id	sid	eid	entity	type
ejpam-5051	1	1	european journal	ORG
ejpam-5051	2	1	17	CARDINAL
ejpam-5051	2	2	1	CARDINAL
ejpam-5051	2	3	2024	DATE
ejpam-5051	2	4	519	CARDINAL
ejpam-5051	3	1	new york	GPE
ejpam-5051	3	2	steinberg	PERSON
ejpam-5051	3	3	steinberg	PERSON
ejpam-5051	3	4	rizalyn s. bongcawel 1,∗	PERSON
ejpam-5051	3	5	b. cabardo1	PERSON
ejpam-5051	3	6	gaudencio c. petalcorin jr.1	PERSON
ejpam-5051	3	7	jocelyn p. vilela1	PERSON
ejpam-5051	4	1	1	CARDINAL
ejpam-5051	4	2	msu-iligan institute of technology	ORG
ejpam-5051	4	3	9200	CARDINAL
ejpam-5051	4	4	iligan city	GPE
ejpam-5051	4	5	philippines	GPE
ejpam-5051	6	1	â	GPE
ejpam-5051	6	2	r.	NORP
ejpam-5051	7	1	steinberg	PERSON
ejpam-5051	7	2	steinberg	PERSON
ejpam-5051	8	1	2020	DATE
ejpam-5051	8	2	20l05	CARDINAL
ejpam-5051	8	3	22a22	CARDINAL
ejpam-5051	8	4	steinberg	PERSON
ejpam-5051	8	5	steinberg	PERSON
ejpam-5051	8	6	steinberg	PERSON
ejpam-5051	8	7	1	CARDINAL
ejpam-5051	8	8	brandt	ORG
ejpam-5051	8	9	1926	DATE
ejpam-5051	8	10	2	CARDINAL
ejpam-5051	9	1	brandt	PERSON
ejpam-5051	9	2	groupoid	ORG
ejpam-5051	9	3	4	CARDINAL
ejpam-5051	10	1	12	CARDINAL
ejpam-5051	10	2	groupoid	ORG
ejpam-5051	11	1	groupoid	ORG
ejpam-5051	12	1	1980s	DATE
ejpam-5051	12	2	renault	ORG
ejpam-5051	12	3	feldman	PERSON
ejpam-5051	13	1	5	CARDINAL
ejpam-5051	13	2	6	CARDINAL
ejpam-5051	13	3	von neumann algebras	PERSON
ejpam-5051	14	1	10	CARDINAL
ejpam-5051	17	1	r. s. bongcawel	PERSON
ejpam-5051	17	2	l. b. cabardo	PERSON
ejpam-5051	17	3	gaudencio.petalcorin@g.msuiit.edu.ph	PERSON
ejpam-5051	17	4	g. c. petalcorin	PERSON
ejpam-5051	17	5	jocelyn.vilela@g.msuiit.edu.ph	GPE
ejpam-5051	17	6	j. p. vilela	ORG
ejpam-5051	18	1	519	CARDINAL
ejpam-5051	18	2	2024	CARDINAL
ejpam-5051	19	1	r. s. bongcawel	PERSON
ejpam-5051	21	1	j. pure	PERSON
ejpam-5051	21	2	17	CARDINAL
ejpam-5051	21	3	1	CARDINAL
ejpam-5051	21	4	2024	CARDINAL
ejpam-5051	21	5	519	CARDINAL
ejpam-5051	21	6	545 520	CARDINAL
ejpam-5051	21	7	13	CARDINAL
ejpam-5051	22	1	8	CARDINAL
ejpam-5051	23	1	renault	ORG
ejpam-5051	23	2	2	CARDINAL
ejpam-5051	25	1	15	CARDINAL
ejpam-5051	25	2	williams	PERSON
ejpam-5051	25	3	renault	ORG
ejpam-5051	25	4	c∗(â⋊r;d	ORG
ejpam-5051	25	5	second	ORDINAL
ejpam-5051	25	6	abelian	NORP
ejpam-5051	26	1	last 2010	DATE
ejpam-5051	26	2	thirty years	DATE
ejpam-5051	26	3	steinberg	PERSON
ejpam-5051	26	4	3	CARDINAL
ejpam-5051	28	1	2021	CARDINAL
ejpam-5051	28	2	becky armstrong	PERSON
ejpam-5051	28	3	lisa clark	PERSON
ejpam-5051	28	4	steinberg	PERSON
ejpam-5051	28	5	1	CARDINAL
ejpam-5051	29	1	renault	ORG
ejpam-5051	30	1	steinberg	PERSON
ejpam-5051	30	2	two	CARDINAL
ejpam-5051	30	3	2	CARDINAL
ejpam-5051	30	4	σ	ORG
ejpam-5051	30	5	steinberg	PERSON
ejpam-5051	31	1	steinberg	PERSON
ejpam-5051	31	2	steinberg	PERSON
ejpam-5051	32	1	first	ORDINAL
ejpam-5051	32	2	r.	NORP
ejpam-5051	33	1	â ⋊r	GPE
ejpam-5051	34	1	steinberg	PERSON
ejpam-5051	34	2	steinberg	PERSON
ejpam-5051	34	3	two	CARDINAL
ejpam-5051	35	1	2	CARDINAL
ejpam-5051	35	2	steinberg	PERSON
ejpam-5051	35	3	steinberg	PERSON
ejpam-5051	36	1	1	CARDINAL
ejpam-5051	37	1	g(2	GPE
ejpam-5051	37	2	7→	CARDINAL
ejpam-5051	37	3	g(2	GPE
ejpam-5051	37	4	γ 7→	ORG
ejpam-5051	38	1	g1	ORG
ejpam-5051	38	2	g(2	GPE
ejpam-5051	38	3	g(2	GPE
ejpam-5051	38	4	γα)β	ORG
ejpam-5051	38	5	g(2	GPE
ejpam-5051	38	6	g3	ORG
ejpam-5051	38	7	g(2	GPE
ejpam-5051	40	1	g(2	GPE
ejpam-5051	41	1	g(2	GPE
ejpam-5051	42	1	r. s. bongcawel	PERSON
ejpam-5051	44	1	j. pure	PERSON
ejpam-5051	44	2	17	CARDINAL
ejpam-5051	44	3	1	CARDINAL
ejpam-5051	44	4	2024	CARDINAL
ejpam-5051	44	5	519	CARDINAL
ejpam-5051	44	6	1	CARDINAL
ejpam-5051	45	1	12	CARDINAL
ejpam-5051	45	2	∈	ORG
ejpam-5051	46	1	g(2	GPE
ejpam-5051	48	1	2	CARDINAL
ejpam-5051	49	1	12	CARDINAL
ejpam-5051	52	1	s(g	PERSON
ejpam-5051	54	1	1	CARDINAL
ejpam-5051	55	1	12	CARDINAL
ejpam-5051	55	2	g(2	GPE
ejpam-5051	57	1	γ−1γ	CARDINAL
ejpam-5051	59	1	d(g	ORG
ejpam-5051	61	1	⋃	PRODUCT
ejpam-5051	63	1	2	CARDINAL
ejpam-5051	65	1	γ	GPE
ejpam-5051	65	2	g(2	GPE
ejpam-5051	67	1	g(2	GPE
ejpam-5051	67	2	∈	ORG
ejpam-5051	68	1	∈	ORG
ejpam-5051	69	1	r(x	PERSON
ejpam-5051	71	1	γ ∈	ORG
ejpam-5051	71	2	g(2	GPE
ejpam-5051	71	3	r(γ)γ	NORP
ejpam-5051	71	4	γs(γ	GPE
ejpam-5051	72	1	3	CARDINAL
ejpam-5051	73	1	12	CARDINAL
ejpam-5051	73	2	gx = s−1(x	ORG
ejpam-5051	73	3	∩gy	PERSON
ejpam-5051	74	1	γ ∈	ORG
ejpam-5051	75	1	⋃	DATE
ejpam-5051	77	1	1	CARDINAL
ejpam-5051	78	1	12	CARDINAL
ejpam-5051	79	1	3	CARDINAL
ejpam-5051	80	1	7	CARDINAL
ejpam-5051	80	2	γ 7→	ORG
ejpam-5051	81	1	4	CARDINAL
ejpam-5051	82	1	12	CARDINAL
ejpam-5051	83	1	5	CARDINAL
ejpam-5051	84	1	12	CARDINAL
ejpam-5051	85	1	⊆	CARDINAL
ejpam-5051	85	2	h(2	PERSON
ejpam-5051	85	3	g(2	GPE
ejpam-5051	86	1	12	CARDINAL
ejpam-5051	87	1	groupoid	ORG
