpam-5528	276	41	second	second	ADJ
ejpam-5528	276	42	kind	kind	NOUN
ejpam-5528	276	43	on	on	ADP
ejpam-5528	276	44	z(s	z(s	PROPN
ejpam-5528	276	45	)	)	PUNCT
ejpam-5528	276	46	.	.	PUNCT
ejpam-5528	277	1	leveraging	leverage	VERB
ejpam-5528	277	2	the	the	DET
ejpam-5528	277	3	results	result	NOUN
ejpam-5528	277	4	derived	derive	VERB
ejpam-5528	277	5	in	in	ADP
ejpam-5528	277	6	the	the	DET
ejpam-5528	277	7	preceding	precede	VERB
ejpam-5528	277	8	section	section	NOUN
ejpam-5528	277	9	,	,	PUNCT
ejpam-5528	277	10	the	the	DET
ejpam-5528	277	11	following	follow	VERB
ejpam-5528	277	12	corollaries	corollary	NOUN
ejpam-5528	277	13	emerge	emerge	VERB
ejpam-5528	277	14	.	.	PUNCT
ejpam-5528	278	1	corollary	corollary	ADJ
ejpam-5528	278	2	4.1	4.1	NUM
ejpam-5528	278	3	.	.	PUNCT
ejpam-5528	279	1	let	let	VERB
ejpam-5528	279	2	s	s	PRON
ejpam-5528	279	3	be	be	AUX
ejpam-5528	279	4	a	a	DET
ejpam-5528	279	5	self	self	NOUN
ejpam-5528	279	6	-	-	PUNCT
ejpam-5528	279	7	adjoint	adjoint	NOUN
ejpam-5528	279	8	standard	standard	ADJ
ejpam-5528	279	9	operator	operator	NOUN
ejpam-5528	279	10	algebra	algebra	NOUN
ejpam-5528	279	11	on	on	ADP
ejpam-5528	279	12	a	a	DET
ejpam-5528	279	13	hilbert	hilbert	NOUN
ejpam-5528	279	14	space	space	NOUN
ejpam-5528	279	15	h.	h.	PROPN
ejpam-5528	279	16	suppose	suppose	VERB
ejpam-5528	279	17	that	that	SCONJ
ejpam-5528	279	18	χ	χ	X
ejpam-5528	279	19	:	:	PUNCT
ejpam-5528	279	20	s	s	X
ejpam-5528	279	21	→	→	SYM
ejpam-5528	279	22	s	s	X
ejpam-5528	279	23	is	be	AUX
ejpam-5528	279	24	a	a	DET
ejpam-5528	279	25	surjective	surjective	ADJ
ejpam-5528	279	26	map	map	NOUN
ejpam-5528	279	27	.	.	PUNCT
ejpam-5528	280	1	then	then	ADV
ejpam-5528	280	2	χ	χ	PRON
ejpam-5528	280	3	is	be	AUX
ejpam-5528	280	4	strong	strong	ADJ
ejpam-5528	280	5	bi	bi	ADJ
ejpam-5528	280	6	-	-	ADJ
ejpam-5528	280	7	skew	skew	ADJ
ejpam-5528	280	8	commutativity	commutativity	NOUN
ejpam-5528	280	9	preserving	preserve	VERB
ejpam-5528	280	10	map	map	NOUN
ejpam-5528	281	1	if	if	SCONJ
ejpam-5528	281	2	and	and	CCONJ
ejpam-5528	281	3	only	only	ADV
ejpam-5528	281	4	if	if	SCONJ
ejpam-5528	281	5	there	there	PRON
ejpam-5528	281	6	exists	exist	VERB
ejpam-5528	281	7	λ	λ	X
ejpam-5528	281	8	∈	∈	PROPN
ejpam-5528	281	9	qms(s	qms(s	PROPN
ejpam-5528	281	10	)	)	PUNCT
ejpam-5528	281	11	with	with	ADP
ejpam-5528	281	12	λλ∗	λλ∗	X
ejpam-5528	282	1	=	=	NOUN
ejpam-5528	282	2	1	1	NUM
ejpam-5528	282	3	such	such	ADJ
ejpam-5528	282	4	that	that	SCONJ
ejpam-5528	282	5	χ(a	χ(a	NOUN
ejpam-5528	282	6	)	)	PUNCT
ejpam-5528	282	7	=	=	SYM
ejpam-5528	282	8	λa	λa	X
ejpam-5528	282	9	for	for	ADP
ejpam-5528	282	10	all	all	DET
ejpam-5528	282	11	a	a	DET
ejpam-5528	282	12	∈	∈	PROPN
ejpam-5528	282	13	s.	s.	PROPN
ejpam-5528	282	14	moin	moin	PROPN
ejpam-5528	282	15	a.	a.	PROPN
ejpam-5528	282	16	ansari	ansari	PROPN
ejpam-5528	282	17	et	et	PROPN
ejpam-5528	282	18	al	al	PROPN
ejpam-5528	282	19	.	.	PUNCT
ejpam-5528	282	20	/	/	SYM
ejpam-5528	282	21	eur	eur	PROPN
ejpam-5528	282	22	.	.	PUNCT
ejpam-5528	283	1	j.	j.	PROPN
ejpam-5528	283	2	pure	pure	PROPN
ejpam-5528	283	3	appl	appl	PROPN
ejpam-5528	283	4	.	.	PROPN
ejpam-5528	283	5	math	math	PROPN
ejpam-5528	283	6	,	,	PUNCT
ejpam-5528	283	7	18	18	NUM
ejpam-5528	283	8	(	(	PUNCT
ejpam-5528	283	9	2	2	NUM
ejpam-5528	283	10	)	)	PUNCT
ejpam-5528	283	11	(	(	PUNCT
ejpam-5528	283	12	2025	2025	NUM
ejpam-5528	283	13	)	)	PUNCT
ejpam-5528	283	14	,	,	PUNCT
ejpam-5528	283	15	5528	5528	NUM
ejpam-5528	283	16	12	12	NUM
ejpam-5528	283	17	of	of	ADP
ejpam-5528	283	18	14	14	NUM
ejpam-5528	283	19	corollary	corollary	ADJ
ejpam-5528	283	20	4.2	4.2	NUM
ejpam-5528	283	21	.	.	PUNCT
ejpam-5528	284	1	let	let	VERB
ejpam-5528	284	2	s	s	PRON
ejpam-5528	284	3	be	be	AUX
ejpam-5528	284	4	a	a	DET
ejpam-5528	284	5	self	self	NOUN
ejpam-5528	284	6	-	-	PUNCT
ejpam-5528	284	7	adjoint	adjoint	NOUN
ejpam-5528	284	8	standard	standard	ADJ
ejpam-5528	284	9	operator	operator	NOUN
ejpam-5528	284	10	algebra	algebra	NOUN
ejpam-5528	284	11	on	on	ADP
ejpam-5528	284	12	a	a	DET
ejpam-5528	284	13	hilbert	hilbert	NOUN
ejpam-5528	284	14	space	space	NOUN
ejpam-5528	284	15	h.	h.	PROPN
ejpam-5528	284	16	then	then	ADV
ejpam-5528	284	17	χ	χ	X
ejpam-5528	284	18	:	:	PUNCT
ejpam-5528	284	19	s	s	X
ejpam-5528	284	20	→	→	SYM
ejpam-5528	284	21	s	s	X
ejpam-5528	284	22	is	be	AUX
ejpam-5528	284	23	a	a	DET
ejpam-5528	284	24	bi	bi	ADJ
ejpam-5528	284	25	-	-	ADJ
ejpam-5528	284	26	skew	skew	ADJ
ejpam-5528	284	27	commuting	commuting	NOUN
ejpam-5528	284	28	map	map	NOUN
ejpam-5528	284	29	if	if	SCONJ
ejpam-5528	284	30	and	and	CCONJ
ejpam-5528	284	31	only	only	ADV
ejpam-5528	284	32	if	if	SCONJ
ejpam-5528	284	33	there	there	PRON
ejpam-5528	284	34	exists	exist	VERB
ejpam-5528	284	35	λ	λ	X
ejpam-5528	284	36	∈	∈	NOUN
ejpam-5528	284	37	r	r	NOUN
ejpam-5528	284	38	such	such	ADJ
ejpam-5528	284	39	that	that	SCONJ
ejpam-5528	284	40	χ(a	χ(a	NOUN
ejpam-5528	284	41	)	)	PUNCT
ejpam-5528	284	42	=	=	SYM
ejpam-5528	284	43	λa	λa	X
ejpam-5528	284	44	for	for	ADP
ejpam-5528	284	45	all	all	DET
ejpam-5528	284	46	a	a	DET
ejpam-5528	284	47	∈	∈	PROPN
ejpam-5528	284	48	s.	s.	PROPN
ejpam-5528	284	49	corollary	corollary	NOUN
ejpam-5528	284	50	4.3	4.3	NUM
ejpam-5528	284	51	.	.	PUNCT
ejpam-5528	285	1	let	let	VERB
ejpam-5528	285	2	s	s	PRON
ejpam-5528	285	3	be	be	AUX
ejpam-5528	285	4	a	a	DET
ejpam-5528	285	5	self	self	NOUN
ejpam-5528	285	6	-	-	PUNCT
ejpam-5528	285	7	adjoint	adjoint	NOUN
ejpam-5528	285	8	standard	standard	ADJ
ejpam-5528	285	9	operator	operator	NOUN
ejpam-5528	285	10	algebra	algebra	NOUN
ejpam-5528	285	11	on	on	ADP
ejpam-5528	285	12	a	a	DET
ejpam-5528	285	13	hilbert	hilbert	NOUN
ejpam-5528	285	14	space	space	NOUN
ejpam-5528	285	15	h.	h.	PROPN
ejpam-5528	285	16	suppose	suppose	VERB
