id	sid	eid	entity	type
cana-6071	1	1	1074	CARDINAL
cana-6071	2	1	2024	CARDINAL
cana-6071	2	2	1180	CARDINAL
cana-6071	2	3	manohar b. bhagirath1	PERSON
cana-6071	2	4	narendrakumar r. dasre2	PERSON
cana-6071	2	5	dr.	PERSON
cana-6071	2	6	pritam gujarathi	PERSON
cana-6071	2	7	1associate	CARDINAL
cana-6071	2	8	college of arts	ORG
cana-6071	2	9	vasai	ORG
cana-6071	2	10	dist	NORP
cana-6071	3	1	401202	DATE
cana-6071	5	1	institute of technology	ORG
cana-6071	5	2	nerul	ORG
cana-6071	5	3	mumbai-400706	DATE
cana-6071	5	4	narendasre@rait.ac.in 3*assistant	CARDINAL
cana-6071	5	5	institute of technology	ORG
cana-6071	5	6	nerul	ORG
cana-6071	5	7	mumbai-400706	DATE
cana-6071	5	8	pritam gujarathi-wani	PERSON
cana-6071	5	9	received:01/11/2024	PERSON
cana-6071	5	10	30/12/2024	DATE
cana-6071	6	1	left)-hereditary	PERSON
cana-6071	6	2	r(r	PRODUCT
cana-6071	8	1	1	CARDINAL
cana-6071	8	2	9	CARDINAL
cana-6071	11	1	12	CARDINAL
cana-6071	13	1	1	CARDINAL
cana-6071	14	1	2	CARDINAL
cana-6071	14	2	6	CARDINAL
cana-6071	14	3	8	CARDINAL
cana-6071	14	4	10	CARDINAL
cana-6071	15	1	2	CARDINAL
cana-6071	16	1	2.1	CARDINAL
cana-6071	17	1	abelian	NORP
cana-6071	17	2	0	CARDINAL
cana-6071	17	3	zero	CARDINAL
cana-6071	17	4	y ∈	PERSON
cana-6071	17	5	r.	NORP
cana-6071	17	6	2.2	CARDINAL
cana-6071	18	1	∈	ORG
cana-6071	18	2	r.	NORP
cana-6071	18	3	2.3	CARDINAL
cana-6071	20	1	2.4	CARDINAL
cana-6071	21	1	brown mccoy	PERSON
cana-6071	22	1	2.5	CARDINAL
cana-6071	25	1	0 ≠ 𝐼	PERSON
cana-6071	27	1	mailto:%20narendasre@rait.ac.in mailto:pritam.wani@rait.ac.in mailto:pritam.wani@rait.ac.in	GPE
cana-6071	27	2	1074	CARDINAL
cana-6071	28	1	2024	CARDINAL
cana-6071	28	2	1181	CARDINAL
cana-6071	29	1	0 ≠ 𝐼	PERSON
cana-6071	32	1	∈	ORG
cana-6071	34	1	2.6	CARDINAL
cana-6071	35	1	r.	NORP
cana-6071	36	1	∈	ORG
cana-6071	36	2	k ∈	PERSON
cana-6071	37	1	i. therefore ak	PERSON
cana-6071	40	1	ea)k + k = k. ak	ORG
cana-6071	43	1	k	GPE
cana-6071	43	2	2.7	CARDINAL
cana-6071	46	1	2.5	CARDINAL
cana-6071	46	2	ρ.	GPE
cana-6071	47	1	r.	NORP
cana-6071	49	1	2.8	CARDINAL
cana-6071	49	2	brown mccoy	PERSON
cana-6071	50	1	2.9	CARDINAL
cana-6071	51	1	dorroh	ORG
cana-6071	53	1	∈	ORG
cana-6071	53	2	n ∈ z+	ORG
cana-6071	53	3	0	CARDINAL
cana-6071	59	1	0	CARDINAL
cana-6071	59	2	1	CARDINAL
cana-6071	59	3	≅	CARDINAL
cana-6071	63	1	r.	NORP
cana-6071	63	2	j ∈	PERSON
cana-6071	63	3	1	CARDINAL