ejpam-5051	87	2	g(2	GPE
ejpam-5051	88	1	topological	ORG
ejpam-5051	88	2	r. s. bongcawel et al	PERSON
ejpam-5051	89	1	j. pure	PERSON
ejpam-5051	89	2	17	CARDINAL
ejpam-5051	89	3	1	CARDINAL
ejpam-5051	89	4	2024	CARDINAL
ejpam-5051	89	5	519	CARDINAL
ejpam-5051	90	1	⊆	CARDINAL
ejpam-5051	93	1	6	CARDINAL
ejpam-5051	94	1	12	CARDINAL
ejpam-5051	96	1	1u	CARDINAL
ejpam-5051	96	2	1u	CARDINAL
ejpam-5051	96	3	1	CARDINAL
ejpam-5051	98	1	7	CARDINAL
ejpam-5051	99	1	12	CARDINAL
ejpam-5051	99	2	1u	CARDINAL
ejpam-5051	101	1	f ∗ g)(x	ORG
ejpam-5051	102	1	∑ y∈g	PERSON
ejpam-5051	102	2	∈	PRODUCT
ejpam-5051	102	3	steinberg	PERSON
ejpam-5051	102	4	steinberg	PERSON
ejpam-5051	102	5	z.	PERSON
ejpam-5051	103	1	2	CARDINAL
ejpam-5051	104	1	12	CARDINAL
ejpam-5051	105	1	1	CARDINAL
ejpam-5051	105	2	g(2	ORG
ejpam-5051	105	3	s(γ	PERSON
ejpam-5051	106	1	1	CARDINAL
ejpam-5051	107	1	1	CARDINAL
ejpam-5051	107	2	1	CARDINAL
ejpam-5051	109	1	∈	ORG
ejpam-5051	109	2	1{r	CARDINAL
ejpam-5051	110	1	1	CARDINAL
ejpam-5051	110	2	f ∗ g)(x	ORG
ejpam-5051	110	3	∑ y∈g	PERSON
ejpam-5051	110	4	steinberg	PERSON
ejpam-5051	110	5	g. r. s. bongcawel et al	PERSON
ejpam-5051	111	1	j. pure	PERSON
ejpam-5051	111	2	17	CARDINAL
ejpam-5051	111	3	1	CARDINAL
ejpam-5051	111	4	2024	CARDINAL
ejpam-5051	111	5	519	CARDINAL
ejpam-5051	111	6	1	CARDINAL
ejpam-5051	111	7	steinberg	PERSON
ejpam-5051	112	1	8	DATE
ejpam-5051	113	1	g(0)×t	ORG
ejpam-5051	113	2	σ	ORG
ejpam-5051	113	3	σ(0	PERSON
ejpam-5051	113	4	1	CARDINAL
ejpam-5051	113	5	2	CARDINAL
ejpam-5051	115	1	i(r(β	GPE
ejpam-5051	115	2	z)pα(β	ORG
ejpam-5051	115	3	bα×t	GPE
ejpam-5051	115	4	q−1(bα	GPE
ejpam-5051	116	1	3	CARDINAL
ejpam-5051	116	2	σ	CARDINAL
ejpam-5051	116	3	i(r(ϵ	PERSON
ejpam-5051	116	4	z)ϵ	GPE
ejpam-5051	117	1	∈	ORG
ejpam-5051	121	1	3	CARDINAL
ejpam-5051	121	2	commutative ring	ORG
ejpam-5051	122	1	−1	CARDINAL
ejpam-5051	122	2	1	CARDINAL
ejpam-5051	124	1	0	CARDINAL
ejpam-5051	124	2	r(x	WORK_OF_ART
ejpam-5051	125	1	x−1	PERSON
ejpam-5051	125	2	0	CARDINAL
ejpam-5051	125	3	0	CARDINAL
ejpam-5051	125	4	z(2	PERSON
ejpam-5051	127	1	z(2	PERSON
ejpam-5051	128	1	2	CARDINAL
ejpam-5051	129	1	1	CARDINAL
ejpam-5051	130	1	z)(β	PERSON
ejpam-5051	131	1	σ(α	ORG
ejpam-5051	131	2	σ(α	ORG
ejpam-5051	133	1	i(x	PERSON
ejpam-5051	133	2	q(γ	GPE
ejpam-5051	133	3	γ ∈ z	ORG
ejpam-5051	134	1	9	CARDINAL
ejpam-5051	137	1	σ(0	PERSON
ejpam-5051	138	1	r. s. bongcawel	PERSON
ejpam-5051	140	1	j. pure	PERSON
ejpam-5051	140	2	17	CARDINAL
ejpam-5051	140	3	1	CARDINAL
ejpam-5051	140	4	2024	CARDINAL
ejpam-5051	140	5	519	CARDINAL
ejpam-5051	140	6	10	CARDINAL
ejpam-5051	141	1	σ	ORG
ejpam-5051	141	2	r.	NORP
ejpam-5051	141	3	f ∈ c(σ	PRODUCT
ejpam-5051	141	4	f(z	DATE
ejpam-5051	142	1	σ	ORG
ejpam-5051	144	1	4	CARDINAL
ejpam-5051	145	1	σ	ORG
ejpam-5051	145	2	c(σ	PRODUCT
ejpam-5051	146	1	11	DATE
ejpam-5051	148	1	σ	ORG
ejpam-5051	149	1	∑ γ∈gs(q(ϵ	PERSON
ejpam-5051	150	1	σ	ORG
ejpam-5051	151	1	σ	ORG
ejpam-5051	151	2	steinberg	PERSON
ejpam-5051	152	1	steinberg	PERSON
ejpam-5051	153	1	4	CARDINAL
ejpam-5051	155	1	7→	CARDINAL
ejpam-5051	155	2	2	CARDINAL
ejpam-5051	156	1	σ	ORG
ejpam-5051	156	2	1{z	CARDINAL
ejpam-5051	156	3	7→	CARDINAL
ejpam-5051	158	1	σ(x	ORG
ejpam-5051	158	2	y)f(x)g(y	DATE
ejpam-5051	158	3	steinberg	PERSON
ejpam-5051	158	4	σ	ORG
ejpam-5051	158	5	σ	ORG
ejpam-5051	159	1	3	CARDINAL
ejpam-5051	159	2	groupoid	ORG
ejpam-5051	161	1	γ ∈	ORG
ejpam-5051	162	1	u ∈ g(0	ORG
ejpam-5051	162	2	γ ∈	ORG
ejpam-5051	165	1	γ ∈	PERSON
ejpam-5051	166	1	∈	ORG
ejpam-5051	166	2	â	GPE
ejpam-5051	166	3	u ∈ g(0	ORG
ejpam-5051	166	4	∈	ORG
ejpam-5051	167	1	1	CARDINAL
ejpam-5051	171	1	m((α̇	CARDINAL
ejpam-5051	172	1	α̇β	PERSON
ejpam-5051	172	2	∈	ORG
ejpam-5051	172	3	g(2	GPE
ejpam-5051	172	4	γ̇−1	ORG
ejpam-5051	173	1	r. s. bongcawel	PERSON
ejpam-5051	175	1	j. pure	PERSON
ejpam-5051	175	2	17	CARDINAL
ejpam-5051	175	3	1	CARDINAL
ejpam-5051	175	4	2024	CARDINAL
ejpam-5051	175	5	519	CARDINAL
ejpam-5051	175	6	γ̇	CARDINAL
ejpam-5051	182	1	∈	ORG
ejpam-5051	183	1	α−1a	ORG
ejpam-5051	184	1	γ̇	CARDINAL
ejpam-5051	184	2	γ̇	CARDINAL
ejpam-5051	184	3	β̇−1β̇	WORK_OF_ART
ejpam-5051	190	1	∈	ORG
ejpam-5051	196	1	= s(αβ)a = s(β)a	PERSON
ejpam-5051	198	1	β̇−1β̇	WORK_OF_ART
ejpam-5051	198	2	a. hence	PERSON
ejpam-5051	199	1	∈	ORG
ejpam-5051	200	1	β̇γ	ORG
ejpam-5051	201	1	r(β̇γ	ORG
ejpam-5051	202	1	β̇γ)(β̇γ)−1	ORG
ejpam-5051	204	1	ββ−1a	CARDINAL
ejpam-5051	208	1	ββ−1a	CARDINAL
ejpam-5051	210	1	∈	ORG
ejpam-5051	210	2	γ̇−1)−1	ORG
ejpam-5051	210	3	γ−1a)−1	ORG
ejpam-5051	210	4	∈	ORG
ejpam-5051	210	5	γ̇	CARDINAL
ejpam-5051	210	6	γ̇−1	ORG
ejpam-5051	211	1	∈	ORG
ejpam-5051	212	1	β̇γ̇)γ̇−1 = β̇(γ̇γ̇−1	PERSON
ejpam-5051	214	1	α̇.	CARDINAL
ejpam-5051	214	2	r(2	NORP
ejpam-5051	214	3	u ×	ORG