ejpam-5528	285	17	that	that	SCONJ
ejpam-5528	285	18	φ	φ	PROPN
ejpam-5528	285	19	:	:	PUNCT
ejpam-5528	285	20	s	s	X
ejpam-5528	285	21	→	→	SYM
ejpam-5528	285	22	s	s	X
ejpam-5528	285	23	is	be	AUX
ejpam-5528	285	24	a	a	DET
ejpam-5528	285	25	generalized	generalized	ADJ
ejpam-5528	285	26	bi	bi	ADJ
ejpam-5528	285	27	-	-	ADJ
ejpam-5528	285	28	skew	skew	ADJ
ejpam-5528	285	29	jordan	jordan	PROPN
ejpam-5528	285	30	derivation	derivation	PROPN
ejpam-5528	285	31	with	with	ADP
ejpam-5528	285	32	ω	ω	NUM
ejpam-5528	285	33	:	:	PUNCT
ejpam-5528	285	34	ℜ	ℜ	PROPN
ejpam-5528	285	35	→	→	SYM
ejpam-5528	285	36	s	s	X
ejpam-5528	285	37	as	as	ADP
ejpam-5528	285	38	associated	associated	ADJ
ejpam-5528	285	39	bi	bi	ADJ
ejpam-5528	285	40	-	-	ADJ
ejpam-5528	285	41	skew	skew	ADJ
ejpam-5528	285	42	jordan	jordan	PROPN
ejpam-5528	285	43	derivation	derivation	PROPN
ejpam-5528	285	44	.	.	PUNCT
ejpam-5528	286	1	then	then	ADV
ejpam-5528	286	2	ω	ω	X
ejpam-5528	286	3	:	:	PUNCT
ejpam-5528	286	4	s	s	X
ejpam-5528	286	5	→	→	SYM
ejpam-5528	286	6	s	s	X
ejpam-5528	286	7	is	be	AUX
ejpam-5528	286	8	an	an	DET
ejpam-5528	286	9	additive	additive	ADJ
ejpam-5528	286	10	∗-derivation	∗-derivation	NOUN
ejpam-5528	286	11	and	and	CCONJ
ejpam-5528	286	12	there	there	PRON
ejpam-5528	286	13	exists	exist	VERB
ejpam-5528	286	14	λ	λ	X
ejpam-5528	286	15	∈	∈	NOUN
ejpam-5528	286	16	r	r	NOUN
ejpam-5528	286	17	such	such	ADJ
ejpam-5528	286	18	that	that	SCONJ
ejpam-5528	286	19	φ(u	φ(u	NOUN
ejpam-5528	286	20	)	)	PUNCT
ejpam-5528	286	21	=	=	SYM
ejpam-5528	286	22	λu+ω(u	λu+ω(u	PROPN
ejpam-5528	286	23	)	)	PUNCT
ejpam-5528	286	24	.	.	PUNCT
ejpam-5528	287	1	factor	factor	NOUN
ejpam-5528	287	2	von	von	PROPN
ejpam-5528	287	3	neumann	neumann	PROPN
ejpam-5528	287	4	algebras	algebras	PROPN
ejpam-5528	287	5	a	a	DET
ejpam-5528	287	6	von	von	PROPN
ejpam-5528	287	7	neumann	neumann	PROPN
ejpam-5528	287	8	algebra	algebra	PROPN
ejpam-5528	287	9	n	n	PART
ejpam-5528	287	10	is	be	AUX
ejpam-5528	287	11	a	a	DET
ejpam-5528	287	12	subalgebra	subalgebra	NOUN
ejpam-5528	287	13	of	of	ADP
ejpam-5528	287	14	b(h	b(h	PROPN
ejpam-5528	287	15	)	)	PUNCT
ejpam-5528	287	16	which	which	PRON
ejpam-5528	287	17	satisfies	satisfy	VERB
ejpam-5528	287	18	the	the	DET
ejpam-5528	287	19	double	double	ADJ
ejpam-5528	287	20	commutant	commutant	ADJ
ejpam-5528	287	21	property	property	NOUN
ejpam-5528	287	22	,	,	PUNCT
ejpam-5528	287	23	that	that	ADV
ejpam-5528	287	24	is	is	ADV
ejpam-5528	287	25	,	,	PUNCT
ejpam-5528	287	26	n	n	PRON
ejpam-5528	287	27	′′	′′	PROPN
ejpam-5528	287	28	=	=	PUNCT
ejpam-5528	287	29	n	n	PROPN
ejpam-5528	287	30	where	where	SCONJ
ejpam-5528	287	31	n	n	ADP
ejpam-5528	287	32	′	′	NUM
ejpam-5528	287	33	=	=	PUNCT
ejpam-5528	287	34	{	{	PUNCT
ejpam-5528	287	35	t	t	PROPN
ejpam-5528	287	36	∈	∈	PROPN
ejpam-5528	287	37	b(h	b(h	PROPN
ejpam-5528	287	38	)	)	PUNCT
ejpam-5528	288	1	|	|	ADV
ejpam-5528	288	2	tf	tf	INTJ
ejpam-5528	288	3	=	=	PUNCT
ejpam-5528	288	4	ft	ft	PROPN
ejpam-5528	288	5	for	for	ADP
ejpam-5528	288	6	all	all	DET
ejpam-5528	288	7	f	f	PROPN
ejpam-5528	288	8	∈	∈	PROPN
ejpam-5528	288	9	n	n	CCONJ
ejpam-5528	288	10	}	}	PUNCT
ejpam-5528	288	11	and	and	CCONJ
ejpam-5528	288	12	m′′	m′′	PROPN
ejpam-5528	288	13	=	=	PUNCT
ejpam-5528	289	1	(	(	PUNCT
ejpam-5528	289	2	m′)′.	m′)′.	PROPN
ejpam-5528	289	3	it	it	PRON
ejpam-5528	289	4	is	be	AUX
ejpam-5528	289	5	clear	clear	ADJ
ejpam-5528	289	6	that	that	SCONJ
ejpam-5528	289	7	a	a	DET
ejpam-5528	289	8	von	von	PROPN
ejpam-5528	289	9	neumann	neumann	PROPN
ejpam-5528	289	10	algebra	algebra	PROPN
ejpam-5528	289	11	is	be	AUX
ejpam-5528	289	12	unital	unital	ADJ
ejpam-5528	289	13	.	.	PUNCT
ejpam-5528	290	1	a	a	DET
ejpam-5528	290	2	von	von	PROPN
ejpam-5528	290	3	neumann	neumann	PROPN
ejpam-5528	290	4	algebra	algebra	PROPN
ejpam-5528	290	5	n	n	PART
ejpam-5528	290	6	is	be	AUX
ejpam-5528	290	7	an	an	DET
ejpam-5528	290	8	algebra	algebra	NOUN
ejpam-5528	290	9	of	of	ADP
ejpam-5528	290	10	characteristic	characteristic	ADJ
ejpam-5528	290	11	zero	zero	NUM
ejpam-5528	290	12	and	and	CCONJ
ejpam-5528	290	13	a	a	DET
ejpam-5528	290	14	map	map	NOUN
ejpam-5528	290	15	t	t	PROPN
ejpam-5528	290	16	7→	7→	NUM
ejpam-5528	290	17	t	t	NOUN
ejpam-5528	290	18	∗	∗	NOUN
ejpam-5528	290	19	,	,	PUNCT
ejpam-5528	290	20	where	where	SCONJ
ejpam-5528	290	21	t	t	PROPN
ejpam-5528	290	22	∗	∗	NOUN
ejpam-5528	290	23	denotes	denote	VERB
ejpam-5528	290	24	the	the	DET
ejpam-5528	290	25	hilbert	hilbert	PROPN
ejpam-5528	290	26	adjoint	adjoint	PROPN
ejpam-5528	290	27	operator	operator	NOUN
ejpam-5528	290	28	of	of	ADP
ejpam-5528	290	29	t	t	PROPN
ejpam-5528	290	30	,	,	PUNCT
ejpam-5528	290	31	is	be	AUX
ejpam-5528	290	32	an	an	DET
ejpam-5528	290	33	involution	involution	NOUN
ejpam-5528	290	34	of	of	ADP
ejpam-5528	290	35	the	the	DET
ejpam-5528	290	36	second	second	ADJ
ejpam-5528	290	37	kind	kind	NOUN
ejpam-5528	290	38	on	on	ADP
ejpam-5528	290	39	z(n	z(n	NOUN
ejpam-5528	290	40	)	)	PUNCT
ejpam-5528	290	41	.	.	PUNCT
ejpam-5528	291	1	a	a	DET
ejpam-5528	291	2	von	von	PROPN
ejpam-5528	291	3	neumann	neumann	PROPN
ejpam-5528	291	4	algebra	algebra	PROPN
ejpam-5528	291	5	n	n	PRON
ejpam-5528	291	6	is	be	AUX
ejpam-5528	291	7	called	call	VERB
ejpam-5528	291	8	a	a	DET
ejpam-5528	291	9	factor	factor	NOUN
ejpam-5528	291	10	von	von	PROPN
ejpam-5528	291	11	neumann	neumann	PROPN
ejpam-5528	291	12	algebra	algebra	PROPN
ejpam-5528	291	13	if	if	SCONJ
ejpam-5528	291	14	its	its	PRON
ejpam-5528	291	15	center	center	NOUN
ejpam-5528	291	16	is	be	AUX
ejpam-5528	291	17	trivial	trivial	ADJ
ejpam-5528	291	18	,	,	PUNCT
ejpam-5528	291	19	that	that	ADV
ejpam-5528	291	20	is	be	AUX
ejpam-5528	291	21	,	,	PUNCT
ejpam-5528	291	22	z(n	z(n	NOUN
ejpam-5528	291	23	)	)	PUNCT
