id	sid	eid	entity	type
ejpam-4827	1	1	european journal	ORG
ejpam-4827	2	1	16	CARDINAL
ejpam-4827	2	2	3	CARDINAL
ejpam-4827	2	3	2023	CARDINAL
ejpam-4827	2	4	1878-1893	DATE
ejpam-4827	2	5	1307-5543	DATE
ejpam-4827	2	6	new york	GPE
ejpam-4827	2	7	1	CARDINAL
ejpam-4827	2	8	university of khartoum	ORG
ejpam-4827	2	9	sudan 2	ORG
ejpam-4827	2	10	najran university	ORG
ejpam-4827	2	11	saudi arabia	GPE
ejpam-4827	3	1	two	CARDINAL
ejpam-4827	3	2	σ	ORG
ejpam-4827	10	1	2020	DATE
ejpam-4827	10	2	16s34	CARDINAL
ejpam-4827	10	3	16s36	CARDINAL
ejpam-4827	10	4	20m25	CARDINAL
ejpam-4827	10	5	1	CARDINAL
ejpam-4827	11	1	mason	ORG
ejpam-4827	11	2	13	CARDINAL
ejpam-4827	11	3	15	CARDINAL
ejpam-4827	11	4	24	CARDINAL
ejpam-4827	12	1	r.	NORP
ejpam-4827	12	2	24	CARDINAL
ejpam-4827	12	3	∈	ORG
ejpam-4827	12	4	xry	PERSON
ejpam-4827	13	1	⊆	CARDINAL
ejpam-4827	13	2	zero	CARDINAL
ejpam-4827	13	3	24	CARDINAL
ejpam-4827	13	4	zero	CARDINAL
ejpam-4827	13	5	∈	ORG
ejpam-4827	13	6	0	CARDINAL
ejpam-4827	13	7	0	CARDINAL
ejpam-4827	15	1	rege	ORG
ejpam-4827	16	1	21	CARDINAL
ejpam-4827	17	1	0	CARDINAL
ejpam-4827	17	2	f(x	ORG
ejpam-4827	18	1	2 +	DATE
ejpam-4827	19	1	2+ ·	DATE
ejpam-4827	19	2	∈	ORG
ejpam-4827	20	1	21	CARDINAL
ejpam-4827	20	2	0	CARDINAL
ejpam-4827	20	3	0	CARDINAL
ejpam-4827	21	1	https://doi.org/10.29020/nybg.ejpam.v16i3.4827	NORP
ejpam-4827	21	2	emali@nu.edu.sa	PERSON
ejpam-4827	21	3	e. ali	PERSON
ejpam-4827	21	4	1878	DATE
ejpam-4827	22	1	2023	CARDINAL
ejpam-4827	23	1	e. ali / eur	PERSON
ejpam-4827	24	1	j. pure	PERSON
ejpam-4827	24	2	16	CARDINAL
ejpam-4827	24	3	3	CARDINAL
ejpam-4827	24	4	2023	CARDINAL
ejpam-4827	24	5	1878-1893 1879	DATE
ejpam-4827	24	6	r.	NORP
ejpam-4827	25	1	⊆	CARDINAL
ejpam-4827	25	2	∈	ORG
ejpam-4827	25	3	0	DATE
ejpam-4827	27	1	6	CARDINAL
ejpam-4827	28	1	xry	DATE
ejpam-4827	28	2	0	CARDINAL
ejpam-4827	28	3	∈	ORG
ejpam-4827	29	1	9	CARDINAL
ejpam-4827	29	2	f(x	ORG
ejpam-4827	30	1	2 +	DATE
ejpam-4827	31	1	2 + ·	DATE
ejpam-4827	33	1	0	CARDINAL
ejpam-4827	33	2	j.	PERSON
ejpam-4827	34	1	10	CARDINAL
ejpam-4827	35	1	22	CARDINAL
ejpam-4827	35	2	∈	ORG
ejpam-4827	35	3	∈	ORG
ejpam-4827	40	1	3	CARDINAL
ejpam-4827	40	2	g ∈	PERSON
ejpam-4827	44	1	1	CARDINAL
ejpam-4827	49	1	3	CARDINAL
ejpam-4827	50	1	1	CARDINAL
ejpam-4827	50	2	22	CARDINAL
ejpam-4827	50	3	15	CARDINAL
ejpam-4827	50	4	13	CARDINAL
ejpam-4827	50	5	4	CARDINAL
ejpam-4827	50	6	5	CARDINAL
ejpam-4827	50	7	2	CARDINAL
ejpam-4827	50	8	18	CARDINAL
ejpam-4827	53	1	r.	NORP
ejpam-4827	53	2	aut(r	PERSON
ejpam-4827	54	1	∈	ORG
ejpam-4827	54	2	σ	CARDINAL
ejpam-4827	55	1	∈	ORG
ejpam-4827	56	1	σ	ORG
ejpam-4827	58	1	xgσg(yh))(gh	GPE
ejpam-4827	60	1	f(x	ORG
ejpam-4827	60	2	f(x	ORG
ejpam-4827	62	1	two	CARDINAL
ejpam-4827	62	2	σ	ORG
ejpam-4827	66	1	e. ali	PERSON
ejpam-4827	67	1	j. pure	PERSON
ejpam-4827	67	2	16	CARDINAL
ejpam-4827	67	3	3	CARDINAL
ejpam-4827	67	4	2023	CARDINAL
ejpam-4827	67	5	1878-1893	DATE
ejpam-4827	71	1	two	CARDINAL
ejpam-4827	71	2	xy	ORG
ejpam-4827	72	1	xy	ORG
ejpam-4827	74	1	zero	CARDINAL
ejpam-4827	75	1	17	CARDINAL
