id	sid	eid	entity	type
iajs-1999	1	1	microsoft	ORG
iajs-1999	1	2	102	CARDINAL
iajs-1999	1	3	102	CARDINAL
iajs-1999	1	4	ibn al-haitham jour	PERSON
iajs-1999	3	1	sci.	ORG
iajs-1999	3	2	ihjpas	PERSON
iajs-1999	3	3	31.3.1999	CARDINAL
iajs-1999	4	1	31	CARDINAL
iajs-1999	5	1	3) 2018	DATE
iajs-1999	5	2	semisecond submodules rasha	ORG
iajs-1999	5	3	i. khalaf	PERSON
iajs-1999	5	4	al-haitham	ORG
iajs-1999	5	5	university of baghdad	ORG
iajs-1999	5	6	baghdad	GPE
iajs-1999	5	7	iraq	GPE
iajs-1999	6	1	15 may 2018	DATE
iajs-1999	6	2	19	CARDINAL
iajs-1999	6	3	december 2018	DATE
iajs-1999	7	1	semisecond submodule	ORG
iajs-1999	7	2	r∈ℛ	PRODUCT
iajs-1999	7	3	n∈z+	ORG
iajs-1999	7	4	rnℵ=rℵ.	PRODUCT
iajs-1999	7	5	semisecond submodule	ORG
iajs-1999	8	1	second	ORDINAL
iajs-1999	8	2	ℬ.	NORP
iajs-1999	8	3	semisecond submodules	PERSON
iajs-1999	8	4	second	ORDINAL
iajs-1999	10	1	1	CARDINAL
iajs-1999	10	2	second	ORDINAL
iajs-1999	10	3	second	ORDINAL
iajs-1999	10	4	second	ORDINAL
iajs-1999	10	5	r∈ℛ	PRODUCT
iajs-1999	10	6	ℬ.	PERSON
iajs-1999	10	7	semisecond submodule	ORG
iajs-1999	10	8	semisecond module	ORG
iajs-1999	10	9	second	ORDINAL
iajs-1999	10	10	second	ORDINAL
iajs-1999	10	11	n∈z+	ORG
iajs-1999	10	12	0	CARDINAL
iajs-1999	10	13	ℬ.	PERSON
iajs-1999	10	14	semisecond submodules.	ORG
iajs-1999	11	1	semisecond submodules	PERSON
iajs-1999	13	1	s.t.	PERSON
iajs-1999	15	1	2	CARDINAL
iajs-1999	15	2	semisecond submodules	PERSON
iajs-1999	16	1	semisecond submodule	PERSON
iajs-1999	16	2	r∈ℛ	PRODUCT
iajs-1999	16	3	n∈z+	ORG
iajs-1999	16	4	rnℵ=rℵ.	PRODUCT
iajs-1999	16	5	semisecond submodule	ORG
iajs-1999	16	6	ℛ	NORP
iajs-1999	16	7	semisecond submodule.	ORG
iajs-1999	17	1	2):ℵ	CARDINAL
iajs-1999	20	1	⟸	PERSON
iajs-1999	21	1	0	CARDINAL
iajs-1999	23	1	0	CARDINAL
iajs-1999	24	1	103	CARDINAL
iajs-1999	24	2	al-haitham jour	ORG
iajs-1999	25	1	sci.	ORG
iajs-1999	25	2	ihjpas	PERSON
iajs-1999	25	3	31.3.1999	CARDINAL
iajs-1999	26	1	31	CARDINAL
iajs-1999	27	1	3) 2018	DATE
iajs-1999	27	2	r(r ℵ)=r2	PERSON
iajs-1999	28	1	0	CARDINAL
iajs-1999	28	2	r∈ℛ	PRODUCT
iajs-1999	28	3	n∈z+.	GPE
iajs-1999	29	1	semisecond submodule.	ORG
iajs-1999	30	1	3	CARDINAL
iajs-1999	30	2	1	CARDINAL
iajs-1999	30	3	second	ORDINAL
iajs-1999	30	4	semisecond	ORG
iajs-1999	32	1	second	ORDINAL
iajs-1999	34	1	r(r	PERSON
iajs-1999	34	2	2.2	CARDINAL
iajs-1999	35	1	z8	DATE
iajs-1999	35	2	2	CARDINAL
iajs-1999	35	3	0,4	CARDINAL
iajs-1999	36	1	second	ORDINAL
iajs-1999	37	1	2k	CARDINAL
iajs-1999	37	2	r2	PERSON
iajs-1999	37	3	semisecond submodule	ORG
iajs-1999	38	1	2	CARDINAL