ejpam-5051	214	4	∈	ORG
ejpam-5051	214	5	∩ r(2	PERSON
ejpam-5051	216	1	r. s. bongcawel et al	PERSON
ejpam-5051	217	1	j. pure	PERSON
ejpam-5051	217	2	17	CARDINAL
ejpam-5051	217	3	1	CARDINAL
ejpam-5051	217	4	2024	CARDINAL
ejpam-5051	217	5	519	CARDINAL
ejpam-5051	217	6	r.	NORP
ejpam-5051	219	1	⊆	CARDINAL
ejpam-5051	220	1	u × u	ORG
ejpam-5051	220	2	∩ r(2	PERSON
ejpam-5051	220	3	∈	ORG
ejpam-5051	220	4	u ×	ORG
ejpam-5051	222	1	r.	NORP
ejpam-5051	222	2	γ ∈	ORG
ejpam-5051	222	3	∈	ORG
ejpam-5051	223	1	γ ∈	ORG
ejpam-5051	223	2	∈	ORG
ejpam-5051	223	3	γ ∈	ORG
ejpam-5051	224	1	∈	ORG
ejpam-5051	225	1	r. hence	GPE
ejpam-5051	227	1	r.	NORP
ejpam-5051	229	1	γ ∈	ORG
ejpam-5051	232	1	∈	ORG
ejpam-5051	234	1	∈	ORG
ejpam-5051	234	2	∩	ORG
ejpam-5051	237	1	π(v̇	ORG
ejpam-5051	237	2	π(v̇	ORG
ejpam-5051	244	1	r.	NORP
ejpam-5051	248	1	s|πr(b	ORG
ejpam-5051	250	1	⊆	CARDINAL
ejpam-5051	250	2	r.	NORP
ejpam-5051	250	3	w ⊆	PRODUCT
ejpam-5051	250	4	w	ORG
ejpam-5051	251	1	γ ∈	ORG
ejpam-5051	255	1	u ′	ORG
ejpam-5051	255	2	r.	NORP
ejpam-5051	255	3	r.	NORP
ejpam-5051	255	4	r.	NORP
ejpam-5051	256	1	â	GPE
ejpam-5051	256	2	∈	ORG
ejpam-5051	257	1	â	GPE
ejpam-5051	257	2	â	GPE
ejpam-5051	257	3	â	GPE
ejpam-5051	257	4	u ×	ORG
ejpam-5051	257	5	∈	ORG
ejpam-5051	262	1	χ′	ORG
ejpam-5051	263	1	γ(a	PERSON
ejpam-5051	265	1	r. s. bongcawel et al	PERSON
ejpam-5051	266	1	j. pure	PERSON
ejpam-5051	266	2	17	CARDINAL
ejpam-5051	266	3	1	CARDINAL
ejpam-5051	266	4	2024	CARDINAL
ejpam-5051	266	5	519-545 527	MONEY
ejpam-5051	269	1	i((χ	PERSON
ejpam-5051	270	1	γ̇−1	ORG
ejpam-5051	270	2	χ′	ORG
ejpam-5051	272	1	2	CARDINAL
ejpam-5051	276	1	′ 1	DATE
ejpam-5051	276	2	γ̇2	PERSON
ejpam-5051	276	3	2	CARDINAL
ejpam-5051	276	4	′ 1	DATE
ejpam-5051	277	1	γ̇2	PERSON
ejpam-5051	277	2	2	CARDINAL
ejpam-5051	278	1	γ̇2	PERSON
ejpam-5051	278	2	1	CARDINAL
ejpam-5051	278	3	χ′	ORG
ejpam-5051	278	4	2	CARDINAL
ejpam-5051	278	5	2	CARDINAL
ejpam-5051	279	1	′ 1	DATE
ejpam-5051	282	1	γ̇2	PERSON
ejpam-5051	282	2	2	CARDINAL
ejpam-5051	283	1	χ′	ORG
ejpam-5051	283	2	χ′	ORG
ejpam-5051	284	1	i((χ	PERSON
ejpam-5051	285	1	γ̇−1	ORG
ejpam-5051	288	1	χ′	ORG
ejpam-5051	289	1	s((χ, γ̇	CARDINAL
ejpam-5051	290	1	χ′	ORG
ejpam-5051	293	1	χ′	ORG
ejpam-5051	293	2	χ′	ORG
ejpam-5051	298	1	χ′	ORG
ejpam-5051	298	2	χ′	ORG
ejpam-5051	301	1	χ′	ORG
ejpam-5051	303	1	s(γγ′	GPE
ejpam-5051	306	1	χ′	ORG
ejpam-5051	306	2	γ′	DATE
ejpam-5051	308	1	r[(χ′	PERSON
ejpam-5051	308	2	γ̇′)(χ′′	PERSON
ejpam-5051	309	1	χ′	ORG
ejpam-5051	310	1	χ′	ORG
ejpam-5051	313	1	γ̇)(χ′	PERSON
ejpam-5051	313	2	χ′	ORG
ejpam-5051	314	1	γ̇γ̇′)(χ′′	NORP
ejpam-5051	314	2	r. s. bongcawel et al	PERSON
ejpam-5051	315	1	j. pure	PERSON
ejpam-5051	315	2	17	CARDINAL
ejpam-5051	315	3	1	CARDINAL
ejpam-5051	315	4	2024	CARDINAL
ejpam-5051	315	5	519	CARDINAL
ejpam-5051	315	6	∈	ORG
ejpam-5051	316	1	γ̇−1	ORG
ejpam-5051	316	2	γ̇−1)−1	ORG
ejpam-5051	318	1	γ̇−1	ORG
ejpam-5051	321	1	∈	ORG
ejpam-5051	321	2	χ′	ORG
ejpam-5051	322	1	χ′	ORG
ejpam-5051	322	2	γ̇′)−1	ORG
ejpam-5051	322	3	γ̇′)−1	ORG
ejpam-5051	326	1	γ̇)(χ′	PERSON
ejpam-5051	329	1	χ′	ORG
ejpam-5051	330	1	5	CARDINAL
ejpam-5051	333	1	â	GPE
ejpam-5051	333	2	r.	NORP
ejpam-5051	333	3	â ×	GPE
ejpam-5051	333	4	χ′	ORG
ejpam-5051	335	1	∈	ORG
ejpam-5051	335	2	r.	NORP
ejpam-5051	335	3	â ×	GPE
ejpam-5051	336	1	⊆	CARDINAL
ejpam-5051	336	2	â ⋊r	GPE
ejpam-5051	337	1	â	GPE
ejpam-5051	337	2	⊆	CARDINAL
ejpam-5051	337	3	w ′	EVENT
ejpam-5051	337	4	â ×	GPE
ejpam-5051	338	1	′ ⊆	CARDINAL
ejpam-5051	339	1	â ×	ORG
ejpam-5051	340	1	χ′	ORG
ejpam-5051	341	1	r. s. bongcawel et al	PERSON
ejpam-5051	342	1	j. pure	PERSON
ejpam-5051	342	2	17	CARDINAL
ejpam-5051	342	3	1	CARDINAL
ejpam-5051	342	4	2024	CARDINAL
ejpam-5051	342	5	519	CARDINAL
ejpam-5051	343	1	χ′	ORG
ejpam-5051	345	1	⊂ m−1(u	GPE
ejpam-5051	346	1	χ′	ORG
ejpam-5051	347	1	∈	ORG
ejpam-5051	348	1	m(((χ	GPE
ejpam-5051	348	2	χ′	ORG
ejpam-5051	351	1	⊆	CARDINAL
ejpam-5051	351	2	χ′	ORG
ejpam-5051	352	1	χ′	ORG
ejpam-5051	353	1	⊂ m−1(u	GPE
ejpam-5051	357	1	â×r	PRODUCT
ejpam-5051	358	1	i−1(u	ORG
ejpam-5051	359	1	i((χ	PERSON
ejpam-5051	360	1	â×r	PRODUCT
ejpam-5051	360	2	⊆	CARDINAL
ejpam-5051	361	1	w	GPE
ejpam-5051	361	2	w ⊆	MONEY
ejpam-5051	361	3	â	GPE
ejpam-5051	361	4	r.	NORP
ejpam-5051	361	5	χ′	ORG
ejpam-5051	362	1	∩ w	ORG
ejpam-5051	363	1	χ′	ORG
ejpam-5051	364	1	∈	ORG
ejpam-5051	365	1	i((χ′	PERSON
ejpam-5051	366	1	∩ w ⊂	ORG
ejpam-5051	366	2	∩ â	FAC
ejpam-5051	366	3	χ′	ORG
ejpam-5051	366	4	i−1(u	ORG
ejpam-5051	367	1	⊆	CARDINAL
ejpam-5051	367	2	i−1(u	ORG
ejpam-5051	368	1	⊆	CARDINAL
ejpam-5051	368	2	⊆	CARDINAL
ejpam-5051	368	3	∩ w	ORG
ejpam-5051	369	1	â	GPE
ejpam-5051	369	2	r. hence	GPE
ejpam-5051	369	3	â	GPE
ejpam-5051	369	4	r.	NORP
ejpam-5051	369	5	i−1(u	ORG
ejpam-5051	370	1	χ′	ORG