ejpam-4827	75	2	19	CARDINAL
ejpam-4827	76	1	monoids	GPE
ejpam-4827	78	1	r.	NORP
ejpam-4827	79	1	2	CARDINAL
ejpam-4827	80	1	2.3	CARDINAL
ejpam-4827	80	2	18	CARDINAL
ejpam-4827	80	3	y ∈ r.	PERSON
ejpam-4827	81	1	1	CARDINAL
ejpam-4827	82	1	0	CARDINAL
ejpam-4827	83	1	0	CARDINAL
ejpam-4827	83	2	+ bngn	PERSON
ejpam-4827	84	1	ψ(r	ORG
ejpam-4827	84	2	0	CARDINAL
ejpam-4827	84	3	1 ≤	QUANTITY
ejpam-4827	84	4	j ≤ m. definition	PERSON
ejpam-4827	84	5	2	CARDINAL
ejpam-4827	85	1	20	CARDINAL
ejpam-4827	86	1	φ	PERSON
ejpam-4827	86	2	∈	ORG
ejpam-4827	86	3	0	CARDINAL
ejpam-4827	87	1	16	CARDINAL
ejpam-4827	87	2	nasr-isfahani	PERSON
ejpam-4827	88	1	y ∈ r.	PERSON
ejpam-4827	88	2	8	CARDINAL
ejpam-4827	89	1	16	CARDINAL
ejpam-4827	90	1	∈	ORG
ejpam-4827	92	1	e. ali	PERSON
ejpam-4827	93	1	j. pure	PERSON
ejpam-4827	93	2	16	CARDINAL
ejpam-4827	93	3	3	CARDINAL
ejpam-4827	93	4	2023	CARDINAL
ejpam-4827	93	5	1878-1893	DATE
ejpam-4827	93	6	1	CARDINAL
ejpam-4827	97	1	σ	ORG
ejpam-4827	97	2	1	CARDINAL
ejpam-4827	97	3	0)(0	CARDINAL
ejpam-4827	97	4	1	CARDINAL
ejpam-4827	97	5	0	CARDINAL
ejpam-4827	97	6	0	DATE
ejpam-4827	97	7	1	CARDINAL
ejpam-4827	97	8	1	CARDINAL
ejpam-4827	98	1	1	CARDINAL
ejpam-4827	100	1	φ	ORG
ejpam-4827	100	2	1	CARDINAL
ejpam-4827	100	3	1	CARDINAL
ejpam-4827	100	4	0	CARDINAL
ejpam-4827	100	5	1)e	CARDINAL
ejpam-4827	100	6	1	CARDINAL
ejpam-4827	101	1	0	CARDINAL
ejpam-4827	103	1	1	CARDINAL
ejpam-4827	107	1	1	CARDINAL
ejpam-4827	107	2	∈	ORG
ejpam-4827	108	1	1 ≤ k	QUANTITY
ejpam-4827	110	1	o(h	PERSON
ejpam-4827	111	1	g ∈	PERSON
ejpam-4827	115	1	φ	GPE
ejpam-4827	118	1	0	CARDINAL
ejpam-4827	119	1	0	CARDINAL
ejpam-4827	120	1	1 ≤	QUANTITY
ejpam-4827	120	2	bjσgj	GPE
ejpam-4827	123	1	∈	ORG
ejpam-4827	123	2	ae = a.	ORG
ejpam-4827	123	3	i ∩ j	ORG
ejpam-4827	123	4	∈	ORG
ejpam-4827	123	5	⊆	CARDINAL
ejpam-4827	123	6	a(i ∩ j	PRODUCT
ejpam-4827	124	1	annihilator lr(ra	PERSON
ejpam-4827	124	2	∈	ORG
ejpam-4827	124	3	r.	NORP
ejpam-4827	124	4	1	CARDINAL
ejpam-4827	125	1	23	CARDINAL
ejpam-4827	126	1	1	CARDINAL
ejpam-4827	131	1	∈	ORG
ejpam-4827	132	1	1	CARDINAL
ejpam-4827	132	2	2	DATE
ejpam-4827	134	1	n. lemma 2	PERSON
ejpam-4827	135	1	1.13	CARDINAL
ejpam-4827	135	2	14	CARDINAL
ejpam-4827	138	1	3	CARDINAL
ejpam-4827	139	1	2.2	CARDINAL
ejpam-4827	140	1	7	CARDINAL
ejpam-4827	141	1	n ≥ 2	ORG
ejpam-4827	142	1	σn−1	ORG
ejpam-4827	144	1	4	CARDINAL
ejpam-4827	145	1	1.1	CARDINAL
ejpam-4827	145	2	5	CARDINAL
ejpam-4827	147	1	gx	ORG
ejpam-4827	148	1	e. ali / eur	PERSON
ejpam-4827	149	1	j. pure	PERSON
ejpam-4827	149	2	16	CARDINAL
ejpam-4827	149	3	3	CARDINAL
ejpam-4827	149	4	2023	CARDINAL
ejpam-4827	149	5	1878-1893	DATE
ejpam-4827	149	6	1	CARDINAL
ejpam-4827	153	1	φ	ORG
ejpam-4827	153	2	∈	ORG
ejpam-4827	153	3	φ(r∗m)ψ	DATE
ejpam-4827	153	4	0	CARDINAL
ejpam-4827	154	1	+bngn	PERSON
ejpam-4827	154	2	∈	ORG
ejpam-4827	155	1	ψ(r	ORG
ejpam-4827	155	2	0	CARDINAL
ejpam-4827	156	1	r.	NORP
ejpam-4827	158	1	0	CARDINAL
ejpam-4827	158	2	2.1	CARDINAL
ejpam-4827	158	3	1 ≤ i ≤ n	QUANTITY
ejpam-4827	158	4	1 ≤	QUANTITY
