id	sid	eid	entity	type
ejpam-2026	1	1	european journal	ORG
ejpam-2026	2	1	10	CARDINAL
ejpam-2026	2	2	3	CARDINAL
ejpam-2026	2	3	2017	DATE
ejpam-2026	2	4	516-520	CARDINAL
ejpam-2026	2	5	new york	GPE
ejpam-2026	2	6	domain waheed ahmad khan	PERSON
ejpam-2026	2	7	university of education lahore	ORG
ejpam-2026	2	8	pakistan	GPE
ejpam-2026	6	1	2010	DATE
ejpam-2026	6	2	13a05	CARDINAL
ejpam-2026	6	3	13a18	DATE
ejpam-2026	6	4	12j20	CARDINAL
ejpam-2026	6	5	submodule	ORG
ejpam-2026	6	6	pvr	ORG
ejpam-2026	7	1	i. kaplansky	PERSON
ejpam-2026	7	2	6	CARDINAL
ejpam-2026	8	1	david eisenbud	PERSON
ejpam-2026	8	2	j. c. robin	PERSON
ejpam-2026	8	3	3	CARDINAL
ejpam-2026	11	1	abelian	NORP
ejpam-2026	11	2	∈	ORG
ejpam-2026	11	3	∈	ORG
ejpam-2026	12	1	1rx	ORDINAL
ejpam-2026	13	1	1r	CARDINAL
ejpam-2026	15	1	n ∈ n	ORG
ejpam-2026	15	2	∈	ORG
ejpam-2026	18	1	⇐⇒	DATE
ejpam-2026	18	2	1	CARDINAL
ejpam-2026	19	1	2	CARDINAL
ejpam-2026	19	2	∈	ORG
ejpam-2026	19	3	∀x	GPE
ejpam-2026	19	4	2	CARDINAL
ejpam-2026	20	1	∈	ORG
ejpam-2026	21	1	∈	ORG
ejpam-2026	23	1	1	CARDINAL
ejpam-2026	24	1	w. a. khan	PERSON
ejpam-2026	25	1	516	CARDINAL
ejpam-2026	25	2	2017	CARDINAL
ejpam-2026	26	1	w. a. khan	PERSON
ejpam-2026	27	1	j. pure	PERSON
ejpam-2026	27	2	10	CARDINAL
ejpam-2026	27	3	3	CARDINAL
ejpam-2026	27	4	2017	CARDINAL
ejpam-2026	27	5	516	CARDINAL
ejpam-2026	27	6	2	CARDINAL
ejpam-2026	28	1	zero	CARDINAL
ejpam-2026	28	2	zero	CARDINAL
ejpam-2026	30	1	xy ∈	ORG
ejpam-2026	30	2	∈	ORG
ejpam-2026	32	1	5	CARDINAL
ejpam-2026	32	2	page2	PERSON
ejpam-2026	33	1	5	CARDINAL
ejpam-2026	33	2	page2	PERSON
ejpam-2026	34	1	∈	ORG
ejpam-2026	34	2	∈	PRODUCT
ejpam-2026	34	3	∈	ORG
ejpam-2026	35	1	5	CARDINAL
ejpam-2026	35	2	1.5(3	CARDINAL
ejpam-2026	36	1	5	CARDINAL
ejpam-2026	37	1	1.1	CARDINAL
ejpam-2026	41	1	4	CARDINAL
ejpam-2026	41	2	560	CARDINAL
ejpam-2026	42	1	x−1	PERSON
ejpam-2026	42	2	⊂m	GPE
ejpam-2026	42	3	5	CARDINAL
ejpam-2026	42	4	1.4	CARDINAL
ejpam-2026	43	1	1	CARDINAL
ejpam-2026	43	2	2	CARDINAL
ejpam-2026	43	3	1	CARDINAL
ejpam-2026	43	4	r.	NORP
ejpam-2026	44	1	1	CARDINAL
ejpam-2026	45	1	abelian	NORP
ejpam-2026	45	2	∈	ORG
ejpam-2026	45	3	∈	ORG
ejpam-2026	45	4	1	CARDINAL
ejpam-2026	45	5	∈	ORG
ejpam-2026	45	6	∈	ORG
ejpam-2026	45	7	∈	ORG
ejpam-2026	46	1	2	CARDINAL
ejpam-2026	47	1	3	CARDINAL
ejpam-2026	47	2	rm+	NORP
ejpam-2026	47	3	4	CARDINAL
ejpam-2026	48	1	second	ORDINAL
ejpam-2026	48	2	third	ORDINAL
ejpam-2026	48	3	fourth	ORDINAL
ejpam-2026	49	1	1	CARDINAL