ejpam-5051	371	1	â ×	GPE
ejpam-5051	371	2	∩	PERSON
ejpam-5051	371	3	∈	ORG
ejpam-5051	371	4	χ′	ORG
ejpam-5051	372	1	∩ â	PERSON
ejpam-5051	373	1	χ′	ORG
ejpam-5051	374	1	u ′ and v ′	LAW
ejpam-5051	376	1	â ⋊r	GPE
ejpam-5051	377	1	â×r	PRODUCT
ejpam-5051	380	1	â×r	PRODUCT
ejpam-5051	381	1	b′	PRODUCT
ejpam-5051	381	2	∈	ORG
ejpam-5051	383	1	1	CARDINAL
ejpam-5051	383	2	∈	ORG
ejpam-5051	383	3	∈	ORG
ejpam-5051	384	1	∈	ORG
ejpam-5051	385	1	â ×	GPE
ejpam-5051	385	2	a′	ORG
ejpam-5051	385	3	a′	ORG
ejpam-5051	386	1	a′′	DATE
ejpam-5051	386	2	χ′	ORG
ejpam-5051	387	1	∈	ORG
ejpam-5051	387	2	χ′	ORG
ejpam-5051	388	1	χ′	ORG
ejpam-5051	389	1	χ′	ORG
ejpam-5051	389	2	∈ a′′	DATE
ejpam-5051	389	3	⊂	GPE
ejpam-5051	390	1	∩	ORG
ejpam-5051	391	1	χ′	ORG
ejpam-5051	391	2	χ′	ORG
ejpam-5051	392	1	a′′ ⊂ r1(b	PERCENT
ejpam-5051	393	1	a′′ ⊆	DATE
ejpam-5051	393	2	a′ ⊂	ORG
ejpam-5051	395	1	a′′	DATE
ejpam-5051	396	1	â ⋊r	GPE
ejpam-5051	400	1	u ∈ g(0	ORG
ejpam-5051	402	1	γ ∈	ORG
ejpam-5051	402	2	γ ∈ a. hence	ORG
ejpam-5051	405	1	â ⊆	ORG
ejpam-5051	407	1	∈	ORG
ejpam-5051	411	1	⊆	CARDINAL
ejpam-5051	411	2	â	GPE
ejpam-5051	411	3	â	GPE
ejpam-5051	412	1	â × â	ORG
ejpam-5051	414	1	r. s. bongcawel et al	PERSON
ejpam-5051	415	1	j. pure	PERSON
ejpam-5051	415	2	17	CARDINAL
ejpam-5051	415	3	1	CARDINAL
ejpam-5051	415	4	2024	CARDINAL
ejpam-5051	415	5	519	CARDINAL
ejpam-5051	415	6	γ̇2	PERSON
ejpam-5051	416	1	γ̇2	PERSON
ejpam-5051	417	1	γ̇1	ORG
ejpam-5051	418	1	γ̇2	PERSON
ejpam-5051	418	2	s((χ2	GPE
ejpam-5051	418	3	γ̇2	PERSON
ejpam-5051	421	1	γ̇2	PERSON
ejpam-5051	422	1	γ̇1	ORG
ejpam-5051	423	1	χ1·γ1	ORG
ejpam-5051	424	1	γ̇2	PERSON
ejpam-5051	426	1	γ̇2	PERSON
ejpam-5051	428	1	â ⋊r	GPE
ejpam-5051	428	2	â ∗ g ×	ORG
ejpam-5051	428	3	∈	ORG
ejpam-5051	428	4	∈	ORG
ejpam-5051	428	5	γ ∈	ORG
ejpam-5051	429	1	γ	GPE
ejpam-5051	430	1	γ	GPE
ejpam-5051	432	1	z′	PERSON
ejpam-5051	432	2	z−1	PERSON
ejpam-5051	433	1	χ′	ORG
ejpam-5051	433	2	z′, γ′	ORG
ejpam-5051	433	3	χ′	ORG
ejpam-5051	434	1	γ(a	PERSON
ejpam-5051	436	1	6	CARDINAL
ejpam-5051	439	1	γ	GPE
ejpam-5051	439	2	χ′	ORG
ejpam-5051	439	3	z′, γ′	ORG
ejpam-5051	439	4	χ′	ORG
ejpam-5051	439	5	z′, γ′	ORG
ejpam-5051	440	1	z−1	PERSON
ejpam-5051	440	2	χ′	ORG
ejpam-5051	441	1	γ′	DATE
ejpam-5051	441	2	z−1)′	LANGUAGE
ejpam-5051	441	3	χ′	ORG
ejpam-5051	441	4	z′	ORG
ejpam-5051	441	5	γ′)−1.	GPE
ejpam-5051	442	1	γ	GPE
ejpam-5051	445	1	z′, γ′)	ORG
ejpam-5051	445	2	γ	GPE
ejpam-5051	445	3	χ′	ORG
ejpam-5051	446	1	z′	PERSON
ejpam-5051	448	1	′ 1	DATE
ejpam-5051	448	2	′ 1	DATE
ejpam-5051	448	3	2	CARDINAL
ejpam-5051	449	1	2	CARDINAL
ejpam-5051	449	2	′ 1	DATE
ejpam-5051	449	3	′ 1	DATE
ejpam-5051	450	1	2)),m(((χ1	CARDINAL
ejpam-5051	450	2	′ 1	DATE
ejpam-5051	450	3	′ 1	DATE
ejpam-5051	451	1	′ 1	CARDINAL
ejpam-5051	454	1	2	CARDINAL
ejpam-5051	455	1	γ1)(χ2	PERSON
ejpam-5051	459	1	r(γ3	PERSON
ejpam-5051	461	1	z2	GPE
ejpam-5051	461	2	γ2)(χ3	GPE
ejpam-5051	461	3	z3	PERSON
ejpam-5051	466	1	r. s. bongcawel et al	PERSON
ejpam-5051	467	1	j. pure	PERSON
ejpam-5051	467	2	17	CARDINAL
ejpam-5051	467	3	1	CARDINAL
ejpam-5051	467	4	2024	CARDINAL
ejpam-5051	467	5	519	CARDINAL
ejpam-5051	467	6	545 531	CARDINAL
ejpam-5051	468	1	γ1)(χ2	PERSON
ejpam-5051	468	2	z2	GPE
ejpam-5051	468	3	γ2)(χ3	GPE
ejpam-5051	468	4	z3	PERSON
ejpam-5051	468	5	2	CARDINAL
ejpam-5051	469	1	γ1)(χ2	PERSON
ejpam-5051	469	2	γ2))(χ3	DATE
ejpam-5051	470	1	z1z2z3	NORP
ejpam-5051	470	2	γ1)(χ2	PERSON
ejpam-5051	470	3	γ2)(χ3	GPE
ejpam-5051	470	4	z3	PERSON
ejpam-5051	471	1	γ)−1)−1	ORG
ejpam-5051	471	2	z−1	PERSON
ejpam-5051	471	3	γ−1)−1	DATE
ejpam-5051	471	4	z−1)−1	ORG
ejpam-5051	473	1	z−1	PERSON
ejpam-5051	476	1	γ	GPE
ejpam-5051	477	1	γ	GPE
ejpam-5051	477	2	2	CARDINAL
ejpam-5051	477	3	γ1)(χ2	PERSON
ejpam-5051	480	1	2	CARDINAL
ejpam-5051	480	2	z1z2z3	NORP
ejpam-5051	482	1	γ1)(χ2	PERSON
ejpam-5051	483	1	1	CARDINAL
ejpam-5051	485	1	∈	ORG
ejpam-5051	486	1	â	GPE
ejpam-5051	486	2	â	PERSON
ejpam-5051	487	1	r. s. bongcawel et al	PERSON
ejpam-5051	488	1	j. pure	PERSON
ejpam-5051	488	2	17	CARDINAL
ejpam-5051	488	3	1	CARDINAL
ejpam-5051	488	4	2024	CARDINAL
ejpam-5051	488	5	519	CARDINAL
ejpam-5051	488	6	545 532	CARDINAL
ejpam-5051	489	1	χ′	ORG
ejpam-5051	489	2	z′, γ′	ORG
ejpam-5051	490	1	â	GPE
ejpam-5051	490	2	â	GPE
ejpam-5051	490	3	χ′	ORG
ejpam-5051	491	1	g1 ∩	ORG
ejpam-5051	491	2	z′	PERSON
ejpam-5051	491	3	τâ∗g×t	ORG
ejpam-5051	492	1	χ′	ORG
ejpam-5051	492	2	z′, γ′	ORG
ejpam-5051	492	3	∩	PERSON
ejpam-5051	493	1	7	CARDINAL
ejpam-5051	494	1	â ×	ORG
ejpam-5051	495	1	â ×	ORG
ejpam-5051	495	2	â ∗ g ×	ORG
ejpam-5051	499	1	iso(â∗g×t	GPE
ejpam-5051	500	1	γ	GPE
ejpam-5051	503	1	u ∈ g(0	ORG
ejpam-5051	505	1	u ∈ g(0	ORG
ejpam-5051	506	1	∈	ORG
ejpam-5051	506	2	â ∗ g ×	ORG
ejpam-5051	507	1	8	CARDINAL
ejpam-5051	507	2	χ′	ORG