ejpam-4827	158	5	j ≤ m.	PERSON
ejpam-4827	158	6	1	CARDINAL
ejpam-4827	158	7	0	CARDINAL
ejpam-4827	159	1	b2σg2(σs(ra1	ORG
ejpam-4827	160	1	∈	ORG
ejpam-4827	160	2	lemma 4, m	ORG
ejpam-4827	161	1	gish1 ̸= gjsh1	PERSON
ejpam-4827	165	1	lemma 1.	ORG
ejpam-4827	166	1	∈	ORG
ejpam-4827	167	1	1	CARDINAL
ejpam-4827	167	2	2	DATE
ejpam-4827	169	1	2	CARDINAL
ejpam-4827	170	1	1 ≤	MONEY
ejpam-4827	170	2	two	CARDINAL
ejpam-4827	170	3	g1	ORG
ejpam-4827	172	1	gn	PERSON
ejpam-4827	172	2	{sh1	PERSON
ejpam-4827	172	3	sh2	PERSON
ejpam-4827	174	1	0	CARDINAL
ejpam-4827	175	1	bpσgp(σs(raq	PERSON
ejpam-4827	177	1	bpσgp(σs(raq	PERSON
ejpam-4827	178	1	0	CARDINAL
ejpam-4827	180	1	∈	ORG
ejpam-4827	180	2	cpσs(raq	GPE
ejpam-4827	180	3	∈	ORG
ejpam-4827	181	1	ℓr(σs(raq	GPE
ejpam-4827	182	1	ℓr(σs(raq	GPE
ejpam-4827	182	2	1	CARDINAL
ejpam-4827	182	3	ℓr(σs(raq	GPE
ejpam-4827	184	1	∈	ORG
ejpam-4827	187	1	+ aq−1hq−1 + aq+1hq+1 + ·	PERSON
ejpam-4827	190	1	+ aq−1hq−1 + aq+1hq+1 + ·	PERSON
ejpam-4827	191	1	2.2	CARDINAL
ejpam-4827	191	2	∈	ORG
ejpam-4827	191	3	1	CARDINAL
ejpam-4827	191	4	2	DATE
ejpam-4827	193	1	1	CARDINAL
ejpam-4827	193	2	2	DATE
ejpam-4827	195	1	q−1	PERSON
ejpam-4827	196	1	m. therefore	PERSON
ejpam-4827	196	2	∈	PRODUCT
ejpam-4827	196	3	ℓr(rσs(aj	PERSON
ejpam-4827	199	1	0	CARDINAL
ejpam-4827	203	1	1	CARDINAL
ejpam-4827	203	2	2	DATE
ejpam-4827	204	1	m.	PERSON
ejpam-4827	204	2	0	CARDINAL
ejpam-4827	204	3	0	CARDINAL
ejpam-4827	209	1	k ∈	PERSON
ejpam-4827	209	2	1	CARDINAL
ejpam-4827	209	3	2	DATE
ejpam-4827	211	1	1	CARDINAL
ejpam-4827	214	1	∈	ORG
ejpam-4827	215	1	bkσgk(σs(raj	PERSON
ejpam-4827	216	1	σgk(ckσs(raj	PERSON
ejpam-4827	218	1	1	CARDINAL
ejpam-4827	218	2	2	DATE
ejpam-4827	219	1	m. hence	PERSON
ejpam-4827	220	1	+bp−1gp−1+bp+1gp+1	PERSON
ejpam-4827	221	1	0	CARDINAL
ejpam-4827	223	1	∈	ORG
ejpam-4827	223	2	∈	ORG
ejpam-4827	223	3	1	CARDINAL
ejpam-4827	223	4	2	DATE
ejpam-4827	225	1	1	CARDINAL
ejpam-4827	225	2	2	DATE
ejpam-4827	226	1	m.	PERSON
ejpam-4827	227	1	0	CARDINAL
ejpam-4827	229	1	0	CARDINAL
ejpam-4827	232	1	e. ali / eur	PERSON
ejpam-4827	233	1	j. pure	PERSON
ejpam-4827	233	2	16	CARDINAL
ejpam-4827	233	3	3	CARDINAL
ejpam-4827	233	4	2023	CARDINAL
ejpam-4827	233	5	1878-1893 1883	DATE
ejpam-4827	234	1	g1	ORG
ejpam-4827	234	2	∈	ORG
ejpam-4827	234	3	hg1	PERSON
ejpam-4827	239	1	ϕ(r	PERSON
ejpam-4827	239	2	0	CARDINAL
ejpam-4827	241	1	j.	PERSON
ejpam-4827	243	1	0	CARDINAL
ejpam-4827	244	1	2.3	CARDINAL
ejpam-4827	246	1	hm.we	ORG
ejpam-4827	246	2	ψ(r	PERSON
ejpam-4827	247	1	1	CARDINAL
ejpam-4827	248	1	2.3	CARDINAL
ejpam-4827	251	1	0	CARDINAL
ejpam-4827	254	1	2.3	CARDINAL
ejpam-4827	256	1	0	CARDINAL
ejpam-4827	257	1	2.4	CARDINAL
ejpam-4827	257	2	1	CARDINAL
ejpam-4827	259	1	0	CARDINAL
ejpam-4827	260	1	1 ≤	QUANTITY
ejpam-4827	260	2	hj	PERSON
ejpam-4827	265	1	1	CARDINAL
ejpam-4827	265	2	2	DATE
ejpam-4827	275	1	hjd−1	PERSON
ejpam-4827	280	1	0	CARDINAL
ejpam-4827	281	1	2	CARDINAL
ejpam-4827	282	1	0	CARDINAL
ejpam-4827	284	1	σ	ORG
ejpam-4827	287	1	j. consequently	PERSON
ejpam-4827	288	1	1 ≤ j ≤ m	QUANTITY