ejpam-5528	292	1	=	=	SYM
ejpam-5528	292	2	ci	ci	PROPN
ejpam-5528	292	3	.	.	PUNCT
ejpam-5528	293	1	every	every	DET
ejpam-5528	293	2	factor	factor	NOUN
ejpam-5528	293	3	von	von	PROPN
ejpam-5528	293	4	neumann	neumann	PROPN
ejpam-5528	293	5	algebra	algebra	PROPN
ejpam-5528	293	6	is	be	AUX
ejpam-5528	293	7	a	a	DET
ejpam-5528	293	8	prime	prime	ADJ
ejpam-5528	293	9	algebra	algebra	NOUN
ejpam-5528	293	10	.	.	PUNCT
ejpam-5528	294	1	corollary	corollary	NOUN
ejpam-5528	294	2	4.4	4.4	NUM
ejpam-5528	294	3	.	.	PUNCT
ejpam-5528	295	1	let	let	VERB
ejpam-5528	295	2	n	n	PRON
ejpam-5528	295	3	be	be	AUX
ejpam-5528	295	4	a	a	DET
ejpam-5528	295	5	factor	factor	NOUN
ejpam-5528	295	6	von	von	PROPN
ejpam-5528	295	7	neumann	neumann	PROPN
ejpam-5528	295	8	algebra	algebra	PROPN
ejpam-5528	295	9	.	.	PUNCT
ejpam-5528	296	1	suppose	suppose	VERB
ejpam-5528	296	2	that	that	SCONJ
ejpam-5528	296	3	χ	χ	X
ejpam-5528	296	4	:	:	PUNCT
ejpam-5528	296	5	n	n	X
ejpam-5528	296	6	→	→	SYM
ejpam-5528	296	7	n	n	X
ejpam-5528	296	8	is	be	AUX
ejpam-5528	296	9	a	a	DET
ejpam-5528	296	10	surjective	surjective	ADJ
ejpam-5528	296	11	map	map	NOUN
ejpam-5528	296	12	.	.	PUNCT
ejpam-5528	297	1	then	then	ADV
ejpam-5528	297	2	χ	χ	PRON
ejpam-5528	297	3	is	be	AUX
ejpam-5528	297	4	strong	strong	ADJ
ejpam-5528	297	5	bi	bi	ADJ
ejpam-5528	297	6	-	-	ADJ
ejpam-5528	297	7	skew	skew	ADJ
ejpam-5528	297	8	commutativity	commutativity	NOUN
ejpam-5528	297	9	preserving	preserve	VERB
ejpam-5528	297	10	map	map	NOUN
ejpam-5528	298	1	if	if	SCONJ
ejpam-5528	298	2	and	and	CCONJ
ejpam-5528	298	3	only	only	ADV
ejpam-5528	298	4	if	if	SCONJ
ejpam-5528	298	5	there	there	PRON
ejpam-5528	298	6	exists	exist	VERB
ejpam-5528	298	7	λ	λ	PROPN
ejpam-5528	298	8	∈	∈	PROPN
ejpam-5528	298	9	qms(n	qms(n	PROPN
ejpam-5528	298	10	)	)	PUNCT
ejpam-5528	298	11	with	with	ADP
ejpam-5528	298	12	λλ∗	λλ∗	X
ejpam-5528	299	1	=	=	NOUN
ejpam-5528	299	2	1	1	NUM
ejpam-5528	299	3	such	such	ADJ
ejpam-5528	299	4	that	that	SCONJ
ejpam-5528	299	5	χ(a	χ(a	NOUN
ejpam-5528	299	6	)	)	PUNCT
ejpam-5528	299	7	=	=	SYM
ejpam-5528	299	8	λa	λa	X
ejpam-5528	299	9	for	for	ADP
ejpam-5528	299	10	all	all	DET
ejpam-5528	299	11	a	a	DET
ejpam-5528	299	12	∈	∈	PROPN
ejpam-5528	299	13	n	n	X
ejpam-5528	299	14	.	.	PUNCT
ejpam-5528	300	1	corollary	corollary	ADJ
ejpam-5528	300	2	4.5	4.5	NUM
ejpam-5528	300	3	.	.	PUNCT
ejpam-5528	301	1	let	let	VERB
ejpam-5528	301	2	n	n	PRON
ejpam-5528	301	3	be	be	AUX
ejpam-5528	301	4	a	a	DET
ejpam-5528	301	5	factor	factor	NOUN
ejpam-5528	301	6	von	von	PROPN
ejpam-5528	301	7	neumann	neumann	PROPN
ejpam-5528	301	8	algebra	algebra	PROPN
ejpam-5528	301	9	.	.	PUNCT
ejpam-5528	302	1	then	then	ADV
ejpam-5528	302	2	χ	χ	X
ejpam-5528	302	3	:	:	PUNCT
ejpam-5528	302	4	n	n	X
ejpam-5528	302	5	→	→	SYM
ejpam-5528	302	6	n	n	X
ejpam-5528	302	7	is	be	AUX
ejpam-5528	302	8	a	a	DET
ejpam-5528	302	9	bi	bi	ADJ
ejpam-5528	302	10	-	-	ADJ
ejpam-5528	302	11	skew	skew	ADJ
ejpam-5528	302	12	commuting	commuting	NOUN
ejpam-5528	302	13	map	map	NOUN
ejpam-5528	303	1	if	if	SCONJ
ejpam-5528	303	2	and	and	CCONJ
ejpam-5528	303	3	only	only	ADV
ejpam-5528	303	4	if	if	SCONJ
ejpam-5528	303	5	there	there	PRON
ejpam-5528	303	6	exists	exist	VERB
ejpam-5528	303	7	λ	λ	X
ejpam-5528	303	8	∈	∈	NOUN
ejpam-5528	303	9	r	r	NOUN
ejpam-5528	303	10	such	such	ADJ
ejpam-5528	303	11	that	that	SCONJ
ejpam-5528	303	12	χ(u	χ(u	NOUN
ejpam-5528	303	13	)	)	PUNCT
ejpam-5528	304	1	=	=	SYM
ejpam-5528	304	2	λu	λu	PROPN
ejpam-5528	304	3	for	for	ADP
ejpam-5528	304	4	all	all	DET
ejpam-5528	304	5	u	u	NOUN
ejpam-5528	304	6	∈	∈	PROPN
ejpam-5528	304	7	n	n	X
ejpam-5528	304	8	.	.	PUNCT
ejpam-5528	305	1	corollary	corollary	ADJ
ejpam-5528	305	2	4.6	4.6	NUM
ejpam-5528	305	3	.	.	PUNCT
ejpam-5528	306	1	let	let	VERB
ejpam-5528	306	2	n	n	PRON
ejpam-5528	306	3	be	be	AUX
ejpam-5528	306	4	a	a	DET
ejpam-5528	306	5	factor	factor	NOUN
ejpam-5528	306	6	von	von	PROPN
ejpam-5528	306	7	neumann	neumann	PROPN
ejpam-5528	306	8	algebra	algebra	PROPN
ejpam-5528	306	9	.	.	PUNCT
ejpam-5528	307	1	suppose	suppose	VERB
ejpam-5528	307	2	that	that	SCONJ
ejpam-5528	307	3	φ	φ	PROPN
ejpam-5528	307	4	:	:	PUNCT
ejpam-5528	307	5	n	n	X
ejpam-5528	307	6	→	→	SYM
ejpam-5528	307	7	n	n	X
ejpam-5528	307	8	is	be	AUX
ejpam-5528	307	9	a	a	DET
ejpam-5528	307	10	generalized	generalized	ADJ
ejpam-5528	307	11	bi	bi	ADJ
ejpam-5528	307	12	-	-	ADJ
ejpam-5528	307	13	skew	skew	ADJ
ejpam-5528	307	14	jordan	jordan	PROPN
ejpam-5528	307	15	derivation	derivation	PROPN
ejpam-5528	307	16	with	with	ADP
ejpam-5528	307	17	ω	ω	PROPN
ejpam-5528	307	18	:	:	PUNCT
ejpam-5528	307	19	n	n	PROPN
ejpam-5528	307	20	→	→	SYM
ejpam-5528	307	21	n	n	CCONJ
ejpam-5528	307	22	as	as	ADP
ejpam-5528	307	23	associated	associated	ADJ
ejpam-5528	307	24	bi	bi	ADJ
ejpam-5528	307	25	-	-	ADJ
ejpam-5528	307	26	skew	skew	ADJ
ejpam-5528	307	27	jordan	jordan	PROPN
ejpam-5528	307	28	derivation	derivation	PROPN
ejpam-5528	307	29	.	.	PUNCT
ejpam-5528	308	1	then	then	ADV
ejpam-5528	308	2	ω	ω	NUM
ejpam-5528	308	3	:	:	PUNCT
ejpam-5528	308	4	n	n	X
ejpam-5528	308	5	→	→	SYM
ejpam-5528	308	6	n	n	X
ejpam-5528	308	7	is	be	AUX
ejpam-5528	308	8	an	an	DET
ejpam-5528	308	9	additive	additive	ADJ
ejpam-5528	308	10	∗-derivation	∗-derivation	NOUN
ejpam-5528	308	11	and	and	CCONJ
ejpam-5528	308	12	there	there	PRON
ejpam-5528	308	13	exists	exist	VERB
ejpam-5528	308	14	λ	λ	X
ejpam-5528	308	15	∈	∈	NOUN
ejpam-5528	308	16	r	r	NOUN
ejpam-5528	308	17	such	such	ADJ
ejpam-5528	308	18	that	that	SCONJ
ejpam-5528	308	19	φ(u	φ(u	NOUN
ejpam-5528	308	20	)	)	PUNCT
ejpam-5528	308	21	=	=	SYM
ejpam-5528	308	22	λu+ω(u	λu+ω(u	PROPN
ejpam-5528	308	23	)	)	PUNCT
ejpam-5528	308	24	for	for	ADP
ejpam-5528	308	25	all	all	DET
ejpam-5528	308	26	u	u	PROPN