ejpam-5051	507	3	z′, γ′	ORG
ejpam-5051	508	1	∈	ORG
ejpam-5051	508	2	γ′.	DATE
ejpam-5051	511	1	∈	ORG
ejpam-5051	511	2	χ(a	ORG
ejpam-5051	511	3	1 ∈	CARDINAL
ejpam-5051	511	4	s(a	PERSON
ejpam-5051	512	1	γ ∈	ORG
ejpam-5051	512	2	s(γ	PERSON
ejpam-5051	512	3	s(γ	PERSON
ejpam-5051	513	1	r(a	PERSON
ejpam-5051	515	1	γ	GPE
ejpam-5051	515	2	χ′	ORG
ejpam-5051	515	3	z′, γ′	ORG
ejpam-5051	515	4	χ′	ORG
ejpam-5051	515	5	z′, γ′	ORG
ejpam-5051	516	1	χ(a)−1z′.	PRODUCT
ejpam-5051	516	2	r(a	PERSON
ejpam-5051	516	3	g(2	GPE
ejpam-5051	516	4	∈	ORG
ejpam-5051	516	5	χ′	ORG
ejpam-5051	516	6	z′, γ′	ORG
ejpam-5051	522	1	8	CARDINAL
ejpam-5051	527	1	γ][χ′	ORG
ejpam-5051	527	2	z′	PERSON
ejpam-5051	530	1	z−1	PERSON
ejpam-5051	531	1	χ′	ORG
ejpam-5051	531	2	z′	ORG
ejpam-5051	531	3	χ′	ORG
ejpam-5051	531	4	γ(a	PERSON
ejpam-5051	532	1	3	CARDINAL
ejpam-5051	534	1	1	CARDINAL
ejpam-5051	535	1	r. s. bongcawel	PERSON
ejpam-5051	537	1	j. pure	PERSON
ejpam-5051	537	2	17	CARDINAL
ejpam-5051	537	3	1	CARDINAL
ejpam-5051	537	4	2024	CARDINAL
ejpam-5051	537	5	519	CARDINAL
ejpam-5051	538	1	χ′	ORG
ejpam-5051	538	2	z′	ORG
ejpam-5051	540	1	χ′	ORG
ejpam-5051	540	2	z′	ORG
ejpam-5051	542	1	z−1	PERSON
ejpam-5051	543	1	χ′	ORG
ejpam-5051	544	1	γ′	DATE
ejpam-5051	544	2	z−1)′	LANGUAGE
ejpam-5051	545	1	χ′	ORG
ejpam-5051	545	2	z′, γ′]−1	ORG
ejpam-5051	550	1	z′	PERSON
ejpam-5051	553	1	χ′	ORG
ejpam-5051	553	2	z′	ORG
ejpam-5051	556	1	′ 1	DATE
ejpam-5051	556	2	′ 1	DATE
ejpam-5051	556	3	′ 2	DATE
ejpam-5051	556	4	2	CARDINAL
ejpam-5051	556	5	′ 1	DATE
ejpam-5051	556	6	′ 1	DATE
ejpam-5051	558	1	′ 2	DATE
ejpam-5051	560	1	′ 1	DATE
ejpam-5051	560	2	′ 1	DATE
ejpam-5051	562	1	′ 1	CARDINAL
ejpam-5051	564	1	′ 2	DATE
ejpam-5051	566	1	d(2	PERSON
ejpam-5051	567	1	γ1][χ2	GPE
ejpam-5051	567	2	z2	GPE
ejpam-5051	572	1	r(γ3	PERSON
ejpam-5051	574	1	γ2][χ3	ORG
ejpam-5051	574	2	z3	PERSON
ejpam-5051	580	1	γ1][χ2	GPE
ejpam-5051	580	2	z2	GPE
ejpam-5051	580	3	γ2][χ3	ORG
ejpam-5051	580	4	z3	PERSON
ejpam-5051	581	1	γ1][χ2	GPE
ejpam-5051	581	2	z2	GPE
ejpam-5051	584	1	z1z2z3	NORP
ejpam-5051	585	1	γ1][χ2	GPE
ejpam-5051	586	1	z2	ORG
ejpam-5051	586	2	γ2][χ3	ORG
ejpam-5051	586	3	z3	PERSON
ejpam-5051	587	1	r. s. bongcawel	PERSON
ejpam-5051	589	1	j. pure	PERSON
ejpam-5051	589	2	17	CARDINAL
ejpam-5051	589	3	1	CARDINAL
ejpam-5051	589	4	2024	CARDINAL
ejpam-5051	589	5	519	CARDINAL
ejpam-5051	591	1	z−1	PERSON
ejpam-5051	591	2	γ−1]−1	DATE
ejpam-5051	592	1	z−1)−1	ORG
ejpam-5051	597	1	γ	GPE
ejpam-5051	597	2	z−1	PERSON
ejpam-5051	602	1	d(2	PERSON
ejpam-5051	603	1	γ1][χ2	GPE
ejpam-5051	603	2	z2	GPE
ejpam-5051	606	1	2	CARDINAL
ejpam-5051	606	2	2	CARDINAL
ejpam-5051	607	1	z1z2z3	NORP
ejpam-5051	613	1	γ1][χ2	GPE
ejpam-5051	613	2	z2	GPE
ejpam-5051	616	1	1	CARDINAL
ejpam-5051	623	1	γ	GPE
ejpam-5051	625	1	τâ∗g×t	ORG
ejpam-5051	625	2	u ×	ORG
ejpam-5051	625	3	∈	ORG
ejpam-5051	627	1	χ′	ORG
ejpam-5051	627	2	z′	ORG
ejpam-5051	627	3	γ) ≁	ORG
ejpam-5051	627	4	χ′	ORG
ejpam-5051	627	5	z′, γ′	ORG
ejpam-5051	627	6	â	GPE
ejpam-5051	627	7	z′, γ′	ORG
ejpam-5051	627	8	γ	GPE
ejpam-5051	629	1	z′	PERSON
ejpam-5051	631	1	χ′	ORG
ejpam-5051	631	2	z′	ORG
ejpam-5051	632	1	χ′	ORG
ejpam-5051	632	2	z′, γ′	ORG
ejpam-5051	632	3	χ′	ORG
ejpam-5051	632	4	z′	ORG
ejpam-5051	632	5	∩	ORG
ejpam-5051	634	1	⊆	CARDINAL
ejpam-5051	636	1	d. r. s. bongcawel et al	NORP
ejpam-5051	637	1	j. pure	PERSON
ejpam-5051	637	2	17	CARDINAL
ejpam-5051	637	3	1	CARDINAL
ejpam-5051	637	4	2024	CARDINAL
ejpam-5051	637	5	519	CARDINAL
ejpam-5051	638	1	r−1	GPE
ejpam-5051	645	1	z−1	PERSON
ejpam-5051	647	1	1	DATE
ejpam-5051	650	1	z−1	PERSON
ejpam-5051	651	1	zz−1	ORG
ejpam-5051	652	1	1	CARDINAL
ejpam-5051	653	1	1	DATE
ejpam-5051	655	1	1	CARDINAL
ejpam-5051	657	1	γ = u ∈ g(0	ORG
ejpam-5051	658	1	1	CARDINAL
ejpam-5051	659	1	i(â×	NORP
ejpam-5051	659	2	1	CARDINAL
ejpam-5051	659	3	i(χ	TIME
ejpam-5051	659	4	1	DATE
ejpam-5051	660	1	1	CARDINAL
ejpam-5051	662	1	1	CARDINAL
ejpam-5051	663	1	â ×	ORG
ejpam-5051	663	2	â ∗ g ×	ORG
ejpam-5051	663	3	lemma 7	ORG
ejpam-5051	664	1	â ×	ORG
ejpam-5051	664	2	1	CARDINAL
ejpam-5051	665	1	â ×	ORG
ejpam-5051	666	1	3	CARDINAL
ejpam-5051	666	2	i((χ	PERSON
ejpam-5051	669	1	9	CARDINAL
ejpam-5051	672	1	χ′	ORG
ejpam-5051	672	2	z′, u′	ORG
ejpam-5051	672	3	χ′	ORG
ejpam-5051	672	4	z′	PERSON
ejpam-5051	674	1	χ′	ORG
ejpam-5051	674	2	z′	PERSON
ejpam-5051	675	1	i((χ	PERSON
ejpam-5051	676	1	z′	PERSON
ejpam-5051	678	1	q[χ1	GPE
ejpam-5051	678	2	̸= q[χ2	PERSON
ejpam-5051	679	1	γ̇2	PERSON
ejpam-5051	680	1	z2	GPE
ejpam-5051	680	2	γ	GPE
ejpam-5051	681	1	γ̇1 ̸= γ̇2	PERSON
ejpam-5051	682	1	∈	ORG
ejpam-5051	687	1	â × t	ORG
ejpam-5051	688	1	u ∈ g(0	ORG
ejpam-5051	689	1	g(0	GPE
ejpam-5051	691	1	â	GPE
ejpam-5051	692	1	γ	GPE
ejpam-5051	693	1	â	GPE
ejpam-5051	693	2	r.	NORP