ejpam-4827	288	2	1 ≤	QUANTITY
ejpam-4827	288	3	σ	ORG
ejpam-4827	289	1	ψ(r	PERSON
ejpam-4827	289	2	0	CARDINAL
ejpam-4827	291	1	2	CARDINAL
ejpam-4827	295	1	1	CARDINAL
ejpam-4827	298	1	σ	ORG
ejpam-4827	299	1	σg(aij	ORG
ejpam-4827	300	1	e. ali / eur	PERSON
ejpam-4827	301	1	j. pure	PERSON
ejpam-4827	301	2	16	CARDINAL
ejpam-4827	301	3	3	CARDINAL
ejpam-4827	301	4	2023	CARDINAL
ejpam-4827	301	5	1878-1893	DATE
ejpam-4827	301	6	1884	DATE
ejpam-4827	301	7	2	CARDINAL
ejpam-4827	302	1	n ≥ 2	ORG
ejpam-4827	309	1	∈	ORG
ejpam-4827	311	1	a1	PERSON
ejpam-4827	314	1	an−2	PERSON
ejpam-4827	316	1	a1	PERSON
ejpam-4827	316	2	0	CARDINAL
ejpam-4827	317	1	bn−1	PERSON
ejpam-4827	318	1	bn−2	PERSON
ejpam-4827	322	1	φ	PERSON
ejpam-4827	323	1	0 φ1 φ2	PERCENT
ejpam-4827	328	1	ψn−2	PERSON
ejpam-4827	335	1	∈	ORG
ejpam-4827	336	1	∈	ORG
ejpam-4827	336	2	a(r	PRODUCT
ejpam-4827	336	3	0	DATE
ejpam-4827	337	1	0	CARDINAL
ejpam-4827	338	1	a1	PERSON
ejpam-4827	339	1	0	CARDINAL
ejpam-4827	339	2	2.5	CARDINAL
ejpam-4827	339	3	0	CARDINAL
ejpam-4827	340	1	2.6	CARDINAL
ejpam-4827	340	2	i)rb2 (j	ORG
ejpam-4827	340	3	0	CARDINAL
ejpam-4827	340	4	2.7	CARDINAL
ejpam-4827	341	1	i)rbn−1	PRODUCT
ejpam-4827	341	2	0	CARDINAL
ejpam-4827	342	1	2.8	CARDINAL
ejpam-4827	342	2	i)rbn (j) + a2	LAW
ejpam-4827	342	3	i)rbn−1	ORG
ejpam-4827	343	1	0	CARDINAL
ejpam-4827	343	2	2.9	CARDINAL
ejpam-4827	346	1	a1(i	GPE
ejpam-4827	346	2	∈	ORG
ejpam-4827	347	1	lemma 1	ORG
ejpam-4827	348	1	1	CARDINAL
ejpam-4827	348	2	2	DATE
ejpam-4827	350	1	n. e. ali / eur	PERSON
ejpam-4827	351	1	j. pure	PERSON
ejpam-4827	351	2	16	CARDINAL
ejpam-4827	351	3	3	CARDINAL
ejpam-4827	351	4	2023	CARDINAL
ejpam-4827	351	5	1878-1893	DATE
ejpam-4827	351	6	rσs(a1	PERSON
ejpam-4827	354	1	0	CARDINAL
ejpam-4827	355	1	∈	ORG
ejpam-4827	356	1	0	CARDINAL
ejpam-4827	357	1	2.10	CARDINAL
ejpam-4827	360	1	0	CARDINAL
ejpam-4827	361	1	lemma 1	ORG
ejpam-4827	364	1	0	CARDINAL
ejpam-4827	365	1	0	CARDINAL
ejpam-4827	367	1	2.10	CARDINAL
ejpam-4827	367	2	a1(i)σgi(rσs(b2	PERSON
ejpam-4827	370	1	0	CARDINAL
ejpam-4827	371	1	tb1	PERSON
ejpam-4827	371	2	∈	ORG
ejpam-4827	372	1	0	CARDINAL
ejpam-4827	373	1	2.11	CARDINAL
ejpam-4827	374	1	0	CARDINAL
ejpam-4827	377	1	∈	ORG
ejpam-4827	378	1	lemma 1.	ORG
ejpam-4827	380	1	0	CARDINAL
ejpam-4827	382	1	2.7	CARDINAL
ejpam-4827	383	1	i)rb2 (j	ORG
ejpam-4827	383	2	0	CARDINAL
ejpam-4827	384	1	2.12	CARDINAL
ejpam-4827	384	2	eq.(2.12	GPE
ejpam-4827	384	3	∈	ORG
ejpam-4827	386	1	0	CARDINAL
ejpam-4827	389	1	0	CARDINAL
ejpam-4827	395	1	tn−1bn−1 (j	ORG
ejpam-4827	397	1	tn−1 ∈	ORG
ejpam-4827	398	1	0	CARDINAL
ejpam-4827	399	1	0	CARDINAL
ejpam-4827	400	1	a2	PERSON
ejpam-4827	404	1	a1	PERSON
ejpam-4827	408	1	ℓr(rσs(bn	GPE
ejpam-4827	408	2	1	CARDINAL
ejpam-4827	415	1	j.	PERSON
ejpam-4827	419	1	e. ali / eur	PERSON
ejpam-4827	420	1	j. pure	PERSON
ejpam-4827	420	2	16	CARDINAL
ejpam-4827	420	3	3	CARDINAL
ejpam-4827	420	4	2023	CARDINAL
ejpam-4827	420	5	1878-1893	DATE
ejpam-4827	420	6	1886	DATE
ejpam-4827	420	7	2	CARDINAL
ejpam-4827	420	8	3.8	CARDINAL