ejpam-2026	50	1	1	CARDINAL
ejpam-2026	50	2	3(4	CARDINAL
ejpam-2026	50	3	∈	ORG
ejpam-2026	50	4	∈	ORG
ejpam-2026	50	5	r.	NORP
ejpam-2026	50	6	1	CARDINAL
ejpam-2026	51	1	abelian	NORP
ejpam-2026	52	1	∈	ORG
ejpam-2026	52	2	∈	ORG
ejpam-2026	52	3	∈	ORG
ejpam-2026	53	1	w. a. khan	PERSON
ejpam-2026	54	1	j. pure	PERSON
ejpam-2026	54	2	10	CARDINAL
ejpam-2026	54	3	3	CARDINAL
ejpam-2026	54	4	2017	CARDINAL
ejpam-2026	54	5	516	CARDINAL
ejpam-2026	55	1	∈	ORG
ejpam-2026	55	2	∈	ORG
ejpam-2026	55	3	∈	ORG
ejpam-2026	55	4	∈	ORG
ejpam-2026	56	1	abelian	NORP
ejpam-2026	56	2	∈	ORG
ejpam-2026	56	3	∈	ORG
ejpam-2026	56	4	∈	ORG
ejpam-2026	57	1	1	CARDINAL
ejpam-2026	57	2	∈	ORG
ejpam-2026	57	3	∈	ORG
ejpam-2026	58	1	1	CARDINAL
ejpam-2026	58	2	∈	ORG
ejpam-2026	58	3	6= 1	DATE
ejpam-2026	59	1	2	CARDINAL
ejpam-2026	59	2	1	CARDINAL
ejpam-2026	62	1	3	CARDINAL
ejpam-2026	64	1	2	CARDINAL
ejpam-2026	65	1	4	CARDINAL
ejpam-2026	65	2	∈	ORG
ejpam-2026	67	1	definition1	LOC
ejpam-2026	68	1	1	CARDINAL
ejpam-2026	69	1	r.	NORP
ejpam-2026	69	2	abelian	NORP
ejpam-2026	69	3	∈	ORG
ejpam-2026	71	1	xb(y	PERSON
ejpam-2026	71	2	1	CARDINAL
ejpam-2026	72	1	xd(y))]r	CARDINAL
ejpam-2026	73	1	2	CARDINAL
ejpam-2026	74	1	xb(y	ORG
ejpam-2026	76	1	a+ xb(y)]r +	PERSON
ejpam-2026	77	1	xd(y)]r	GPE
ejpam-2026	78	1	3	CARDINAL
ejpam-2026	80	1	a+ xb(y)]r	PERSON
ejpam-2026	82	1	xb(y)]s	ORG
ejpam-2026	83	1	2	CARDINAL
ejpam-2026	84	1	1	CARDINAL
ejpam-2026	84	2	2	CARDINAL
ejpam-2026	84	3	∈	ORG
ejpam-2026	84	4	2	CARDINAL
ejpam-2026	86	1	∈	ORG
ejpam-2026	88	1	∈	ORG
ejpam-2026	89	1	∈	ORG
ejpam-2026	89	2	n	ORG
ejpam-2026	89	3	∈	ORG
ejpam-2026	89	4	1	CARDINAL
ejpam-2026	90	1	2	CARDINAL
ejpam-2026	90	2	∈	ORG
ejpam-2026	92	1	2	CARDINAL
ejpam-2026	92	2	∈	ORG
ejpam-2026	93	1	1	CARDINAL
ejpam-2026	95	1	2	CARDINAL
ejpam-2026	95	2	∈	ORG
ejpam-2026	95	3	∈	ORG
ejpam-2026	95	4	xd(y).m+ n(y))]p ∈ r[x	ORG
ejpam-2026	96	1	w. a. khan	PERSON
ejpam-2026	97	1	j. pure	PERSON
ejpam-2026	97	2	10	CARDINAL
ejpam-2026	97	3	3	CARDINAL
ejpam-2026	97	4	2017	CARDINAL
ejpam-2026	97	5	516	CARDINAL
ejpam-2026	98	1	5	CARDINAL
ejpam-2026	100	1	1	CARDINAL
ejpam-2026	101	1	2	CARDINAL
ejpam-2026	102	1	3	CARDINAL
ejpam-2026	102	2	abelian	NORP
ejpam-2026	102	3	→m	ORG
ejpam-2026	103	1	3	CARDINAL
ejpam-2026	104	1	∈	ORG
ejpam-2026	104	2	∈ m(an	ORG
ejpam-2026	104	3	abelian	NORP
ejpam-2026	104	4	1	CARDINAL
ejpam-2026	104	5	∈	ORG
ejpam-2026	104	6	∈	ORG
ejpam-2026	105	1	2	CARDINAL