ejpam-5051	693	3	∩ â	PERSON
ejpam-5051	693	4	â ×	GPE
ejpam-5051	694	1	γ	GPE
ejpam-5051	695	1	∈	ORG
ejpam-5051	696	1	∈	ORG
ejpam-5051	696	2	∈	ORG
ejpam-5051	698	1	r. s. bongcawel	PERSON
ejpam-5051	700	1	j. pure	PERSON
ejpam-5051	700	2	17	CARDINAL
ejpam-5051	700	3	1	CARDINAL
ejpam-5051	700	4	2024	CARDINAL
ejpam-5051	700	5	519	CARDINAL
ejpam-5051	700	6	⊆	CARDINAL
ejpam-5051	704	1	2	CARDINAL
ejpam-5051	704	2	d(2	PERSON
ejpam-5051	704	3	χ′	ORG
ejpam-5051	704	4	z′, u′	ORG
ejpam-5051	705	1	χ′	ORG
ejpam-5051	705	2	z′	PERSON
ejpam-5051	706	1	d(2	PERSON
ejpam-5051	707	1	d(2	PERSON
ejpam-5051	707	2	χ′	ORG
ejpam-5051	707	3	z′	ORG
ejpam-5051	708	1	χ′	ORG
ejpam-5051	710	1	i((χ	PERSON
ejpam-5051	710	2	z′	PERSON
ejpam-5051	713	1	i((χ	PERSON
ejpam-5051	713	2	z′	PERSON
ejpam-5051	715	1	u][χ′	ORG
ejpam-5051	715	2	z′	ORG
ejpam-5051	718	1	z	ORG
ejpam-5051	718	2	γ][χ′	ORG
ejpam-5051	718	3	z′	PERSON
ejpam-5051	718	4	z′	PERSON
ejpam-5051	718	5	γ̇)(χ′	PERSON
ejpam-5051	721	1	â ×	ORG
ejpam-5051	722	1	9	CARDINAL
ejpam-5051	724	1	â	GPE
ejpam-5051	726	1	â	GPE
ejpam-5051	731	1	9	CARDINAL
ejpam-5051	733	1	π−1	PERSON
ejpam-5051	733	2	â	GPE
ejpam-5051	734	1	∈	ORG
ejpam-5051	736	1	â	GPE
ejpam-5051	736	2	r.	NORP
ejpam-5051	736	3	q(y	GPE
ejpam-5051	736	4	q−1	PRODUCT
ejpam-5051	738	1	â	GPE
ejpam-5051	738	2	r.	NORP
ejpam-5051	738	3	first	ORDINAL
ejpam-5051	739	1	4	CARDINAL
ejpam-5051	751	1	r. s. bongcawel	PERSON
ejpam-5051	753	1	j. pure	PERSON
ejpam-5051	753	2	17	CARDINAL
ejpam-5051	753	3	1	CARDINAL
ejpam-5051	753	4	2024	CARDINAL
ejpam-5051	753	5	519	CARDINAL
ejpam-5051	754	1	z2	GPE
ejpam-5051	757	1	∈	ORG
ejpam-5051	757	2	χ(a	ORG
ejpam-5051	757	3	1	CARDINAL
ejpam-5051	757	4	1)z2	CARDINAL
ejpam-5051	758	1	a′	ORG
ejpam-5051	758	2	∈	PRODUCT
ejpam-5051	761	1	9	CARDINAL
ejpam-5051	762	1	∈	ORG
ejpam-5051	763	1	d.	NORP
ejpam-5051	764	1	5	CARDINAL
ejpam-5051	765	1	i(r(β	GPE
ejpam-5051	765	2	z)pα(β	ORG
ejpam-5051	765	3	q−1(bα	GPE
ejpam-5051	767	1	∈	ORG
ejpam-5051	767	2	pα((χ	PERSON
ejpam-5051	770	1	d.	NORP
ejpam-5051	771	1	â	GPE
ejpam-5051	773	1	∈	ORG
ejpam-5051	773	2	∩ â	PERSON
ejpam-5051	773	3	r.	NORP
ejpam-5051	773	4	∈	ORG
ejpam-5051	773	5	â	GPE
ejpam-5051	773	6	r.	NORP
ejpam-5051	780	1	q−1(βα	PERSON
ejpam-5051	781	1	⊆	CARDINAL
ejpam-5051	781	2	â	GPE
ejpam-5051	781	3	q−1(βα	PERSON
ejpam-5051	781	4	⊆	CARDINAL
ejpam-5051	781	5	d.	NORP
ejpam-5051	781	6	q−1(βα	PERSON
ejpam-5051	782	1	u ′	ORG
ejpam-5051	782	2	′/	NORP
ejpam-5051	782	3	∈	ORG
ejpam-5051	782	4	u ′	ORG
ejpam-5051	783	1	u ′	ORG
ejpam-5051	784	1	u ′	EVENT
ejpam-5051	784	2	â	GPE
ejpam-5051	786	1	∈ â	ORG
ejpam-5051	786	2	θ(χ	PRODUCT
ejpam-5051	786	3	∈	ORG
ejpam-5051	787	1	′/	NORP
ejpam-5051	787	2	u ′	DATE
ejpam-5051	788	1	∈	ORG
ejpam-5051	788	2	γ ∈	ORG
ejpam-5051	791	1	q−1(βα	PERSON
ejpam-5051	793	1	t ′	DATE
ejpam-5051	795	1	r. s. bongcawel et al	PERSON
ejpam-5051	796	1	j. pure	PERSON
ejpam-5051	796	2	17	CARDINAL
ejpam-5051	796	3	1	CARDINAL
ejpam-5051	796	4	2024	CARDINAL
ejpam-5051	796	5	519	CARDINAL
ejpam-5051	796	6	∈	ORG
ejpam-5051	796	7	t ′	DATE
ejpam-5051	797	1	∈	ORG
ejpam-5051	798	1	∩	PERSON
ejpam-5051	798	2	∈	ORG
ejpam-5051	798	3	â	GPE
ejpam-5051	798	4	∈	ORG
ejpam-5051	798	5	r.	NORP
ejpam-5051	798	6	π−1	PERSON
ejpam-5051	800	1	q−1(bα	GPE
ejpam-5051	802	1	6	CARDINAL
ejpam-5051	803	1	z)[χ	PERSON
ejpam-5051	806	1	z′ ∈	PERSON
ejpam-5051	808	1	z′	PERSON
ejpam-5051	809	1	r(γ)γ	NORP
ejpam-5051	811	1	z′	PERSON
ejpam-5051	813	1	γ]i((χ	NORP
ejpam-5051	813	2	z′	PERSON
ejpam-5051	814	1	z′	PERSON
ejpam-5051	820	1	z′	PERSON
ejpam-5051	820	2	theorems 4	ORG
ejpam-5051	820	3	5	DATE
ejpam-5051	820	4	6	CARDINAL
ejpam-5051	820	5	1	CARDINAL
ejpam-5051	822	1	4.	CARDINAL
ejpam-5051	822	2	steinberg	PERSON
ejpam-5051	822	3	steinberg	PERSON
ejpam-5051	822	4	= z. let	PERSON
ejpam-5051	823	1	= z.	PERSON
ejpam-5051	823	2	multiplicative	ORG
ejpam-5051	823	3	−1	CARDINAL
ejpam-5051	823	4	1	CARDINAL
ejpam-5051	824	1	s(y	PERSON
ejpam-5051	825	1	y ∈	PERSON
ejpam-5051	826	1	0	CARDINAL
ejpam-5051	829	1	0	CARDINAL
ejpam-5051	829	2	r(x	WORK_OF_ART
ejpam-5051	830	1	0	CARDINAL
ejpam-5051	831	1	z	ORG
ejpam-5051	832	1	0̇	CARDINAL
ejpam-5051	833	1	+ z.	PERSON
ejpam-5051	833	2	a0 = z. also	PERSON
ejpam-5051	833	3	χ2|χi	PERSON
ejpam-5051	833	4	1,−1	CARDINAL
ejpam-5051	833	5	1	CARDINAL
ejpam-5051	833	6	2	CARDINAL
ejpam-5051	833	7	1	CARDINAL
ejpam-5051	833	8	1	CARDINAL
ejpam-5051	833	9	∈	ORG
ejpam-5051	833	10	∈	ORG
ejpam-5051	833	11	r. s. bongcawel	PERSON
ejpam-5051	835	1	j. pure	PERSON
ejpam-5051	835	2	17	CARDINAL
ejpam-5051	835	3	1	CARDINAL
ejpam-5051	835	4	2024	CARDINAL
ejpam-5051	835	5	519	CARDINAL
ejpam-5051	835	6	545 539	CARDINAL
ejpam-5051	836	1	∈	ORG
ejpam-5051	836	2	1	DATE
ejpam-5051	836	3	1	CARDINAL