cana-6071	63	4	2	DATE
cana-6071	63	5	3	DATE
cana-6071	63	6	0	ORG
cana-6071	64	1	1	CARDINAL
cana-6071	64	2	2	DATE
cana-6071	64	3	3	DATE
cana-6071	64	4	li	PERSON
cana-6071	65	1	∈	ORG
cana-6071	65	2	1	CARDINAL
cana-6071	65	3	2	DATE
cana-6071	65	4	3	DATE
cana-6071	65	5	i)(x	ORG
cana-6071	65	6	0	ORG
cana-6071	66	1	x(i	PERSON
cana-6071	66	2	⋃	DATE
cana-6071	66	3	𝑥∈𝑅 xj	PERSON
cana-6071	66	4	i)(x	ORG
cana-6071	68	1	r(r	PERSON
cana-6071	70	1	2.10	CARDINAL
cana-6071	73	1	2.11	CARDINAL
cana-6071	74	1	r.	NORP
cana-6071	74	2	2.12	CARDINAL
cana-6071	77	1	r(i	PERSON
cana-6071	77	2	r.	PERSON
cana-6071	81	1	⊆	CARDINAL
cana-6071	81	2	r(r	PRODUCT
cana-6071	85	1	⊆	CARDINAL
cana-6071	85	2	⊆	CARDINAL
cana-6071	85	3	2.13	CARDINAL
cana-6071	88	1	1	CARDINAL
cana-6071	88	2	∈	ORG
cana-6071	88	3	2	CARDINAL
cana-6071	88	4	⊆	CARDINAL
cana-6071	88	5	r(r	PRODUCT
cana-6071	89	1	1074	CARDINAL
cana-6071	90	1	2024	CARDINAL
cana-6071	90	2	1182 proof	TIME
cana-6071	91	1	r(r	PERSON
cana-6071	91	2	1	CARDINAL
cana-6071	91	3	⊆	CARDINAL
cana-6071	91	4	r(r	PRODUCT
cana-6071	92	1	r(r	PERSON
cana-6071	95	1	2	CARDINAL
cana-6071	95	2	⊆	CARDINAL
cana-6071	95	3	r(r	PRODUCT
cana-6071	96	1	2.14	CARDINAL
cana-6071	99	1	1	CARDINAL
cana-6071	100	1	∈	ORG
cana-6071	101	1	r(r (n	FAC
cana-6071	102	1	⊆	CARDINAL
cana-6071	103	1	2.12 r(r	QUANTITY
cana-6071	103	2	= i(n	PERSON
cana-6071	103	3	r.	NORP
cana-6071	103	4	1	CARDINAL
cana-6071	103	5	r.	NORP
cana-6071	103	6	r(r	PERSON
cana-6071	105	1	r(r (n	FAC
cana-6071	107	1	2	CARDINAL
cana-6071	108	1	⊆	CARDINAL
cana-6071	109	1	r(r	PERSON
cana-6071	110	1	2.15	CARDINAL
cana-6071	112	1	∈	ORG
cana-6071	112	2	r.	NORP
cana-6071	113	1	1	CARDINAL
cana-6071	113	2	2	DATE
cana-6071	113	3	3	DATE
cana-6071	113	4	1	CARDINAL
cana-6071	113	5	2	DATE
cana-6071	113	6	3	DATE
cana-6071	115	1	xj	GPE
cana-6071	115	2	xj	ORG
cana-6071	115	3	r(r	PERSON
cana-6071	117	1	⊆	CARDINAL
cana-6071	118	1	xj	PERSON
cana-6071	119	1	⊆	CARDINAL
cana-6071	120	1	i ≠ j. and j	PERSON
cana-6071	120	2	ri ⊆ r(r	ORG
cana-6071	121	1	r(i	PERSON
cana-6071	122	1	⊆	CARDINAL
cana-6071	122	2	r(r	PRODUCT
cana-6071	123	1	j ∈	PERSON
cana-6071	123	2	1	CARDINAL
cana-6071	123	3	2	DATE
cana-6071	123	4	3	DATE
cana-6071	124	1	∑	GPE
cana-6071	126	1	r. theorem2.16	PERSON
cana-6071	128	1	∈ r. theorem2.17	ORG
cana-6071	130	1	∈	ORG
cana-6071	130	2	∈	ORG
cana-6071	130	3	2.18	CARDINAL