ejpam-5528	308	27	∈	∈	PROPN
ejpam-5528	308	28	n	n	X
ejpam-5528	308	29	.	.	PUNCT
ejpam-5528	309	1	conflict	conflict	NOUN
ejpam-5528	309	2	of	of	ADP
ejpam-5528	309	3	interest	interest	NOUN
ejpam-5528	309	4	:	:	PUNCT
ejpam-5528	309	5	the	the	DET
ejpam-5528	309	6	authors	author	NOUN
ejpam-5528	309	7	declare	declare	VERB
ejpam-5528	309	8	that	that	SCONJ
ejpam-5528	309	9	they	they	PRON
ejpam-5528	309	10	have	have	VERB
ejpam-5528	309	11	no	no	DET
ejpam-5528	309	12	conflict	conflict	NOUN
ejpam-5528	309	13	of	of	ADP
ejpam-5528	309	14	interest	interest	NOUN
ejpam-5528	309	15	references	reference	NOUN
ejpam-5528	310	1	[	[	X
ejpam-5528	310	2	1	1	NUM
ejpam-5528	310	3	]	]	PUNCT
ejpam-5528	310	4	konstant	konstant	NOUN
ejpam-5528	310	5	i	i	PRON
ejpam-5528	310	6	beidar	beidar	NOUN
ejpam-5528	310	7	,	,	PUNCT
ejpam-5528	310	8	wallace	wallace	PROPN
ejpam-5528	310	9	s	s	PROPN
ejpam-5528	310	10	martindale	martindale	PROPN
ejpam-5528	310	11	,	,	PUNCT
ejpam-5528	310	12	and	and	CCONJ
ejpam-5528	310	13	alexander	alexander	PROPN
ejpam-5528	310	14	v	v	PROPN
ejpam-5528	310	15	mikhalev	mikhalev	PROPN
ejpam-5528	310	16	.	.	PUNCT
ejpam-5528	311	1	rings	ring	NOUN
ejpam-5528	311	2	with	with	ADP
ejpam-5528	311	3	generalized	generalized	ADJ
ejpam-5528	311	4	identities	identity	NOUN
ejpam-5528	311	5	.	.	PUNCT
ejpam-5528	312	1	crc	crc	PROPN
ejpam-5528	312	2	press	press	PROPN
ejpam-5528	312	3	,	,	PUNCT
ejpam-5528	312	4	1995	1995	NUM
ejpam-5528	312	5	.	.	PUNCT
ejpam-5528	313	1	[	[	X
ejpam-5528	313	2	2	2	NUM
ejpam-5528	313	3	]	]	X
ejpam-5528	313	4	scott	scott	PROPN
ejpam-5528	313	5	lanning	lanning	PROPN
ejpam-5528	313	6	.	.	PUNCT
ejpam-5528	314	1	the	the	DET
ejpam-5528	314	2	maximal	maximal	ADJ
ejpam-5528	314	3	symmetric	symmetric	ADJ
ejpam-5528	314	4	ring	ring	NOUN
ejpam-5528	314	5	of	of	ADP
ejpam-5528	314	6	quotients	quotient	NOUN
ejpam-5528	314	7	.	.	PUNCT
ejpam-5528	315	1	journal	journal	NOUN
ejpam-5528	315	2	of	of	ADP
ejpam-5528	315	3	algebra	algebra	PROPN
ejpam-5528	315	4	,	,	PUNCT
ejpam-5528	315	5	179(1):47–91	179(1):47–91	NUM
ejpam-5528	315	6	,	,	PUNCT
ejpam-5528	315	7	1996	1996	NUM
ejpam-5528	315	8	.	.	PUNCT
ejpam-5528	316	1	[	[	X
ejpam-5528	316	2	3	3	X
ejpam-5528	316	3	]	]	X
ejpam-5528	316	4	matej	matej	PROPN
ejpam-5528	316	5	brešar	brešar	PROPN
ejpam-5528	316	6	.	.	PUNCT
ejpam-5528	317	1	functional	functional	ADJ
ejpam-5528	317	2	identities	identity	NOUN
ejpam-5528	317	3	and	and	CCONJ
ejpam-5528	317	4	rings	ring	NOUN
ejpam-5528	317	5	of	of	ADP
ejpam-5528	317	6	quotients	quotient	NOUN
ejpam-5528	317	7	.	.	PUNCT
ejpam-5528	318	1	algebras	algebras	PROPN
ejpam-5528	318	2	and	and	CCONJ
ejpam-5528	318	3	representation	representation	NOUN
ejpam-5528	318	4	theory	theory	NOUN
ejpam-5528	318	5	,	,	PUNCT
ejpam-5528	318	6	19:1437–1450	19:1437–1450	NUM
ejpam-5528	318	7	,	,	PUNCT
ejpam-5528	318	8	2016	2016	NUM
ejpam-5528	318	9	.	.	PUNCT
ejpam-5528	319	1	[	[	X
ejpam-5528	319	2	4	4	X
ejpam-5528	319	3	]	]	PUNCT
ejpam-5528	319	4	cui	cui	NOUN
ejpam-5528	319	5	jianlian	jianlian	NOUN
ejpam-5528	319	6	and	and	CCONJ
ejpam-5528	319	7	choonkil	choonkil	ADJ
ejpam-5528	319	8	park	park	NOUN
ejpam-5528	319	9	.	.	PUNCT
ejpam-5528	320	1	maps	map	NOUN
ejpam-5528	320	2	preserving	preserve	VERB
ejpam-5528	320	3	strong	strong	ADJ
ejpam-5528	320	4	skew	skew	ADJ
ejpam-5528	320	5	lie	lie	NOUN
ejpam-5528	320	6	product	product	NOUN
ejpam-5528	320	7	on	on	ADP
ejpam-5528	320	8	factor	factor	NOUN
ejpam-5528	320	9	von	von	PROPN
ejpam-5528	320	10	neumann	neumann	PROPN
ejpam-5528	320	11	algebras	algebras	PROPN
ejpam-5528	320	12	.	.	PUNCT
ejpam-5528	321	1	acta	acta	PROPN
ejpam-5528	321	2	mathematica	mathematica	PROPN
ejpam-5528	321	3	scientia	scientia	PROPN
ejpam-5528	321	4	,	,	PUNCT
ejpam-5528	321	5	32(2):531–538	32(2):531–538	NUM
ejpam-5528	321	6	,	,	PUNCT
ejpam-5528	321	7	2012	2012	NUM
ejpam-5528	321	8	.	.	PUNCT
ejpam-5528	322	1	[	[	X
ejpam-5528	322	2	5	5	X
ejpam-5528	322	3	]	]	PUNCT
ejpam-5528	322	4	jianlian	jianlian	ADJ
ejpam-5528	322	5	cui	cui	NOUN
ejpam-5528	322	6	and	and	CCONJ
ejpam-5528	322	7	chi	chi	PROPN
ejpam-5528	322	8	-	-	PUNCT
ejpam-5528	322	9	kwong	kwong	PROPN
ejpam-5528	322	10	li	li	PROPN
ejpam-5528	322	11	.	.	PROPN
ejpam-5528	322	12	maps	map	NOUN
ejpam-5528	322	13	preserving	preserve	VERB
ejpam-5528	322	14	product	product	NOUN
ejpam-5528	322	15	xy	xy	PROPN
ejpam-5528	322	16	−	−	PROPN
ejpam-5528	322	17	yx∗	yx∗	PROPN
ejpam-5528	322	18	on	on	ADP
ejpam-5528	322	19	factor	factor	PROPN
ejpam-5528	322	20	von	von	PROPN
ejpam-5528	322	21	neumann	neumann	PROPN
ejpam-5528	322	22	algebras	algebras	PROPN
ejpam-5528	322	23	.	.	PUNCT
ejpam-5528	323	1	linear	linear	PROPN
ejpam-5528	323	2	algebra	algebra	PROPN
ejpam-5528	323	3	and	and	CCONJ
ejpam-5528	323	4	its	its	PRON
ejpam-5528	323	5	applications	application	NOUN
ejpam-5528	323	6	,	,	PUNCT
ejpam-5528	323	7	431(5	431(5	NUM
ejpam-5528	323	8	-	-	SYM
ejpam-5528	323	9	7):833–842	7):833–842	NUM
ejpam-5528	323	10	,	,	PUNCT
ejpam-5528	323	11	2009	2009	NUM
ejpam-5528	323	12	.	.	PUNCT
ejpam-5528	324	1	moin	moin	PROPN
ejpam-5528	324	2	a.	a.	PROPN
ejpam-5528	324	3	ansari	ansari	PROPN
ejpam-5528	324	4	et	et	PROPN
ejpam-5528	324	5	al	al	PROPN
ejpam-5528	324	6	.	.	PUNCT
ejpam-5528	324	7	/	/	SYM
ejpam-5528	324	8	eur	eur	PROPN
ejpam-5528	324	9	.	.	PUNCT
ejpam-5528	325	1	j.	j.	PROPN
ejpam-5528	325	2	pure	pure	PROPN
ejpam-5528	325	3	appl	appl	PROPN
ejpam-5528	325	4	.	.	PROPN
ejpam-5528	325	5	math	math	PROPN
ejpam-5528	325	6	,	,	PUNCT
ejpam-5528	325	7	18	18	NUM
ejpam-5528	325	8	(	(	PUNCT
ejpam-5528	325	9	2	2	NUM
ejpam-5528	325	10	)	)	PUNCT
ejpam-5528	325	11	(	(	PUNCT
ejpam-5528	325	12	2025	2025	NUM
ejpam-5528	325	13	)	)	PUNCT
ejpam-5528	325	14	,	,	PUNCT