ejpam-5051	838	1	1	CARDINAL
ejpam-5051	838	2	1	CARDINAL
ejpam-5051	840	1	1	CARDINAL
ejpam-5051	841	1	1	CARDINAL
ejpam-5051	842	1	1	CARDINAL
ejpam-5051	844	1	1	CARDINAL
ejpam-5051	844	2	2	DATE
ejpam-5051	844	3	1	CARDINAL
ejpam-5051	844	4	χ′	ORG
ejpam-5051	844	5	z′	ORG
ejpam-5051	847	1	z′	PERSON
ejpam-5051	847	2	x′	DATE
ejpam-5051	847	3	x′)|∃	ORG
ejpam-5051	848	1	∈	ORG
ejpam-5051	848	2	1	CARDINAL
ejpam-5051	849	1	z′	PERSON
ejpam-5051	849	2	x′	DATE
ejpam-5051	849	3	1	CARDINAL
ejpam-5051	849	4	x′	DATE
ejpam-5051	849	5	1	CARDINAL
ejpam-5051	849	6	1	CARDINAL
ejpam-5051	849	7	1	CARDINAL
ejpam-5051	849	8	1,−1	CARDINAL
ejpam-5051	849	9	1	CARDINAL
ejpam-5051	849	10	0	DATE
ejpam-5051	849	11	1	CARDINAL
ejpam-5051	849	12	1	CARDINAL
ejpam-5051	850	1	χ′	ORG
ejpam-5051	850	2	z′	ORG
ejpam-5051	850	3	∈	ORG
ejpam-5051	852	1	z′	PERSON
ejpam-5051	852	2	x′	DATE
ejpam-5051	852	3	x′)|∃	ORG
ejpam-5051	852	4	∈	ORG
ejpam-5051	853	1	1	CARDINAL
ejpam-5051	854	1	z′	PERSON
ejpam-5051	854	2	x′	DATE
ejpam-5051	854	3	x′)|∃	ORG
ejpam-5051	854	4	x′	DATE
ejpam-5051	854	5	x)|a	PERSON
ejpam-5051	854	6	1	CARDINAL
ejpam-5051	854	7	0	DATE
ejpam-5051	854	8	1	CARDINAL
ejpam-5051	854	9	1	CARDINAL
ejpam-5051	855	1	1	CARDINAL
ejpam-5051	856	1	1	CARDINAL
ejpam-5051	857	1	1	CARDINAL
ejpam-5051	859	1	1	CARDINAL
ejpam-5051	860	1	1	CARDINAL
ejpam-5051	861	1	1	CARDINAL
ejpam-5051	864	1	0]−1[χ1,−1	CARDINAL
ejpam-5051	865	1	0	DATE
ejpam-5051	865	2	0][χ1,−1	DATE
ejpam-5051	866	1	0(0	CARDINAL
ejpam-5051	868	1	1	CARDINAL
ejpam-5051	871	1	0][χ1,−1	DATE
ejpam-5051	872	1	0	DATE
ejpam-5051	872	2	r. s. bongcawel et al	PERSON
ejpam-5051	873	1	j. pure	PERSON
ejpam-5051	873	2	17	CARDINAL
ejpam-5051	873	3	1	CARDINAL
ejpam-5051	873	4	2024	CARDINAL
ejpam-5051	873	5	519	CARDINAL
ejpam-5051	875	1	1	CARDINAL
ejpam-5051	877	1	0]−1[χ2,−1	CARDINAL
ejpam-5051	878	1	0	DATE
ejpam-5051	879	1	0(0	CARDINAL
ejpam-5051	881	1	1	CARDINAL
ejpam-5051	885	1	0][χ2	CARDINAL
ejpam-5051	885	2	0	DATE
ejpam-5051	887	1	1	CARDINAL
ejpam-5051	888	1	1	DATE
ejpam-5051	891	1	1	CARDINAL
ejpam-5051	891	2	1	CARDINAL
ejpam-5051	894	1	1	CARDINAL
ejpam-5051	894	2	1	CARDINAL
ejpam-5051	895	1	1{z	CARDINAL
ejpam-5051	895	2	z.	PERSON
ejpam-5051	895	3	steinberg	PERSON
ejpam-5051	896	1	a1a21{z1+z2	DATE
ejpam-5051	897	1	2	CARDINAL
ejpam-5051	897	2	0	DATE
ejpam-5051	897	3	0	CARDINAL
ejpam-5051	898	1	0	DATE
ejpam-5051	898	2	0	DATE
ejpam-5051	898	3	0	DATE
ejpam-5051	898	4	0	DATE
ejpam-5051	898	5	0	DATE
ejpam-5051	898	6	0	DATE
ejpam-5051	898	7	r. s. bongcawel et al	PERSON
ejpam-5051	899	1	j. pure	PERSON
ejpam-5051	899	2	17	CARDINAL
ejpam-5051	899	3	1	CARDINAL
ejpam-5051	899	4	2024	CARDINAL
ejpam-5051	899	5	519	CARDINAL
ejpam-5051	899	6	0	DATE
ejpam-5051	900	1	0	DATE
ejpam-5051	900	2	0	DATE
ejpam-5051	900	3	−1	DATE
ejpam-5051	900	4	0	DATE
ejpam-5051	900	5	0	DATE
ejpam-5051	900	6	0	DATE
ejpam-5051	900	7	0	DATE
ejpam-5051	901	1	0	DATE
ejpam-5051	901	2	0	DATE
ejpam-5051	902	1	0	DATE
ejpam-5051	902	2	0	DATE
ejpam-5051	903	1	0	DATE
ejpam-5051	903	2	0	DATE
ejpam-5051	903	3	0̇)(χ2	GPE
ejpam-5051	903	4	0	DATE
ejpam-5051	903	5	0	DATE
ejpam-5051	903	6	0	DATE
ejpam-5051	904	1	0	DATE
ejpam-5051	904	2	0̇)(χ2	GPE
ejpam-5051	904	3	0	DATE
ejpam-5051	904	4	−1	DATE
ejpam-5051	904	5	0	DATE
ejpam-5051	904	6	0̇)(χ2	CARDINAL
ejpam-5051	904	7	0	DATE
ejpam-5051	904	8	0	DATE
ejpam-5051	904	9	0	DATE
ejpam-5051	905	1	0	DATE
ejpam-5051	905	2	0	DATE
ejpam-5051	906	1	7	CARDINAL
ejpam-5051	911	1	∈	ORG
ejpam-5051	911	2	∈	ORG
ejpam-5051	912	1	n ∈ z	ORG
ejpam-5051	914	1	z(f + g)(r((χi	DATE
ejpam-5051	916	1	+ zg(r((χi	PERSON
ejpam-5051	921	1	z	ORG
ejpam-5051	922	1	zf(r((χi	GPE
ejpam-5051	923	1	χ′	ORG
ejpam-5051	923	2	χ′	ORG
ejpam-5051	924	1	′)f	PERSON
ejpam-5051	924	2	′′)−1	ORG
ejpam-5051	924	3	∈	ORG
ejpam-5051	924	4	r(χi	ORG
ejpam-5051	925	1	0̇)(χ2	GPE
ejpam-5051	928	1	0̇)))g(r((χ1	DATE
ejpam-5051	929	1	r. s. bongcawel	PERSON
ejpam-5051	931	1	j. pure	PERSON
ejpam-5051	931	2	17	CARDINAL
ejpam-5051	931	3	1	CARDINAL
ejpam-5051	931	4	2024	CARDINAL
ejpam-5051	931	5	519	CARDINAL
ejpam-5051	931	6	545 542	CARDINAL
ejpam-5051	931	7	γ])(χ2	PERSON
ejpam-5051	932	1	f)(χ2	GPE
ejpam-5051	933	1	f)(χ2	GPE
ejpam-5051	934	1	f)(χ2	GPE
ejpam-5051	934	2	zf(r((χ2	PERSON
ejpam-5051	934	3	0̇)))g(r((χ2	DATE
ejpam-5051	935	1	∈	ORG
ejpam-5051	935	2	zf(r((χi	GPE
ejpam-5051	935	3	γ̇)))zg(r((χi	GPE
ejpam-5051	936	1	z	ORG
ejpam-5051	938	1	0	CARDINAL
ejpam-5051	938	2	d.	NORP
ejpam-5051	938	3	zf(r((χi	GPE
ejpam-5051	939	1	γ ∈ z	ORG
ejpam-5051	940	1	0	CARDINAL
ejpam-5051	940	2	â	GPE
ejpam-5051	940	3	â	PERSON
ejpam-5051	940	4	∈ â	ORG
ejpam-5051	940	5	r((χi	ORG
ejpam-5051	942	1	∈ â	ORG
ejpam-5051	943	1	0	CARDINAL
ejpam-5051	943	2	0	CARDINAL
ejpam-5051	945	1	â	PERSON