ejpam-4827	420	9	12	CARDINAL
ejpam-4827	421	1	n ≥ 2	ORG
ejpam-4827	423	1	3	CARDINAL
ejpam-4827	425	1	+ bngn	PERSON
ejpam-4827	425	2	∈	ORG
ejpam-4827	426	1	φ ∈	PERSON
ejpam-4827	428	1	φ ∈ nil(r	ORG
ejpam-4827	428	2	φ	ORG
ejpam-4827	429	1	φ ∈	ORG
ejpam-4827	429	2	φ	ORG
ejpam-4827	430	1	18	CARDINAL
ejpam-4827	431	1	3	CARDINAL
ejpam-4827	432	1	∈	ORG
ejpam-4827	434	1	+ bngn	PERSON
ejpam-4827	435	1	∈	ORG
ejpam-4827	435	2	∈	ORG
ejpam-4827	436	1	∈	ORG
ejpam-4827	438	1	nil(r	ORG
ejpam-4827	440	1	3	CARDINAL
ejpam-4827	443	1	+ bngn	PERSON
ejpam-4827	445	1	∈	ORG
ejpam-4827	445	2	aj	PERSON
ejpam-4827	447	1	1 ≤	QUANTITY
ejpam-4827	447	2	1 ≤ k ≤ d and	QUANTITY
ejpam-4827	447	3	1 ≤	QUANTITY
ejpam-4827	447	4	σ	ORG
ejpam-4827	450	1	lemma 4	ORG
ejpam-4827	451	1	∈	ORG
ejpam-4827	451	2	1	CARDINAL
ejpam-4827	452	1	2	CARDINAL
ejpam-4827	453	1	1 ≤	QUANTITY
ejpam-4827	453	2	two	CARDINAL
ejpam-4827	455	1	g1	ORG
ejpam-4827	456	1	gn	PERSON
ejpam-4827	456	2	sh1	PERSON
ejpam-4827	456	3	sh2	PERSON
ejpam-4827	459	1	j = m.	PERSON
ejpam-4827	460	1	∈	ORG
ejpam-4827	460	2	integer k ≥ 1	PERSON
ejpam-4827	462	1	0	CARDINAL
ejpam-4827	464	1	0	CARDINAL
ejpam-4827	469	1	0	CARDINAL
ejpam-4827	473	1	∈	ORG
ejpam-4827	474	1	∈ nil(r	ORG
ejpam-4827	474	2	nil(r	GPE
ejpam-4827	474	3	e. ali	PERSON
ejpam-4827	475	1	j. pure	PERSON
ejpam-4827	475	2	16	CARDINAL
ejpam-4827	475	3	3	CARDINAL
ejpam-4827	475	4	2023	CARDINAL
ejpam-4827	475	5	1878-1893 1887	DATE
ejpam-4827	475	6	r.	NORP
ejpam-4827	476	1	0	CARDINAL
ejpam-4827	476	2	i.	PERSON
ejpam-4827	476	3	aj	PERSON
ejpam-4827	477	1	∈	ORG
ejpam-4827	479	1	3	CARDINAL
ejpam-4827	480	1	1	CARDINAL
ejpam-4827	481	1	2	CARDINAL
ejpam-4827	483	1	1	CARDINAL
ejpam-4827	485	1	x−2, x−1	GPE
ejpam-4827	485	2	1	DATE
ejpam-4827	485	3	σxn(λ	GPE
ejpam-4827	485	4	∈	ORG
ejpam-4827	485	5	x−1	GPE
ejpam-4827	485	6	3	CARDINAL
ejpam-4827	485	7	2	CARDINAL
ejpam-4827	485	8	1	CARDINAL
ejpam-4827	485	9	σxn(λ	GPE
ejpam-4827	486	1	0	CARDINAL
ejpam-4827	486	2	∈	ORG
ejpam-4827	486	3	3	CARDINAL
ejpam-4827	486	4	4	CARDINAL
ejpam-4827	486	5	3.1	CARDINAL
ejpam-4827	486	6	20	CARDINAL
ejpam-4827	488	1	5	CARDINAL
ejpam-4827	489	1	nil(r	ORG
ejpam-4827	489	2	r.	NORP
ejpam-4827	491	1	nil(r	GPE
ejpam-4827	492	1	3	CARDINAL
ejpam-4827	493	1	3	CARDINAL
ejpam-4827	494	1	2	CARDINAL
ejpam-4827	495	1	2	CARDINAL
ejpam-4827	498	1	0 1	CARDINAL
ejpam-4827	498	2	1	CARDINAL
ejpam-4827	498	3	1 1	CARDINAL
ejpam-4827	498	4	1 1	CARDINAL
ejpam-4827	499	1	1	CARDINAL
ejpam-4827	499	2	∈	ORG
ejpam-4827	500	1	0 1	CARDINAL
ejpam-4827	501	1	1	CARDINAL
ejpam-4827	502	1	0	CARDINAL
ejpam-4827	503	1	mohammed	PERSON
ejpam-4827	504	1	22	CARDINAL
ejpam-4827	504	2	nil(r	ORG
ejpam-4827	504	3	2	CARDINAL
ejpam-4827	505	1	4	CARDINAL
ejpam-4827	506	1	2	CARDINAL
ejpam-4827	506	2	nil(r	ORG
ejpam-4827	508	1	e. ali / eur	PERSON
ejpam-4827	509	1	j. pure	PERSON
ejpam-4827	509	2	16	CARDINAL
ejpam-4827	509	3	3	CARDINAL
ejpam-4827	509	4	2023	CARDINAL
ejpam-4827	509	5	1878-1893	DATE
ejpam-4827	510	1	∈	ORG
ejpam-4827	510	2	∈	ORG
ejpam-4827	514	1	0	CARDINAL