iajs-1999	38	2	semisecond submodule	ORG
iajs-1999	38	3	semisecond submodule of q.	ORG
iajs-1999	38	4	3	CARDINAL
iajs-1999	38	5	zp∞	GPE
iajs-1999	38	6	semisecond submodule	ORG
iajs-1999	39	1	4	CARDINAL
iajs-1999	42	1	semisecond submodule	ORG
iajs-1999	43	1	5	CARDINAL
iajs-1999	46	1	r2f(ℵ)=f(0	PERSON
iajs-1999	48	1	6	CARDINAL
iajs-1999	48	2	semisecond submodule	ORG
iajs-1999	48	3	2	CARDINAL
iajs-1999	48	4	semisecond submodule	ORG
iajs-1999	48	5	z6	GPE
iajs-1999	49	1	2.3	CARDINAL
iajs-1999	50	1	1	CARDINAL
iajs-1999	50	2	i.d.	GPE
iajs-1999	50	3	2.p.45	CARDINAL
iajs-1999	51	1	4):-if	CARDINAL
iajs-1999	53	1	second	ORDINAL
iajs-1999	55	1	semisecond submodule	PERSON
iajs-1999	55	2	ℛ	ORG
iajs-1999	56	1	∈ℵ s.t.	PERSON
iajs-1999	58	1	second	ORDINAL
iajs-1999	59	1	5):if	CARDINAL
iajs-1999	59	2	second	ORDINAL
iajs-1999	61	1	104 ibn al-haitham jour	QUANTITY
iajs-1999	63	1	sci.	ORG
iajs-1999	63	2	ihjpas	PERSON
iajs-1999	63	3	31.3.1999	CARDINAL
iajs-1999	64	1	31	CARDINAL
iajs-1999	65	1	2018	DATE
iajs-1999	68	1	6):if	CARDINAL
iajs-1999	69	1	r.	NORP
iajs-1999	69	2	r∈ ℛ	GPE
iajs-1999	73	1	1	CARDINAL
iajs-1999	75	1	0	CARDINAL
iajs-1999	79	1	2.2	CARDINAL
iajs-1999	82	1	semisecond submodule	ORG
iajs-1999	83	1	2.6	CARDINAL
iajs-1999	83	2	z6	ORG
iajs-1999	88	1	3z	CARDINAL
iajs-1999	88	2	3z)=0	CARDINAL
iajs-1999	88	3	3z	CARDINAL
iajs-1999	89	1	7):n.z	CARDINAL
iajs-1999	92	1	ℛ-submodule	GPE
iajs-1999	95	1	8):if	CARDINAL
iajs-1999	96	1	semisecond submodule iff	ORG
iajs-1999	97	1	9):let	CARDINAL
iajs-1999	98	1	semisecond submodule	ORG
iajs-1999	99	1	2.3.(4	CARDINAL
iajs-1999	99	2	semisecond submodule ℛ / ℛ	ORG
iajs-1999	100	1	2.8	CARDINAL
iajs-1999	101	1	105	CARDINAL
iajs-1999	101	2	al-haitham jour	ORG
iajs-1999	103	1	sci.	ORG
iajs-1999	103	2	ihjpas	PERSON
iajs-1999	103	3	31.3.1999	CARDINAL
iajs-1999	104	1	31	CARDINAL
iajs-1999	105	1	2018	DATE
iajs-1999	105	2	10):if	CARDINAL
iajs-1999	105	3	semisecond submodule	ORG
iajs-1999	105	4	ℬ=ℬ1⊕ℬ2	GPE
iajs-1999	105	5	ℬ 1	DATE
iajs-1999	106	1	2.3.(5	CARDINAL
iajs-1999	107	1	11):let	CARDINAL
iajs-1999	107	2	1⊕	CARDINAL
iajs-1999	108	1	semisecond submodules	ORG
iajs-1999	108	2	1⊕	CARDINAL
iajs-1999	108	3	semisecond submodule	ORG
iajs-1999	108	4	ℬ =z6⊕z16	ORG
iajs-1999	108	5	semisecond submodule	ORG
iajs-1999	108	6	z6	GPE
iajs-1999	108	7	2	CARDINAL
iajs-1999	108	8	semisecond submodule	ORG
iajs-1999	109	1	2	CARDINAL
iajs-1999	109	2	4	CARDINAL
iajs-1999	109	3	22	CARDINAL
iajs-1999	109	4	8	CARDINAL
iajs-1999	109	5	22	CARDINAL
iajs-1999	109	6	≠2	GPE
iajs-1999	110	1	two	CARDINAL
iajs-1999	111	1	12):let	CARDINAL