cana-6071	132	1	∈	ORG
cana-6071	132	2	r.	NORP
cana-6071	132	3	2.19	CARDINAL
cana-6071	134	1	r(r (n	FAC
cana-6071	135	1	r(r	PERSON
cana-6071	136	1	rajendra p. deore	PERSON
cana-6071	137	1	al-thani	ORG
cana-6071	137	2	h. m. j. weak	PERSON
cana-6071	137	3	tamkang journal of mathematics, 35(4)	ORG
cana-6071	137	4	359-369	CARDINAL
cana-6071	137	5	2004	DATE
cana-6071	138	1	2	CARDINAL
cana-6071	138	2	dutta t. k.	PERSON
cana-6071	138	3	das m. l.	PERSON
cana-6071	138	4	siutheast asian	NORP
cana-6071	138	5	35	DATE
cana-6071	138	6	389	CARDINAL
cana-6071	138	7	2011	DATE
cana-6071	139	1	3	CARDINAL
cana-6071	139	2	b. j. gardner	PERSON
cana-6071	140	1	scand.	PERSON
cana-6071	140	2	31	DATE
cana-6071	140	3	1972	DATE
cana-6071	140	4	83-88	DATE
cana-6071	141	1	4	CARDINAL
cana-6071	141	2	gardner b. j.	PERSON
cana-6071	141	3	wiegandt	GPE
cana-6071	141	4	r. radical	PERSON
cana-6071	141	5	marcel dekker	PERSON
cana-6071	141	6	2004	DATE
cana-6071	142	1	5	CARDINAL
cana-6071	142	2	b. j. gardner	PERSON
cana-6071	142	3	abelian	NORP
cana-6071	143	1	acad	ORG
cana-6071	144	1	sci.	PERSON
cana-6071	144	2	24(3	CARDINAL
cana-6071	144	3	259	CARDINAL
cana-6071	144	4	1973	DATE
cana-6071	145	1	6	CARDINAL
cana-6071	145	2	golan j. s.	PERSON
cana-6071	145	3	kluwer	ORG
cana-6071	145	4	1999	DATE
cana-6071	146	1	7	CARDINAL
cana-6071	146	2	n. v. loi	PERSON
cana-6071	146	3	r. wiegandt	PERSON
cana-6071	146	4	mathe matics	PERSON
cana-6071	146	5	3	CARDINAL
cana-6071	146	6	92-100	CARDINAL
cana-6071	146	7	2006	DATE
cana-6071	147	1	8	CARDINAL
cana-6071	147	2	morak b.	PERSON
cana-6071	149	1	geom	PERSON
cana-6071	149	2	40,533	CARDINAL
cana-6071	149	3	1999	DATE
cana-6071	150	1	9	CARDINAL
cana-6071	150	2	olson d. m.	PERSON
cana-6071	150	3	jenkins t. l.	PERSON
cana-6071	150	4	1074	CARDINAL
cana-6071	151	1	2024	CARDINAL
cana-6071	151	2	1183	CARDINAL
cana-6071	152	1	10	CARDINAL
cana-6071	152	2	pawar k. f. deore r. p.	PERSON
cana-6071	153	1	14(4	CARDINAL
cana-6071	153	2	697	CARDINAL
cana-6071	153	3	2009	DATE
cana-6071	154	1	11	CARDINAL
cana-6071	154	2	pawar k. f. radical	PERSON
cana-6071	155	1	2011	DATE
cana-6071	156	1	12	CARDINAL
cana-6071	156	2	s. tumurbat	PERSON
cana-6071	156	3	r. wiegandt	GPE
cana-6071	156	4	j. maths	PERSON
cana-6071	156	5	29	CARDINAL
cana-6071	156	6	4	CARDINAL
cana-6071	156	7	425-434	CARDINAL
cana-6071	156	8	2003	DATE