ejpam-5528	325	15	5528	5528	NUM
ejpam-5528	325	16	13	13	NUM
ejpam-5528	325	17	of	of	ADP
ejpam-5528	325	18	14	14	NUM
ejpam-5528	325	19	[	[	SYM
ejpam-5528	325	20	6	6	NUM
ejpam-5528	325	21	]	]	X
ejpam-5528	325	22	jinchuan	jinchuan	PROPN
ejpam-5528	325	23	hou	hou	PROPN
ejpam-5528	325	24	and	and	CCONJ
ejpam-5528	325	25	wei	wei	PROPN
ejpam-5528	325	26	wang	wang	PROPN
ejpam-5528	325	27	.	.	PUNCT
ejpam-5528	326	1	strong	strong	ADJ
ejpam-5528	326	2	2	2	NUM
ejpam-5528	326	3	-	-	PUNCT
ejpam-5528	326	4	skew	skew	NOUN
ejpam-5528	326	5	commutativity	commutativity	NOUN
ejpam-5528	326	6	preserving	preserve	VERB
ejpam-5528	326	7	maps	map	NOUN
ejpam-5528	326	8	on	on	ADP
ejpam-5528	326	9	prime	prime	ADJ
ejpam-5528	326	10	rings	ring	NOUN
ejpam-5528	326	11	with	with	ADP
ejpam-5528	326	12	involution	involution	NOUN
ejpam-5528	326	13	.	.	PUNCT
ejpam-5528	327	1	bulletin	bulletin	NOUN
ejpam-5528	327	2	of	of	ADP
ejpam-5528	327	3	the	the	DET
ejpam-5528	327	4	malaysian	malaysian	PROPN
ejpam-5528	327	5	mathematical	mathematical	PROPN
ejpam-5528	327	6	sciences	sciences	PROPN
ejpam-5528	327	7	society	society	NOUN
ejpam-5528	327	8	,	,	PUNCT
ejpam-5528	327	9	42:33–49	42:33–49	NUM
ejpam-5528	327	10	,	,	PUNCT
ejpam-5528	327	11	2019	2019	NUM
ejpam-5528	327	12	.	.	PUNCT
ejpam-5528	328	1	[	[	X
ejpam-5528	328	2	7	7	X
ejpam-5528	328	3	]	]	X
ejpam-5528	328	4	liang	liang	PROPN
ejpam-5528	328	5	kong	kong	PROPN
ejpam-5528	328	6	and	and	CCONJ
ejpam-5528	328	7	jianhua	jianhua	PROPN
ejpam-5528	328	8	zhang	zhang	PROPN
ejpam-5528	328	9	.	.	PUNCT
ejpam-5528	329	1	nonlinear	nonlinear	PROPN
ejpam-5528	329	2	skew	skew	ADJ
ejpam-5528	329	3	lie	lie	NOUN
ejpam-5528	329	4	derivations	derivation	NOUN
ejpam-5528	329	5	on	on	ADP
ejpam-5528	329	6	prime	prime	ADJ
ejpam-5528	329	7	∗-rings	∗-ring	NOUN
ejpam-5528	329	8	.	.	PUNCT
ejpam-5528	330	1	indian	indian	ADJ
ejpam-5528	330	2	journal	journal	PROPN
ejpam-5528	330	3	of	of	ADP
ejpam-5528	330	4	pure	pure	ADJ
ejpam-5528	330	5	and	and	CCONJ
ejpam-5528	330	6	applied	applied	ADJ
ejpam-5528	330	7	mathematics	mathematic	NOUN
ejpam-5528	330	8	,	,	PUNCT
ejpam-5528	330	9	54(2):475–484	54(2):475–484	PROPN
ejpam-5528	330	10	,	,	PUNCT
ejpam-5528	330	11	2023	2023	NUM
ejpam-5528	330	12	.	.	PUNCT
ejpam-5528	331	1	[	[	X
ejpam-5528	331	2	8	8	NUM
ejpam-5528	331	3	]	]	X
ejpam-5528	331	4	tsiu	tsiu	ADJ
ejpam-5528	331	5	-	-	PUNCT
ejpam-5528	331	6	kwen	kwen	NOUN
ejpam-5528	331	7	lee	lee	PROPN
ejpam-5528	331	8	and	and	CCONJ
ejpam-5528	331	9	tsai	tsai	PROPN
ejpam-5528	331	10	-	-	PUNCT
ejpam-5528	331	11	lien	lien	PROPN
ejpam-5528	331	12	wong	wong	PROPN
ejpam-5528	331	13	.	.	PROPN
ejpam-5528	331	14	nonadditive	nonadditive	PROPN
ejpam-5528	331	15	strong	strong	ADJ
ejpam-5528	331	16	commutativity	commutativity	NOUN
ejpam-5528	331	17	preserving	preserve	VERB
ejpam-5528	331	18	maps	map	NOUN
ejpam-5528	331	19	.	.	PUNCT
ejpam-5528	332	1	communications	communication	NOUN
ejpam-5528	332	2	in	in	ADP
ejpam-5528	332	3	algebra	algebra	NOUN
ejpam-5528	332	4	,	,	PUNCT
ejpam-5528	332	5	40(6):2213–2218	40(6):2213–2218	NUM
ejpam-5528	332	6	,	,	PUNCT
ejpam-5528	332	7	2012	2012	NUM
ejpam-5528	332	8	.	.	PUNCT
ejpam-5528	333	1	[	[	X
ejpam-5528	333	2	9	9	NUM
ejpam-5528	333	3	]	]	X
ejpam-5528	333	4	chang	chang	PROPN
ejpam-5528	333	5	jing	jing	PROPN
ejpam-5528	333	6	li	li	PROPN
ejpam-5528	333	7	and	and	CCONJ
ejpam-5528	333	8	quan	quan	PROPN
ejpam-5528	333	9	yuan	yuan	PROPN
ejpam-5528	333	10	chen	chen	PROPN
ejpam-5528	333	11	.	.	PUNCT
ejpam-5528	334	1	strong	strong	ADJ
ejpam-5528	334	2	skew	skew	ADJ
ejpam-5528	334	3	commutativity	commutativity	NOUN
ejpam-5528	334	4	preserving	preserve	VERB
ejpam-5528	334	5	maps	map	NOUN
ejpam-5528	334	6	on	on	ADP
ejpam-5528	334	7	rings	ring	NOUN
ejpam-5528	334	8	with	with	ADP
ejpam-5528	334	9	involution	involution	NOUN
ejpam-5528	334	10	.	.	PUNCT
ejpam-5528	335	1	acta	acta	PROPN
ejpam-5528	335	2	mathematica	mathematica	PROPN
ejpam-5528	335	3	sinica	sinica	PROPN
ejpam-5528	335	4	,	,	PUNCT
ejpam-5528	335	5	english	english	ADJ
ejpam-5528	335	6	series	series	NOUN
ejpam-5528	335	7	,	,	PUNCT
ejpam-5528	335	8	32(6):745–752	32(6):745–752	PROPN
ejpam-5528	335	9	,	,	PUNCT
ejpam-5528	335	10	2016	2016	NUM
ejpam-5528	335	11	.	.	PUNCT
ejpam-5528	336	1	[	[	X
ejpam-5528	336	2	10	10	NUM
ejpam-5528	336	3	]	]	X
ejpam-5528	336	4	jer	jer	NOUN
ejpam-5528	336	5	-	-	PUNCT
ejpam-5528	336	6	shyong	shyong	PROPN
ejpam-5528	336	7	lin	lin	PROPN
ejpam-5528	336	8	and	and	CCONJ
ejpam-5528	336	9	cheng	cheng	PROPN
ejpam-5528	336	10	-	-	PUNCT
ejpam-5528	336	11	kai	kai	PROPN
ejpam-5528	336	12	liu	liu	PROPN
ejpam-5528	336	13	.	.	PUNCT
ejpam-5528	337	1	strong	strong	ADJ
ejpam-5528	337	2	commutativity	commutativity	NOUN
ejpam-5528	337	3	preserving	preserve	VERB
ejpam-5528	337	4	maps	map	NOUN
ejpam-5528	337	5	in	in	ADP
ejpam-5528	337	6	prime	prime	ADJ
ejpam-5528	337	7	rings	ring	NOUN
ejpam-5528	337	8	with	with	ADP
ejpam-5528	337	9	involution	involution	NOUN
ejpam-5528	337	10	.	.	PUNCT
ejpam-5528	338	1	linear	linear	ADJ
ejpam-5528	338	2	algebra	algebra	NOUN
ejpam-5528	338	3	and	and	CCONJ
ejpam-5528	338	4	its	its	PRON
ejpam-5528	338	5	applications	application	NOUN
ejpam-5528	338	6	,	,	PUNCT
ejpam-5528	338	7	432(1):14–23	432(1):14–23	NUM
ejpam-5528	338	8	,	,	PUNCT
ejpam-5528	338	9	2010	2010	NUM
ejpam-5528	338	10	.	.	PUNCT
ejpam-5528	339	1	[	[	X
ejpam-5528	339	2	11	11	NUM
ejpam-5528	339	3	]	]	X
ejpam-5528	339	4	jer	jer	NOUN
ejpam-5528	339	5	-	-	PUNCT
ejpam-5528	339	6	shyong	shyong	PROPN
ejpam-5528	339	7	lin	lin	PROPN
ejpam-5528	339	8	and	and	CCONJ
ejpam-5528	339	9	cheng	cheng	PROPN
ejpam-5528	339	10	-	-	PUNCT
ejpam-5528	339	11	kai	kai	PROPN
ejpam-5528	339	12	liu	liu	PROPN
ejpam-5528	339	13	.	.	PUNCT