ejpam-2026	105	2	x−1ax−1b)m	GPE
ejpam-2026	106	1	3	CARDINAL
ejpam-2026	107	1	4	CARDINAL
ejpam-2026	108	1	rm+	NORP
ejpam-2026	109	1	3	CARDINAL
ejpam-2026	111	1	abelian	NORP
ejpam-2026	112	1	1	CARDINAL
ejpam-2026	113	1	xb)(c+	PERSON
ejpam-2026	113	2	2	CARDINAL
ejpam-2026	113	3	xbr	ORG
ejpam-2026	113	4	xdr	ORG
ejpam-2026	113	5	3	CARDINAL
ejpam-2026	113	6	xbr	ORG
ejpam-2026	113	7	3	CARDINAL
ejpam-2026	114	1	abelian	NORP
ejpam-2026	114	2	xb)m ∈m	ORG
ejpam-2026	117	1	∈	ORG
ejpam-2026	117	2	x−1ax−1b)m	GPE
ejpam-2026	118	1	∈	ORG
ejpam-2026	119	1	x−1am+ x−1an	PERSON
ejpam-2026	119	2	r.	NORP
ejpam-2026	121	1	n ∈ n	ORG
ejpam-2026	121	2	∈	ORG
ejpam-2026	122	1	4	DATE
ejpam-2026	124	1	1	CARDINAL
ejpam-2026	124	2	2	CARDINAL
ejpam-2026	125	1	∈	ORG
ejpam-2026	126	1	n ∈ n	ORG
ejpam-2026	126	2	520	CARDINAL
ejpam-2026	126	3	4	CARDINAL
ejpam-2026	128	1	n = f(x	ORG
ejpam-2026	128	2	n(a+xb	DATE
ejpam-2026	130	1	4	CARDINAL
ejpam-2026	131	1	abelian	NORP
ejpam-2026	133	1	x−1an ∈	PERSON
ejpam-2026	133	2	x−1an ∈	PERSON
ejpam-2026	135	1	m. as x−1an ∈	PERSON
ejpam-2026	136	1	∈	ORG
ejpam-2026	137	1	2nd	ORDINAL
ejpam-2026	137	2	2	CARDINAL
ejpam-2026	137	3	n′ ∈ n ∀ n	PERSON
ejpam-2026	140	1	23	CARDINAL
ejpam-2026	140	2	12	CARDINAL
ejpam-2026	141	1	4365–4373, 1995	DATE
ejpam-2026	142	1	2	CARDINAL
ejpam-2026	142	2	s. dummit	PERSON
ejpam-2026	143	1	richard m. foote	PERSON
ejpam-2026	145	1	2nd	ORDINAL
ejpam-2026	145	2	2005	DATE
ejpam-2026	145	3	997151429x	DATE
ejpam-2026	145	4	9789971514297	DATE
ejpam-2026	145	5	978-9971514297	CARDINAL
ejpam-2026	145	6	john wiley &	ORG
ejpam-2026	146	1	3	CARDINAL
ejpam-2026	146	2	d.	NORP
ejpam-2026	146	3	robin	GPE
ejpam-2026	146	4	j. c.:	PERSON
ejpam-2026	147	1	j. algebra	PERSON
ejpam-2026	147	2	16	CARDINAL
ejpam-2026	147	3	67-85	DATE
ejpam-2026	147	4	1970	DATE
ejpam-2026	148	1	4	CARDINAL
ejpam-2026	148	2	gilmer	GPE
ejpam-2026	148	3	r. multiplicative	NORP
ejpam-2026	148	4	queens university press	ORG
ejpam-2026	148	5	kingston	GPE
ejpam-2026	148	6	ontario	GPE
ejpam-2026	148	7	1968	DATE
ejpam-2026	149	1	5	CARDINAL
ejpam-2026	149	2	j. r.	PERSON
ejpam-2026	149	3	houston	GPE
ejpam-2026	149	4	e. g.:	PERSON
ejpam-2026	150	1	75 (1978	DATE
ejpam-2026	150	2	1	CARDINAL
ejpam-2026	150	3	137	CARDINAL
ejpam-2026	151	1	6	CARDINAL
ejpam-2026	151	2	kaplansky	GPE
ejpam-2026	151	3	i.	PERSON
ejpam-2026	153	1	amer	PERSON
ejpam-2026	155	1	72	DATE
ejpam-2026	155	2	1952	DATE
ejpam-2026	157	1	327–340	CARDINAL