iajs-1999	111	2	semisecond submodules	PERSON
iajs-1999	111	3	ℬ1	DATE
iajs-1999	112	1	semisecond submodule	ORG
iajs-1999	112	2	ℬ=ℬ1⊕ℬ2	GPE
iajs-1999	113	1	r2ℵ2=0	ORG
iajs-1999	115	1	r2ℵ1=0	GPE
iajs-1999	118	1	semisecond submodules	PERSON
iajs-1999	119	1	r∈ℛ	PERSON
iajs-1999	119	2	r2m∈ℵ	GPE
iajs-1999	120	1	ℬ.	NORP
iajs-1999	120	2	13):let	ORDINAL
iajs-1999	120	3	ℛ-module	PERSON
iajs-1999	120	4	ℬ.	PERSON
iajs-1999	120	5	a2ℵ=0	NORP
iajs-1999	120	6	a2ℵ=aℵ.	ORG
iajs-1999	122	1	a2ℵ=aℵ.	ORG
iajs-1999	123	1	0	CARDINAL
iajs-1999	124	1	a(x-n2	PERSON
iajs-1999	124	2	0	CARDINAL
iajs-1999	128	1	5	CARDINAL
iajs-1999	129	1	second	ORDINAL
iajs-1999	129	2	6	CARDINAL
iajs-1999	130	1	106	CARDINAL
iajs-1999	130	2	al-haitham jour	ORG
iajs-1999	131	1	sci.	ORG
iajs-1999	131	2	ihjpas	PERSON
iajs-1999	131	3	31.3.1999	CARDINAL
iajs-1999	132	1	31	CARDINAL
iajs-1999	133	1	3) 2018	DATE
iajs-1999	133	2	4	CARDINAL
iajs-1999	134	1	14):let	CARDINAL
iajs-1999	135	1	second	ORDINAL
iajs-1999	135	2	semisecond	PERSON
iajs-1999	136	1	ℛ-submodule	GPE
iajs-1999	136	2	3,prop.(1-10	CARDINAL
iajs-1999	136	3	6,prop(2.4.7	DATE
iajs-1999	136	4	second	ORDINAL
iajs-1999	137	1	15):let	CARDINAL
iajs-1999	137	2	von neuman	PERSON
iajs-1999	139	1	2.13	CARDINAL
iajs-1999	140	1	⟸	PERSON
iajs-1999	140	2	6	CARDINAL
iajs-1999	140	3	2.14	CARDINAL
iajs-1999	141	1	second	ORDINAL
iajs-1999	143	1	16):let	TIME
iajs-1999	143	2	ℛ-submodule	GPE
iajs-1999	144	1	second	ORDINAL
iajs-1999	144	2	semisecond	PERSON
iajs-1999	145	1	r∈ℛ	PRODUCT
iajs-1999	147	1	r∈ ℛ	GPE
iajs-1999	147	2	second	ORDINAL
iajs-1999	148	1	17	CARDINAL
iajs-1999	149	1	second	ORDINAL
iajs-1999	150	1	17	CARDINAL
iajs-1999	150	2	z8	DATE
iajs-1999	150	3	2	CARDINAL
iajs-1999	150	4	semisecond	ORG
iajs-1999	152	1	18	CARDINAL
iajs-1999	153	1	4	CARDINAL
iajs-1999	154	1	19	CARDINAL
iajs-1999	156	1	ℛs-submodule	ORG
iajs-1999	156	2	ℬs	ORG
iajs-1999	156	3	s.t.	PERSON
iajs-1999	156	4	r.	NORP
iajs-1999	156	5	r∈ℛ	PERSON
iajs-1999	157	1	2	CARDINAL
iajs-1999	158	1	≠	PERSON
iajs-1999	159	1	107	CARDINAL
iajs-1999	159	2	al-haitham jour	ORG
iajs-1999	161	1	sci.	ORG
iajs-1999	161	2	ihjpas	PERSON
iajs-1999	161	3	31.3.1999	CARDINAL
iajs-1999	162	1	31	CARDINAL
iajs-1999	163	1	2018	DATE
iajs-1999	163	2	r2ℵ≠0.but	PERSON
iajs-1999	164	1	r)sℵs	PERSON
iajs-1999	164	2	21):let	CARDINAL
iajs-1999	164	3	ℛp-submodule	ORG
iajs-1999	164	4	ℬp	GPE
iajs-1999	164	5	prome	PERSON
iajs-1999	164	6	semisecond modules yass	ORG
iajs-1999	164	7	1	CARDINAL
iajs-1999	164	8	second	ORDINAL
iajs-1999	164	9	second	ORDINAL
iajs-1999	165	1	second	ORDINAL