ejpam-5528	340	1	strong	strong	ADJ
ejpam-5528	340	2	commutativity	commutativity	NOUN
ejpam-5528	340	3	preserving	preserve	VERB
ejpam-5528	340	4	maps	map	NOUN
ejpam-5528	340	5	on	on	ADP
ejpam-5528	340	6	lie	lie	NOUN
ejpam-5528	340	7	ideals	ideal	NOUN
ejpam-5528	340	8	.	.	PUNCT
ejpam-5528	341	1	linear	linear	ADJ
ejpam-5528	341	2	algebra	algebra	NOUN
ejpam-5528	341	3	and	and	CCONJ
ejpam-5528	341	4	its	its	PRON
ejpam-5528	341	5	applications	application	NOUN
ejpam-5528	341	6	,	,	PUNCT
ejpam-5528	341	7	428(7):1601–1609	428(7):1601–1609	NOUN
ejpam-5528	341	8	,	,	PUNCT
ejpam-5528	341	9	2008	2008	NUM
ejpam-5528	341	10	.	.	PUNCT
ejpam-5528	342	1	[	[	X
ejpam-5528	342	2	12	12	NUM
ejpam-5528	342	3	]	]	X
ejpam-5528	342	4	lei	lei	PROPN
ejpam-5528	342	5	liu	liu	PROPN
ejpam-5528	342	6	.	.	PUNCT
ejpam-5528	343	1	strong	strong	ADJ
ejpam-5528	343	2	skew	skew	ADJ
ejpam-5528	343	3	commutativity	commutativity	NOUN
ejpam-5528	343	4	preserving	preserve	VERB
ejpam-5528	343	5	maps	map	NOUN
ejpam-5528	343	6	on	on	ADP
ejpam-5528	343	7	rings	ring	NOUN
ejpam-5528	343	8	.	.	PUNCT
ejpam-5528	344	1	journal	journal	PROPN
ejpam-5528	344	2	of	of	ADP
ejpam-5528	344	3	the	the	DET
ejpam-5528	344	4	australian	australian	ADJ
ejpam-5528	344	5	mathematical	mathematical	ADJ
ejpam-5528	344	6	society	society	NOUN
ejpam-5528	344	7	,	,	PUNCT
ejpam-5528	344	8	100(1):78–85	100(1):78–85	NUM
ejpam-5528	344	9	,	,	PUNCT
ejpam-5528	344	10	2016	2016	NUM
ejpam-5528	344	11	.	.	PUNCT
ejpam-5528	345	1	[	[	X
ejpam-5528	345	2	13	13	NUM
ejpam-5528	345	3	]	]	PUNCT
ejpam-5528	345	4	xiaofei	xiaofei	PROPN
ejpam-5528	345	5	qi	qi	PROPN
ejpam-5528	345	6	and	and	CCONJ
ejpam-5528	345	7	yazhou	yazhou	PROPN
ejpam-5528	345	8	zhang	zhang	PROPN
ejpam-5528	345	9	.	.	PUNCT
ejpam-5528	346	1	k	k	ADJ
ejpam-5528	346	2	-	-	PUNCT
ejpam-5528	346	3	skew	skew	ADJ
ejpam-5528	346	4	lie	lie	NOUN
ejpam-5528	346	5	products	product	NOUN
ejpam-5528	346	6	on	on	ADP
ejpam-5528	346	7	prime	prime	ADJ
ejpam-5528	346	8	rings	ring	NOUN
ejpam-5528	346	9	with	with	ADP
ejpam-5528	346	10	involution	involution	NOUN
ejpam-5528	346	11	.	.	PUNCT
ejpam-5528	347	1	communications	communication	NOUN
ejpam-5528	347	2	in	in	ADP
ejpam-5528	347	3	algebra	algebra	NOUN
ejpam-5528	347	4	,	,	PUNCT
ejpam-5528	347	5	46(3):1001–1010	46(3):1001–1010	PROPN
ejpam-5528	347	6	,	,	PUNCT
ejpam-5528	347	7	2018	2018	NUM
ejpam-5528	347	8	.	.	PUNCT
ejpam-5528	348	1	[	[	X
ejpam-5528	348	2	14	14	NUM
ejpam-5528	348	3	]	]	PUNCT
ejpam-5528	348	4	xiaofei	xiaofei	PROPN
ejpam-5528	348	5	qi	qi	PROPN
ejpam-5528	348	6	and	and	CCONJ
ejpam-5528	348	7	jinchuan	jinchuan	PROPN
ejpam-5528	348	8	hou	hou	PROPN
ejpam-5528	348	9	.	.	PUNCT
ejpam-5528	349	1	strong	strong	ADJ
ejpam-5528	349	2	skew	skew	ADJ
ejpam-5528	349	3	commutativity	commutativity	NOUN
ejpam-5528	349	4	preserving	preserve	VERB
ejpam-5528	349	5	maps	map	NOUN
ejpam-5528	349	6	on	on	ADP
ejpam-5528	349	7	von	von	PROPN
ejpam-5528	349	8	neumann	neumann	PROPN
ejpam-5528	349	9	algebras	algebras	PROPN
ejpam-5528	349	10	.	.	PROPN
ejpam-5528	350	1	journal	journal	PROPN
ejpam-5528	350	2	of	of	ADP
ejpam-5528	350	3	mathematical	mathematical	ADJ
ejpam-5528	350	4	analysis	analysis	NOUN
ejpam-5528	350	5	and	and	CCONJ
ejpam-5528	350	6	applications	application	NOUN
ejpam-5528	350	7	,	,	PUNCT
ejpam-5528	350	8	397(1):362	397(1):362	NUM
ejpam-5528	350	9	–	–	PUNCT
ejpam-5528	350	10	370	370	NUM
ejpam-5528	350	11	,	,	PUNCT
ejpam-5528	350	12	2013	2013	NUM
ejpam-5528	350	13	.	.	PUNCT
ejpam-5528	351	1	[	[	X
ejpam-5528	351	2	15	15	NUM
ejpam-5528	351	3	]	]	X
ejpam-5528	351	4	xiaofei	xiaofei	PROPN
ejpam-5528	351	5	qi	qi	PROPN
ejpam-5528	351	6	and	and	CCONJ
ejpam-5528	351	7	jinchuan	jinchuan	PROPN
ejpam-5528	351	8	hou	hou	PROPN
ejpam-5528	351	9	.	.	PUNCT
ejpam-5528	352	1	nonlinear	nonlinear	ADJ
ejpam-5528	352	2	strong	strong	ADJ
ejpam-5528	352	3	commutativity	commutativity	NOUN
ejpam-5528	352	4	preserving	preserve	VERB
ejpam-5528	352	5	maps	map	NOUN
ejpam-5528	352	6	on	on	ADP
ejpam-5528	352	7	prime	prime	ADJ
ejpam-5528	352	8	rings	ring	NOUN
ejpam-5528	352	9	.	.	PUNCT
ejpam-5528	353	1	communications	communication	NOUN
ejpam-5528	353	2	in	in	ADP
ejpam-5528	353	3	algebra	algebra	PROPN
ejpam-5528	353	4	®	®	NOUN
ejpam-5528	353	5	,	,	PUNCT
ejpam-5528	353	6	38(8):2790–2796	38(8):2790–2796	NUM
ejpam-5528	353	7	,	,	PUNCT
ejpam-5528	353	8	2010	2010	NUM
ejpam-5528	353	9	.	.	PUNCT
ejpam-5528	354	1	[	[	X
ejpam-5528	354	2	16	16	NUM
ejpam-5528	354	3	]	]	PUNCT
ejpam-5528	354	4	xiaofei	xiaofei	PROPN
ejpam-5528	354	5	qi	qi	PROPN
ejpam-5528	354	6	and	and	CCONJ
ejpam-5528	354	7	shaobo	shaobo	PROPN
ejpam-5528	354	8	chen	chen	PROPN
ejpam-5528	354	9	.	.	PUNCT
ejpam-5528	355	1	strong	strong	ADJ
ejpam-5528	355	2	bi	bi	ADJ
ejpam-5528	355	3	-	-	ADJ
ejpam-5528	355	4	skew	skew	ADJ
ejpam-5528	355	5	commutativity	commutativity	NOUN
ejpam-5528	355	6	preserving	preserve	VERB
ejpam-5528	355	7	maps	map	NOUN
ejpam-5528	355	8	on	on	ADP
ejpam-5528	355	9	von	von	PROPN
ejpam-5528	355	10	neumann	neumann	PROPN
ejpam-5528	355	11	algebras	algebras	PROPN
ejpam-5528	355	12	.	.	PUNCT
ejpam-5528	356	1	bulletin	bulletin	NOUN
ejpam-5528	356	2	of	of	ADP
ejpam-5528	356	3	the	the	DET
ejpam-5528	356	4	iranian	iranian	PROPN
ejpam-5528	356	5	mathematical	mathematical	PROPN
ejpam-5528	356	6	society	society	NOUN
ejpam-5528	356	7	,	,	PUNCT
ejpam-5528	356	8	49(2):15	49(2):15	NOUN
ejpam-5528	356	9	,	,	PUNCT
ejpam-5528	356	10	2023	2023	NUM
ejpam-5528	356	11	.	.	PUNCT
ejpam-5528	357	1	[	[	X
ejpam-5528	357	2	17	17	NUM
ejpam-5528	357	3	]	]	X
ejpam-5528	357	4	l	l	PROPN
ejpam-5528	357	5	kong	kong	PROPN
ejpam-5528	357	6	and	and	CCONJ
ejpam-5528	357	7	j	j	PROPN
ejpam-5528	357	8	zhang	zhang	PROPN