ejpam-4827	515	1	σ	ORG
ejpam-4827	518	1	3.4	CARDINAL
ejpam-4827	519	1	20	CARDINAL
ejpam-4827	521	1	5	CARDINAL
ejpam-4827	521	2	monoid	ORG
ejpam-4827	522	1	nil(r	GPE
ejpam-4827	525	1	φ	ORG
ejpam-4827	525	2	∈	ORG
ejpam-4827	525	3	∈	ORG
ejpam-4827	526	1	φ	PERSON
ejpam-4827	527	1	+ bngn	PERSON
ejpam-4827	527	2	g1	ORG
ejpam-4827	534	1	+ b̄ngn)(rs)(ā1h1	PERSON
ejpam-4827	534	2	b1 + i)σ̄g1(r(a1 +	ORG
ejpam-4827	537	1	b1σ̄g1(r a1	PERSON
ejpam-4827	541	1	∈	ORG
ejpam-4827	541	2	biσgi(r aj	PERSON
ejpam-4827	541	3	∈	ORG
ejpam-4827	543	1	0	CARDINAL
ejpam-4827	543	2	b1σg1(σs(r a1	PERSON
ejpam-4827	544	1	nil(r	GPE
ejpam-4827	545	1	bir aj	PERSON
ejpam-4827	545	2	0	CARDINAL
ejpam-4827	545	3	1 ≤	QUANTITY
ejpam-4827	545	4	hj	PERSON
ejpam-4827	546	1	w.	PERSON
ejpam-4827	547	1	w.	PERSON
ejpam-4827	550	1	1	CARDINAL
ejpam-4827	550	2	2	DATE
ejpam-4827	552	1	gik	PERSON
ejpam-4827	556	1	hjk	ORG
ejpam-4827	560	1	0	CARDINAL
ejpam-4827	561	1	2	CARDINAL
ejpam-4827	561	2	gi1hjt	PERSON
ejpam-4827	562	1	0	CARDINAL
ejpam-4827	564	1	σgit (ajt)i(bi1	ORG
ejpam-4827	564	2	⊆	CARDINAL
ejpam-4827	564	3	ajtibi1	ORG
ejpam-4827	564	4	2	CARDINAL
ejpam-4827	567	1	2	CARDINAL
ejpam-4827	567	2	0	CARDINAL
ejpam-4827	567	3	2	CARDINAL
ejpam-4827	567	4	0	CARDINAL
ejpam-4827	568	1	0	CARDINAL
ejpam-4827	569	1	e. ali	PERSON
ejpam-4827	570	1	j. pure	PERSON
ejpam-4827	570	2	16	CARDINAL
ejpam-4827	570	3	3	CARDINAL
ejpam-4827	570	4	2023	CARDINAL
ejpam-4827	570	5	1878-1893 1889	DATE
ejpam-4827	571	1	2	CARDINAL
ejpam-4827	571	2	0	CARDINAL
ejpam-4827	573	1	2	CARDINAL
ejpam-4827	576	1	3	CARDINAL
ejpam-4827	576	2	⊆	CARDINAL
ejpam-4827	577	1	0	CARDINAL
ejpam-4827	578	1	0	CARDINAL
ejpam-4827	579	1	∈ nil(r	ORG
ejpam-4827	579	2	t ≥ 2.multiplying	DATE
ejpam-4827	579	3	2	CARDINAL
ejpam-4827	579	4	0	CARDINAL
ejpam-4827	581	1	0	CARDINAL
ejpam-4827	583	1	0	CARDINAL
ejpam-4827	583	2	1	CARDINAL
ejpam-4827	585	1	k.	PERSON
ejpam-4827	586	1	nil(r	GPE
ejpam-4827	586	2	w.	PERSON
ejpam-4827	587	1	j.	PERSON
ejpam-4827	591	1	φ̄	PERSON
ejpam-4827	591	2	∈	ORG
ejpam-4827	592	1	+bngn	PERSON
ejpam-4827	593	1	nil(r	GPE
ejpam-4827	593	2	σg(x+nil(r	PERSON
ejpam-4827	595	1	σ	ORG
ejpam-4827	598	1	xy ∈ nil(r	ORG
ejpam-4827	599	1	+ nil(r	GPE
ejpam-4827	602	1	σ	ORG
ejpam-4827	604	1	+ bngn	PERSON
ejpam-4827	604	2	∈	ORG
ejpam-4827	609	1	integer ℓ ∈ n	ORG
ejpam-4827	609	2	∈	ORG
ejpam-4827	611	1	⊆	CARDINAL
ejpam-4827	612	1	∈	ORG
ejpam-4827	613	1	∈	ORG
ejpam-4827	615	1	3	CARDINAL
ejpam-4827	616	1	abelian	NORP
ejpam-4827	619	1	abelian	NORP
ejpam-4827	621	1	2	CARDINAL
ejpam-4827	622	1	3	CARDINAL
ejpam-4827	623	1	3	CARDINAL
ejpam-4827	626	1	2.6	CARDINAL
ejpam-4827	626	2	13	CARDINAL
ejpam-4827	626	3	kwak	PERSON
ejpam-4827	626	4	lee	PERSON
ejpam-4827	627	1	r.	NORP
ejpam-4827	628	1	e. ali / eur	PERSON
ejpam-4827	629	1	j. pure	PERSON
ejpam-4827	629	2	16	CARDINAL
ejpam-4827	629	3	3	CARDINAL
ejpam-4827	629	4	2023	CARDINAL
ejpam-4827	629	5	1878-1893	DATE
ejpam-4827	629	6	3	CARDINAL
ejpam-4827	631	1	1	CARDINAL
ejpam-4827	631	2	nil(r	ORG
ejpam-4827	632	1	2	CARDINAL