ejpam-5051	946	1	1	CARDINAL
ejpam-5051	947	1	z.	PERSON
ejpam-5051	947	2	fh	ORG
ejpam-5051	948	1	â ⋊r	GPE
ejpam-5051	948	2	fh	ORG
ejpam-5051	949	1	∈	ORG
ejpam-5051	951	1	= h([χi	ORG
ejpam-5051	952	1	1	CARDINAL
ejpam-5051	952	2	1	CARDINAL
ejpam-5051	952	3	fh(χ2	NORP
ejpam-5051	952	4	1	DATE
ejpam-5051	952	5	1	DATE
ejpam-5051	953	1	0	CARDINAL
ejpam-5051	953	2	∈ â	ORG
ejpam-5051	956	1	fh ∈	ORG
ejpam-5051	957	1	z	ORG
ejpam-5051	958	1	r. s. bongcawel et al	PERSON
ejpam-5051	959	1	j. pure	PERSON
ejpam-5051	959	2	17	CARDINAL
ejpam-5051	959	3	1	CARDINAL
ejpam-5051	959	4	2024	CARDINAL
ejpam-5051	959	5	519	CARDINAL
ejpam-5051	960	1	γ	GPE
ejpam-5051	960	2	z	ORG
ejpam-5051	965	1	â	GPE
ejpam-5051	966	1	az(â⋊r	PERSON
ejpam-5051	966	2	1{(χ	CARDINAL
ejpam-5051	966	3	1	CARDINAL
ejpam-5051	966	4	0	CARDINAL
ejpam-5051	968	1	â	GPE
ejpam-5051	968	2	1{(χ1,0̇	DATE
ejpam-5051	968	3	1{(χ2,0̇	DATE
ejpam-5051	971	1	steinberg	PERSON
ejpam-5051	971	2	1{(χ1,0̇	DATE
ejpam-5051	971	3	1{(χ2,0̇	DATE
ejpam-5051	972	1	â	GPE
ejpam-5051	972	2	2	CARDINAL
ejpam-5051	973	1	1{z	CARDINAL
ejpam-5051	976	1	section 3	LAW
ejpam-5051	976	2	0	CARDINAL
ejpam-5051	979	1	4	CARDINAL
ejpam-5051	980	1	commutative ring	ORG
ejpam-5051	983	1	â	GPE
ejpam-5051	983	2	r.	NORP
ejpam-5051	983	3	â	GPE
ejpam-5051	983	4	steinberg	PERSON
ejpam-5051	983	5	â	GPE
ejpam-5051	985	1	544	CARDINAL
ejpam-5051	985	2	msu-iligan institute of technology	ORG
ejpam-5051	986	1	1	CARDINAL
ejpam-5051	986	2	b. armstrong	PERSON
ejpam-5051	986	3	l. orloff clark	PERSON
ejpam-5051	986	4	k. courtney	PERSON
ejpam-5051	986	5	y. lin	PERSON
ejpam-5051	986	6	k. mccormick	PERSON
ejpam-5051	986	7	j. ramagge	PERSON
ejpam-5051	987	1	steinberg algebras	PERSON
ejpam-5051	987	2	226:6–28	CARDINAL
ejpam-5051	987	3	2022	CARDINAL
ejpam-5051	988	1	2	CARDINAL
ejpam-5051	988	2	h. brandt	PERSON
ejpam-5051	989	1	idealtheorie	PERSON
ejpam-5051	990	1	mathematische annalen	PERSON
ejpam-5051	990	2	99:1–29,	DATE
ejpam-5051	990	3	1928	DATE
ejpam-5051	991	1	3	CARDINAL
ejpam-5051	991	2	m.a rieffel	PERSON
ejpam-5051	993	1	71:394–407	CARDINAL
ejpam-5051	993	2	1977	DATE
ejpam-5051	994	1	4	CARDINAL
ejpam-5051	994	2	s. eilenberg	PERSON
ejpam-5051	994	3	s. maclane	PERSON
ejpam-5051	996	1	american mathematical society	ORG
ejpam-5051	996	2	58:231–294	CARDINAL
ejpam-5051	997	1	5	CARDINAL
ejpam-5051	997	2	j. feldman	PERSON
ejpam-5051	997	3	moore	PERSON
ejpam-5051	998	1	ergodic equivalence	ORG
ejpam-5051	998	2	von neumann algebras	PERSON
ejpam-5051	998	3	i. american	PERSON
ejpam-5051	998	4	234:289–324, 1977	DATE
ejpam-5051	999	1	6	CARDINAL
ejpam-5051	999	2	j. feldman	PERSON
ejpam-5051	999	3	moore	PERSON
ejpam-5051	1000	1	ergodic equivalence	ORG
ejpam-5051	1000	2	von neumann algebras	PERSON
ejpam-5051	1002	1	american	NORP
ejpam-5051	1002	2	1977	DATE
ejpam-5051	1003	1	7	CARDINAL
ejpam-5051	1003	2	p. hahn	PERSON
ejpam-5051	1004	1	haar	PERSON
ejpam-5051	1005	1	american mathematical society	ORG
ejpam-5051	1005	2	242:1–33, 1978	DATE
ejpam-5051	1006	1	8	CARDINAL
ejpam-5051	1006	2	f. bruno leonardo macedo	PERSON
ejpam-5051	1006	3	c. bruno tadeu	PERSON
ejpam-5051	1007	1	jordan	GPE
ejpam-5051	1007	2	bulletin	PERSON
ejpam-5051	1007	3	iranian	NORP
ejpam-5051	1007	4	48:1679–1690	CARDINAL
ejpam-5051	1007	5	2022	CARDINAL
ejpam-5051	1008	1	9	CARDINAL
ejpam-5051	1008	2	i. raebum	PERSON
ejpam-5051	1008	3	j.l. taylor	ORG
ejpam-5051	1010	1	australian	NORP
ejpam-5051	1010	2	38:394–407	CARDINAL
ejpam-5051	1010	3	1985	DATE
ejpam-5051	1011	1	10	CARDINAL
ejpam-5051	1011	2	j. renault	PERSON
ejpam-5051	1012	1	groupoid	ORG
ejpam-5051	1012	2	berlin	GPE
ejpam-5051	1012	3	germany	GPE
ejpam-5051	1012	4	1980	DATE
ejpam-5051	1013	1	11	CARDINAL
ejpam-5051	1013	2	j. renault	PERSON
ejpam-5051	1014	1	cartan subalgebras	ORG
ejpam-5051	1014	2	c*-algebras	GPE
ejpam-5051	1015	1	61:29	TIME
ejpam-5051	1015	2	63, 2008	DATE
ejpam-5051	1016	1	12	CARDINAL
ejpam-5051	1016	2	s. rigby	PERSON
ejpam-5051	1017	1	steinberg algebras	PERSON
ejpam-5051	1017	2	leavitt	PERSON
ejpam-5051	1018	1	masteral thesis	ORG
ejpam-5051	1018	2	university of cape town	ORG
ejpam-5051	1018	3	2018	DATE
ejpam-5051	1019	1	13	CARDINAL
ejpam-5051	1019	2	n. ruth	PERSON
ejpam-5051	1019	3	m. ferreira	PERSON
ejpam-5051	1019	4	b. leonardo	PERSON
ejpam-5051	1019	5	g. henrique	PERSON
ejpam-5051	1019	6	c. bruno tadeu	PERSON
ejpam-5051	1021	1	50:5145–5154	CARDINAL
ejpam-5051	1021	2	2022	CARDINAL
ejpam-5051	1022	1	14	CARDINAL
ejpam-5051	1023	1	de baum	PERSON
ejpam-5051	1024	1	17:215–264, 1999	DATE
ejpam-5051	1025	1	545	CARDINAL
ejpam-5051	1025	2	15	CARDINAL
ejpam-5051	1025	3	d. williams	PERSON
ejpam-5051	1025	4	j. renault	PERSON
ejpam-5051	1028	1	american	NORP
ejpam-5051	1028	2	348:3621–3641, 1996	DATE