ejpam-5528	357	9	.	.	PUNCT
ejpam-5528	358	1	nonlinear	nonlinear	ADJ
ejpam-5528	358	2	skew	skew	ADJ
ejpam-5528	358	3	commuting	commuting	NOUN
ejpam-5528	358	4	maps	map	NOUN
ejpam-5528	358	5	on	on	ADP
ejpam-5528	358	6	∗-rings	∗-ring	NOUN
ejpam-5528	358	7	.	.	PUNCT
ejpam-5528	359	1	ukrainian	ukrainian	ADJ
ejpam-5528	359	2	mathematical	mathematical	ADJ
ejpam-5528	359	3	journal	journal	NOUN
ejpam-5528	359	4	,	,	PUNCT
ejpam-5528	359	5	74(6):946–952	74(6):946–952	PROPN
ejpam-5528	359	6	,	,	PUNCT
ejpam-5528	359	7	2022	2022	NUM
ejpam-5528	359	8	.	.	PUNCT
ejpam-5528	360	1	[	[	X
ejpam-5528	360	2	18	18	NUM
ejpam-5528	360	3	]	]	X
ejpam-5528	360	4	mohammad	mohammad	PROPN
ejpam-5528	360	5	aslam	aslam	PROPN
ejpam-5528	360	6	siddeeque	siddeeque	PROPN
ejpam-5528	360	7	and	and	CCONJ
ejpam-5528	360	8	abbas	abbas	PROPN
ejpam-5528	360	9	hussain	hussain	PROPN
ejpam-5528	360	10	shikeh	shikeh	PROPN
ejpam-5528	360	11	.	.	PUNCT
ejpam-5528	361	1	on	on	ADP
ejpam-5528	361	2	the	the	DET
ejpam-5528	361	3	characterization	characterization	NOUN
ejpam-5528	361	4	of	of	ADP
ejpam-5528	361	5	skew	skew	ADJ
ejpam-5528	361	6	jordan	jordan	PROPN
ejpam-5528	361	7	derivations	derivation	NOUN
ejpam-5528	361	8	in	in	ADP
ejpam-5528	361	9	∗-rings	∗-ring	NOUN
ejpam-5528	361	10	.	.	PUNCT
ejpam-5528	362	1	iranian	iranian	ADJ
ejpam-5528	362	2	journal	journal	PROPN
ejpam-5528	362	3	of	of	ADP
ejpam-5528	362	4	science	science	PROPN
ejpam-5528	362	5	,	,	PUNCT
ejpam-5528	362	6	47(5):1605–1611	47(5):1605–1611	NUM
ejpam-5528	362	7	,	,	PUNCT
ejpam-5528	362	8	2023	2023	NUM
ejpam-5528	362	9	.	.	PUNCT
ejpam-5528	363	1	[	[	X
ejpam-5528	363	2	19	19	NUM
ejpam-5528	363	3	]	]	X
ejpam-5528	363	4	vahid	vahid	PROPN
ejpam-5528	363	5	darvish	darvish	PROPN
ejpam-5528	363	6	,	,	PUNCT
ejpam-5528	363	7	mojtaba	mojtaba	PROPN
ejpam-5528	363	8	nouri	nouri	PROPN
ejpam-5528	363	9	,	,	PUNCT
ejpam-5528	363	10	and	and	CCONJ
ejpam-5528	363	11	mehran	mehran	PROPN
ejpam-5528	363	12	razeghi	razeghi	PROPN
ejpam-5528	363	13	.	.	PUNCT
ejpam-5528	364	1	non	non	ADJ
ejpam-5528	364	2	-	-	ADJ
ejpam-5528	364	3	linear	linear	ADJ
ejpam-5528	364	4	bi	bi	ADJ
ejpam-5528	364	5	-	-	ADJ
ejpam-5528	364	6	skew	skew	ADJ
ejpam-5528	364	7	jordan	jordan	PROPN
ejpam-5528	364	8	derivations	derivation	NOUN
ejpam-5528	364	9	on	on	ADP
ejpam-5528	364	10	∗-algebra	∗-algebra	NOUN
ejpam-5528	364	11	.	.	PUNCT
ejpam-5528	365	1	filomat	filomat	PROPN
ejpam-5528	365	2	,	,	PUNCT
ejpam-5528	365	3	36(10):3231–3239	36(10):3231–3239	NUM
ejpam-5528	365	4	,	,	PUNCT
ejpam-5528	365	5	2022	2022	NUM
ejpam-5528	365	6	.	.	PUNCT
ejpam-5528	366	1	[	[	X
ejpam-5528	366	2	20	20	NUM
ejpam-5528	366	3	]	]	X
ejpam-5528	366	4	mohammad	mohammad	PROPN
ejpam-5528	366	5	aslam	aslam	PROPN
ejpam-5528	366	6	siddeeque	siddeeque	PROPN
ejpam-5528	366	7	and	and	CCONJ
ejpam-5528	366	8	abbas	abbas	PROPN
ejpam-5528	366	9	hussain	hussain	PROPN
ejpam-5528	366	10	shikeh	shikeh	PROPN
ejpam-5528	366	11	.	.	PUNCT
ejpam-5528	367	1	nonlinear	nonlinear	ADJ
ejpam-5528	367	2	bi	bi	ADJ
ejpam-5528	367	3	-	-	ADJ
ejpam-5528	367	4	skew	skew	ADJ
ejpam-5528	367	5	jordan	jordan	PROPN
ejpam-5528	367	6	derivations	derivation	NOUN
ejpam-5528	367	7	in	in	ADP
ejpam-5528	367	8	prime	prime	ADJ
ejpam-5528	367	9	∗-rings	∗-ring	NOUN
ejpam-5528	367	10	.	.	PUNCT
ejpam-5528	368	1	journal	journal	NOUN
ejpam-5528	368	2	of	of	ADP
ejpam-5528	368	3	algebra	algebra	PROPN
ejpam-5528	368	4	and	and	CCONJ
ejpam-5528	368	5	its	its	PRON
ejpam-5528	368	6	applications	application	NOUN
ejpam-5528	368	7	,	,	PUNCT
ejpam-5528	368	8	23(14):2550001	23(14):2550001	NUM
ejpam-5528	368	9	,	,	PUNCT
ejpam-5528	368	10	2024	2024	NUM
ejpam-5528	368	11	.	.	PUNCT
ejpam-5528	369	1	[	[	X
ejpam-5528	369	2	21	21	NUM
ejpam-5528	369	3	]	]	X
ejpam-5528	369	4	asma	asma	PROPN
ejpam-5528	369	5	ali	ali	PROPN
ejpam-5528	369	6	,	,	PUNCT
ejpam-5528	369	7	amal	amal	PROPN
ejpam-5528	369	8	s	s	PART
ejpam-5528	369	9	alali	alali	ADJ
ejpam-5528	369	10	,	,	PUNCT
ejpam-5528	369	11	and	and	CCONJ
ejpam-5528	369	12	mohd	mohd	PROPN
ejpam-5528	369	13	tasleem	tasleem	NOUN
ejpam-5528	369	14	.	.	PUNCT
ejpam-5528	370	1	characterization	characterization	NOUN
ejpam-5528	370	2	of	of	ADP
ejpam-5528	370	3	non	non	ADJ
ejpam-5528	370	4	-	-	ADJ
ejpam-5528	370	5	linear	linear	ADJ
ejpam-5528	370	6	bi	bi	ADJ
ejpam-5528	370	7	-	-	ADJ
ejpam-5528	370	8	skew	skew	NOUN
ejpam-5528	370	9	jordan	jordan	PROPN
ejpam-5528	370	10	n	n	CCONJ
ejpam-5528	370	11	-	-	PUNCT
ejpam-5528	370	12	derivations	derivation	NOUN
ejpam-5528	370	13	on	on	ADP
ejpam-5528	370	14	prime	prime	ADJ
ejpam-5528	370	15	∗-algebras	∗-algebra	NOUN
ejpam-5528	370	16	.	.	PUNCT
ejpam-5528	371	1	axioms	axiom	NOUN
ejpam-5528	371	2	,	,	PUNCT
ejpam-5528	371	3	12(8):753	12(8):753	NUM
ejpam-5528	371	4	,	,	PUNCT
ejpam-5528	371	5	2023	2023	NUM
ejpam-5528	371	6	.	.	PUNCT
ejpam-5528	372	1	[	[	X
ejpam-5528	372	2	22	22	NUM
ejpam-5528	372	3	]	]	X
ejpam-5528	372	4	mohammad	mohammad	PROPN
ejpam-5528	372	5	ashraf	ashraf	PROPN
ejpam-5528	372	6	,	,	PUNCT
ejpam-5528	372	7	md	md	PROPN
ejpam-5528	372	8	shamim	shamim	PROPN
ejpam-5528	372	9	akhter	akhter	PROPN
ejpam-5528	372	10	,	,	PUNCT
ejpam-5528	372	11	and	and	CCONJ
ejpam-5528	372	12	mohammad	mohammad	PROPN
ejpam-5528	372	13	afajal	afajal	VERB
ejpam-5528	372	14	ansari	ansari	X
ejpam-5528	372	15	.	.	PUNCT
ejpam-5528	373	1	nonlinear	nonlinear	ADJ
ejpam-5528	373	2	generalized	generalize	VERB
ejpam-5528	373	3	bi	bi	ADJ
ejpam-5528	373	4	-	-	ADJ
ejpam-5528	373	5	skew	skew	NOUN
ejpam-5528	373	6	jordan	jordan	PROPN
ejpam-5528	373	7	n	n	CCONJ
ejpam-5528	373	8	-	-	PUNCT
ejpam-5528	373	9	derivations	derivation	NOUN
ejpam-5528	373	10	on	on	ADP
ejpam-5528	373	11	∗-algebras	∗-algebra	NOUN