ejpam-4827	634	1	3	CARDINAL
ejpam-4827	636	1	0	CARDINAL
ejpam-4827	636	2	a2n	PERSON
ejpam-4827	639	1	aij ∈	ORG
ejpam-4827	639	2	1 ≤	CARDINAL
ejpam-4827	641	1	n ≥ 4	DATE
ejpam-4827	641	2	1	CARDINAL
ejpam-4827	642	1	φ	ORG
ejpam-4827	642	2	∈	ORG
ejpam-4827	642	3	∈	ORG
ejpam-4827	642	4	+ bngn	PERSON
ejpam-4827	645	1	biσi(σs(caj	PRODUCT
ejpam-4827	646	1	j.	PERSON
ejpam-4827	646	2	aj	PERSON
ejpam-4827	650	1	2	CARDINAL
ejpam-4827	651	1	4	CARDINAL
ejpam-4827	652	1	nil(r	PERSON
ejpam-4827	658	1	nil(r	PERSON
ejpam-4827	660	1	1	CARDINAL
ejpam-4827	661	1	acb	ORG
ejpam-4827	663	1	3	CARDINAL
ejpam-4827	664	1	2.3	CARDINAL
ejpam-4827	664	2	13	CARDINAL
ejpam-4827	665	1		GPE
ejpam-4827	665	2	0 α 	TIME
ejpam-4827	666	1	γ ∈ s 	ORG
ejpam-4827	666	2	1.2	CARDINAL
ejpam-4827	666	3	11	CARDINAL
ejpam-4827	668	1	∈	ORG
ejpam-4827	670	1	e. ali	PERSON
ejpam-4827	671	1	j. pure	PERSON
ejpam-4827	671	2	16	CARDINAL
ejpam-4827	671	3	3	CARDINAL
ejpam-4827	671	4	2023	CARDINAL
ejpam-4827	671	5	1878-1893	DATE
ejpam-4827	671	6	1891	DATE
ejpam-4827	674	1	0	CARDINAL
ejpam-4827	674	2	a2n	PERSON
ejpam-4827	677	1	∈	ORG
ejpam-4827	677	2	aij ∈	PERSON
ejpam-4827	677	3	1 ≤	CARDINAL
ejpam-4827	679	1	1	CARDINAL
ejpam-4827	680	1	example 3(2	CARDINAL
ejpam-4827	680	2	r.	NORP
ejpam-4827	683	1	integer n. proof	PERSON
ejpam-4827	684	1	φ	ORG
ejpam-4827	684	2	∈	ORG
ejpam-4827	685	1	φ	ORG
ejpam-4827	685	2	bij	ORG
ejpam-4827	685	3	aij	ORG
ejpam-4827	687	1	1 ≤	QUANTITY
ejpam-4827	687	2	biiσgii(σs(ciiaii	NORP
ejpam-4827	690	1	∗ m. therefore	PERSON
ejpam-4827	691	1	5	CARDINAL
ejpam-4827	695	1	1	CARDINAL
ejpam-4827	698	1	0	CARDINAL
ejpam-4827	699	1	φ	PERSON
ejpam-4827	699	2	∈	ORG
ejpam-4827	699	3	∈	ORG
ejpam-4827	702	1	σ	ORG
ejpam-4827	702	2	∈	ORG
ejpam-4827	702	3	∈	ORG
ejpam-4827	702	4	k=1 ik	PERSON
ejpam-4827	702	5	0	CARDINAL
ejpam-4827	703	1	0	CARDINAL
ejpam-4827	703	2	σ	ORG
ejpam-4827	705	1	∈	ORG
ejpam-4827	706	1	4.	CARDINAL
ejpam-4827	706	2	two	CARDINAL
ejpam-4827	709	1	1892	DATE
ejpam-4827	710	1	noncommutative	NORP
ejpam-4827	712	1	1	CARDINAL
ejpam-4827	712	2	e. ali	PERSON
ejpam-4827	715	1	12(11):676–692	CARDINAL
ejpam-4827	715	2	2022	CARDINAL
ejpam-4827	716	1	2	CARDINAL
ejpam-4827	716	2	e. ali	PERSON
ejpam-4827	719	1	j. anal	PERSON
ejpam-4827	720	1	21:69	LOC
ejpam-4827	720	2	2023	CARDINAL
ejpam-4827	721	1	3	CARDINAL
ejpam-4827	721	2	e. ali	PERSON
ejpam-4827	724	1	sci	ORG
ejpam-4827	725	1	j.	PERSON
ejpam-4827	725	2	12(1):287–306	DATE
ejpam-4827	725	3	2023	CARDINAL
ejpam-4827	726	1	4	CARDINAL
ejpam-4827	726	2	r. antoine	PERSON
ejpam-4827	728	1	j. algebra	PERSON
ejpam-4827	728	2	2008	DATE
ejpam-4827	729	1	5	CARDINAL
ejpam-4827	729	2	g. f. birkenmeier	PERSON
ejpam-4827	729	3	j. k. park	PERSON
ejpam-4827	731	1	j. algebra	PERSON
ejpam-4827	731	2	265:457–477, 2003	DATE
ejpam-4827	732	1	6	CARDINAL
ejpam-4827	732	2	r. c. courter	PERSON
ejpam-4827	734	1	canad	PERSON
ejpam-4827	736	1	bull.	PERSON
ejpam-4827	736	2	12(4):417–426	ORG
ejpam-4827	736	3	1969	DATE
ejpam-4827	737	1	7	CARDINAL
ejpam-4827	737	2	m. habibi	PERSON
ejpam-4827	737	3	a. moussavi	PERSON
ejpam-4827	739	1	j. algebra	PERSON
ejpam-4827	739	2	11(4):1250080, 2012	DATE
ejpam-4827	740	1	8	CARDINAL
ejpam-4827	740	2	a. moussavi	PERSON
ejpam-4827	743	1	hungar	PERSON
ejpam-4827	743	2	107(3):207–224, 2005	DATE
ejpam-4827	744	1	9	CARDINAL
ejpam-4827	746	1	j. pure	PERSON
ejpam-4827	747	1	168:45–52, 2002	DATE
ejpam-4827	748	1	10	CARDINAL
ejpam-4827	748	2	n. k. kim	PERSON
ejpam-4827	748	3	y. lee	PERSON
ejpam-4827	750	1	j. pure	PERSON
ejpam-4827	751	1	223	CARDINAL
ejpam-4827	751	2	2003	DATE
ejpam-4827	752	1	11	CARDINAL
ejpam-4827	752	2	n. k. kim	PERSON
ejpam-4827	752	3	y. lee	PERSON
ejpam-4827	753	1	j. pure	PERSON
ejpam-4827	754	1	223	CARDINAL
ejpam-4827	754	2	2003	DATE
ejpam-4827	755	1	12	CARDINAL
ejpam-4827	755	2	t. kwak	PERSON
ejpam-4827	755	3	y. lee	PERSON
ejpam-4827	755	4	s. yun	PERSON
ejpam-4827	756	1	endomorphisms	ORG
ejpam-4827	757	1	korean	NORP
ejpam-4827	757	2	j. math.	PERSON
ejpam-4827	757	3	22(2):217–234, 2014	DATE
ejpam-4827	758	1	1893	DATE
ejpam-4827	759	1	13	CARDINAL
ejpam-4827	759	2	t. k. kwak	PERSON
ejpam-4827	759	3	y. lee	PERSON
ejpam-4827	762	1	40:1576–1594, 2012	DATE
ejpam-4827	763	1	14	CARDINAL
ejpam-4827	763	2	z. k. liu	PERSON
ejpam-4827	765	1	33(3):649–661	CARDINAL
ejpam-4827	765	2	2005	DATE
ejpam-4827	766	1	15	CARDINAL
ejpam-4827	769	1	9(17):1709–1724, 1981	DATE
ejpam-4827	770	1	16	CARDINAL
ejpam-4827	770	2	a. r. nasr-isfahani	PERSON
ejpam-4827	770	3	a. moussavi	PERSON
ejpam-4827	771	1	glasg	PERSON
ejpam-4827	773	1	j.	PERSON
ejpam-4827	773	2	51(3):425–440	DATE
ejpam-4827	773	3	2009	DATE
ejpam-4827	774	1	17	CARDINAL
ejpam-4827	774	2	j. okninski	PERSON
ejpam-4827	776	1	w. a. benjamin	PERSON
ejpam-4827	776	2	new york	GPE
ejpam-4827	776	3	1991	DATE
ejpam-4827	777	1	18	CARDINAL
ejpam-4827	777	2	l. ouyang	PERSON
ejpam-4827	780	1	39(11):4259–4272, 2011	DATE
ejpam-4827	781	1	19	CARDINAL
ejpam-4827	781	2	d. s. passman	PERSON
ejpam-4827	783	1	wiley	ORG
ejpam-4827	783	2	new york	GPE
ejpam-4827	783	3	1977	DATE
ejpam-4827	784	1	20	CARDINAL
ejpam-4827	784	2	z. peng	PERSON
ejpam-4827	784	3	q. gu	PERSON
ejpam-4827	784	4	l. zhao	PERSON
ejpam-4827	786	1	asian-european journal of mathematics	ORG
ejpam-4827	786	2	2015	DATE
ejpam-4827	787	1	21	CARDINAL
ejpam-4827	787	2	s. rege	PERSON
ejpam-4827	787	3	m. b. andchhawchharia	PERSON
ejpam-4827	790	1	japan	GPE
ejpam-4827	791	1	ser	PERSON
ejpam-4827	793	1	sci.	ORG
ejpam-4827	793	2	73(1):14–17	CARDINAL
ejpam-4827	793	3	1997	DATE
ejpam-4827	794	1	22	CARDINAL
ejpam-4827	794	2	s. safarisabe	PERSON
ejpam-4827	794	3	e. mohammed	PERSON
ejpam-4827	796	1	asian	NORP
ejpam-4827	797	1	j.	PERSON
ejpam-4827	797	2	10(1):1550033	CARDINAL
ejpam-4827	797	3	2017	DATE
ejpam-4827	798	1	23	CARDINAL
ejpam-4827	798	2	h. tominaga	PERSON
ejpam-4827	801	1	j. okayama univ.	PERSON
ejpam-4827	801	2	18:117–134, 1976	DATE
ejpam-4827	802	1	24	CARDINAL
ejpam-4827	802	2	l. zhao	PERSON
ejpam-4827	802	3	x. zhu	PERSON
ejpam-4827	802	4	q. gu	PERSON
ejpam-4827	804	1	63(3):417–430	CARDINAL
ejpam-4827	804	2	2013	DATE