ejpam-5528	373	12	.	.	PUNCT
ejpam-5528	374	1	bulletin	bulletin	NOUN
ejpam-5528	374	2	of	of	ADP
ejpam-5528	374	3	the	the	DET
ejpam-5528	374	4	malaysian	malaysian	PROPN
ejpam-5528	374	5	mathematical	mathematical	PROPN
ejpam-5528	374	6	sciences	sciences	PROPN
ejpam-5528	374	7	society	society	NOUN
ejpam-5528	374	8	,	,	PUNCT
ejpam-5528	374	9	47(1):18	47(1):18	PROPN
ejpam-5528	374	10	,	,	PUNCT
ejpam-5528	374	11	2024	2024	NUM
ejpam-5528	374	12	.	.	PUNCT
ejpam-5528	375	1	[	[	X
ejpam-5528	375	2	23	23	NUM
ejpam-5528	375	3	]	]	X
ejpam-5528	375	4	tsiu	tsiu	ADJ
ejpam-5528	375	5	-	-	PUNCT
ejpam-5528	375	6	kwen	kwen	NOUN
ejpam-5528	375	7	lee	lee	PROPN
ejpam-5528	375	8	and	and	CCONJ
ejpam-5528	375	9	tsai	tsai	PROPN
ejpam-5528	375	10	-	-	PUNCT
ejpam-5528	375	11	lien	lien	PROPN
ejpam-5528	375	12	wong	wong	PROPN
ejpam-5528	375	13	.	.	PUNCT
ejpam-5528	376	1	right	right	ADJ
ejpam-5528	376	2	centralizers	centralizer	NOUN
ejpam-5528	376	3	of	of	ADP
ejpam-5528	376	4	semiprime	semiprime	NOUN
ejpam-5528	376	5	rings	ring	NOUN
ejpam-5528	376	6	.	.	PUNCT
ejpam-5528	377	1	communications	communication	NOUN
ejpam-5528	377	2	in	in	ADP
ejpam-5528	377	3	algebra	algebra	NOUN
ejpam-5528	377	4	,	,	PUNCT
ejpam-5528	377	5	42(7):2923–2927	42(7):2923–2927	NUM
ejpam-5528	377	6	,	,	PUNCT
ejpam-5528	377	7	2014	2014	NUM
ejpam-5528	377	8	.	.	PUNCT
ejpam-5528	378	1	[	[	X
ejpam-5528	378	2	24	24	NUM
ejpam-5528	378	3	]	]	PUNCT
ejpam-5528	378	4	matej	matej	PROPN
ejpam-5528	378	5	brešar	brešar	PROPN
ejpam-5528	378	6	and	and	CCONJ
ejpam-5528	378	7	c	c	PROPN
ejpam-5528	378	8	robert	robert	PROPN
ejpam-5528	378	9	miers	miers	PROPN
ejpam-5528	378	10	.	.	PUNCT
ejpam-5528	379	1	strong	strong	ADJ
ejpam-5528	379	2	commutativity	commutativity	NOUN
ejpam-5528	379	3	preserving	preserve	VERB
ejpam-5528	379	4	maps	map	NOUN
ejpam-5528	379	5	of	of	ADP
ejpam-5528	379	6	semiprime	semiprime	NOUN
ejpam-5528	379	7	rings	ring	NOUN
ejpam-5528	379	8	.	.	PUNCT
ejpam-5528	380	1	canadian	canadian	PROPN
ejpam-5528	380	2	mathematical	mathematical	ADJ
ejpam-5528	380	3	bulletin	bulletin	NOUN
ejpam-5528	380	4	,	,	PUNCT
ejpam-5528	380	5	37(4):457–460	37(4):457–460	NUM
ejpam-5528	380	6	,	,	PUNCT
ejpam-5528	380	7	1994	1994	NUM
ejpam-5528	380	8	.	.	PUNCT
ejpam-5528	381	1	moin	moin	PROPN
ejpam-5528	381	2	a.	a.	PROPN
ejpam-5528	381	3	ansari	ansari	PROPN
ejpam-5528	381	4	et	et	PROPN
ejpam-5528	381	5	al	al	PROPN
ejpam-5528	381	6	.	.	PUNCT
ejpam-5528	381	7	/	/	SYM
ejpam-5528	381	8	eur	eur	PROPN
ejpam-5528	381	9	.	.	PUNCT
ejpam-5528	382	1	j.	j.	PROPN
ejpam-5528	382	2	pure	pure	PROPN
ejpam-5528	382	3	appl	appl	PROPN
ejpam-5528	382	4	.	.	PROPN
ejpam-5528	382	5	math	math	PROPN
ejpam-5528	382	6	,	,	PUNCT
ejpam-5528	382	7	18	18	NUM
ejpam-5528	382	8	(	(	PUNCT
ejpam-5528	382	9	2	2	NUM
ejpam-5528	382	10	)	)	PUNCT
ejpam-5528	382	11	(	(	PUNCT
ejpam-5528	382	12	2025	2025	NUM
ejpam-5528	382	13	)	)	PUNCT
ejpam-5528	382	14	,	,	PUNCT
ejpam-5528	382	15	5528	5528	NUM
ejpam-5528	382	16	14	14	NUM
ejpam-5528	382	17	of	of	ADP
ejpam-5528	382	18	14	14	NUM
ejpam-5528	382	19	[	[	X
ejpam-5528	382	20	25	25	NUM
ejpam-5528	382	21	]	]	X
ejpam-5528	382	22	mohammad	mohammad	PROPN
ejpam-5528	382	23	aslam	aslam	PROPN
ejpam-5528	382	24	siddeeque	siddeeque	PROPN
ejpam-5528	382	25	,	,	PUNCT
ejpam-5528	382	26	abbas	abbas	PROPN
ejpam-5528	382	27	hussain	hussain	PROPN
ejpam-5528	382	28	shikeh	shikeh	PROPN
ejpam-5528	382	29	,	,	PUNCT
ejpam-5528	382	30	and	and	CCONJ
ejpam-5528	382	31	raof	raof	VERB
ejpam-5528	382	32	ahmad	ahmad	PROPN
ejpam-5528	382	33	bhat	bhat	PROPN
ejpam-5528	382	34	.	.	PUNCT
ejpam-5528	383	1	on	on	ADP
ejpam-5528	383	2	the	the	DET
ejpam-5528	383	3	structure	structure	NOUN
ejpam-5528	383	4	of	of	ADP
ejpam-5528	383	5	some	some	DET
ejpam-5528	383	6	nonlinear	nonlinear	ADJ
ejpam-5528	383	7	maps	map	NOUN
ejpam-5528	383	8	in	in	ADP
ejpam-5528	383	9	prime	prime	ADJ
ejpam-5528	383	10	∗-rings	∗-ring	NOUN
ejpam-5528	383	11	.	.	PUNCT
ejpam-5528	384	1	filomat	filomat	NOUN
ejpam-5528	384	2	,	,	PUNCT
ejpam-5528	384	3	38(1):261–269	38(1):261–269	PROPN
ejpam-5528	384	4	,	,	PUNCT
ejpam-5528	384	5	2024	2024	NUM
ejpam-5528	384	6	.	.	PUNCT
ejpam-5528	385	1	[	[	X
ejpam-5528	385	2	26	26	NUM
ejpam-5528	385	3	]	]	SYM
ejpam-5528	385	4	louis	louis	PROPN
ejpam-5528	385	5	rowen	rowen	NOUN
ejpam-5528	385	6	.	.	PUNCT
ejpam-5528	386	1	some	some	DET
ejpam-5528	386	2	results	result	NOUN
ejpam-5528	386	3	on	on	ADP
ejpam-5528	386	4	the	the	DET
ejpam-5528	386	5	center	center	NOUN
ejpam-5528	386	6	of	of	ADP
ejpam-5528	386	7	a	a	DET
ejpam-5528	386	8	ring	ring	NOUN
ejpam-5528	386	9	with	with	ADP
ejpam-5528	386	10	polynomial	polynomial	ADJ
ejpam-5528	386	11	identity	identity	NOUN
ejpam-5528	386	12	.	.	PUNCT
ejpam-5528	387	1	1973	1973	NUM
ejpam-5528	387	2	.	.	PUNCT
ejpam-5528	388	1	[	[	X
ejpam-5528	388	2	27	27	NUM
ejpam-5528	388	3	]	]	PUNCT
ejpam-5528	388	4	konstantin	konstantin	PROPN
ejpam-5528	388	5	i	i	PROPN
ejpam-5528	388	6	beidar	beidar	PROPN
ejpam-5528	388	7	and	and	CCONJ
ejpam-5528	388	8	ws	ws	PROPN
ejpam-5528	388	9	martindale	martindale	PROPN
ejpam-5528	388	10	iii	iii	PROPN
ejpam-5528	388	11	.	.	PUNCT
ejpam-5528	389	1	on	on	ADP
ejpam-5528	389	2	functional	functional	ADJ
ejpam-5528	389	3	identities	identity	NOUN
ejpam-5528	389	4	in	in	ADP
ejpam-5528	389	5	prime	prime	ADJ
ejpam-5528	389	6	rings	ring	NOUN
ejpam-5528	389	7	with	with	ADP
ejpam-5528	389	8	involution	involution	NOUN
ejpam-5528	389	9	.	.	PUNCT
ejpam-5528	390	1	journal	journal	PROPN
ejpam-5528	390	2	of	of	ADP
ejpam-5528	390	3	algebra	algebra	PROPN
ejpam-5528	390	4	,	,	PUNCT
ejpam-5528	390	5	203(2):491–532	203(2):491–532	PROPN
ejpam-5528	390	6	,	,	PUNCT
ejpam-5528	390	7	1998	1998	NUM
ejpam-5528	390	8	.	.	PUNCT