iajs-1999	165	2	second	ORDINAL
iajs-1999	165	3	ℬ.	PERSON
iajs-1999	165	4	semisecond module	ORG
iajs-1999	165	5	second	ORDINAL
iajs-1999	166	1	semisecond module	ORG
iajs-1999	167	1	semisecond submodule	ORG
iajs-1999	167	2	r∈ℛ	PRODUCT
iajs-1999	168	1	23	CARDINAL
iajs-1999	168	2	1	CARDINAL
iajs-1999	168	3	second	ORDINAL
iajs-1999	168	4	semisecond	ORG
iajs-1999	168	5	z4	PERSON
iajs-1999	168	6	second	ORDINAL
iajs-1999	168	7	2z4≠z4	CARDINAL
iajs-1999	168	8	z4	PERSON
iajs-1999	168	9	semisecond module	ORG
iajs-1999	169	1	2	CARDINAL
iajs-1999	169	2	r∈ℛ	PRODUCT
iajs-1999	169	3	r2z≠(0	ORG
iajs-1999	170	1	3	CARDINAL
iajs-1999	170	2	zp∞	GPE
iajs-1999	170	3	zp∞	GPE
iajs-1999	170	4	0	CARDINAL
iajs-1999	171	1	zp∞	GPE
iajs-1999	171	2	zp∞	GPE
iajs-1999	171	3	semisecond	ORG
iajs-1999	172	1	4	CARDINAL
iajs-1999	172	2	semisecond module	ORG
iajs-1999	173	1	5	CARDINAL
iajs-1999	173	2	6	CARDINAL
iajs-1999	174	1	6	CARDINAL
iajs-1999	174	2	ℛ/i	ORG
iajs-1999	174	3	7	CARDINAL
iajs-1999	175	1	7	CARDINAL
iajs-1999	175	2	semisecond ℛ/ ℛ ℬ-module	LOC
iajs-1999	176	1	8)	CARDINAL
iajs-1999	177	1	8)let	CARDINAL
iajs-1999	177	2	semisecond ℬ'-module	ORG
iajs-1999	178	1	9	CARDINAL
iajs-1999	178	2	ℛ-module	PERSON
iajs-1999	178	3	ℬs	ORG
iajs-1999	178	4	semisecond ℛs	PERSON
iajs-1999	178	5	s.t. s	PERSON
iajs-1999	178	6	20	CARDINAL
iajs-1999	179	1	10	CARDINAL
iajs-1999	179	2	ℛ-module	PERSON
iajs-1999	179	3	ℬp	GPE
iajs-1999	179	4	21	CARDINAL
iajs-1999	180	1	108	CARDINAL
iajs-1999	180	2	al-haitham jour	ORG
iajs-1999	181	1	sci.	ORG
iajs-1999	181	2	ihjpas	PERSON
iajs-1999	181	3	31.3.1999	CARDINAL
iajs-1999	182	1	31	CARDINAL
iajs-1999	183	1	3) 2018	CARDINAL
iajs-1999	183	2	1	CARDINAL
iajs-1999	183	3	yassemi	PERSON
iajs-1999	183	4	s.	PERSON
iajs-1999	187	1	2001	DATE
iajs-1999	187	2	73	DATE
iajs-1999	187	3	273	CARDINAL
iajs-1999	188	1	2	CARDINAL
iajs-1999	188	2	abdul-baste	PERSON
iajs-1999	188	3	smith	GPE
iajs-1999	191	1	1988	DATE
iajs-1999	191	2	16	DATE
iajs-1999	191	3	755	CARDINAL
iajs-1999	192	1	3	CARDINAL
iajs-1999	192	2	athab	PERSON
iajs-1999	192	3	i.a.	GPE
iajs-1999	194	1	university of baghdad.	ORG
iajs-1999	195	1	1996	DATE
iajs-1999	196	1	4	CARDINAL
iajs-1999	196	2	j. prime	ORG
iajs-1999	196	3	one	CARDINAL
iajs-1999	197	1	third	ORDINAL
iajs-1999	198	1	1980	DATE
iajs-1999	198	2	301	CARDINAL
iajs-1999	199	1	5	CARDINAL
iajs-1999	199	2	annin	ORG
iajs-1999	199	3	s.	PERSON
iajs-1999	201	1	university of berkeley	ORG
iajs-1999	202	1	2002	DATE
iajs-1999	203	1	6	CARDINAL
iajs-1999	203	2	rasha	NORP
iajs-1999	203	3	i.k.	GPE
iajs-1999	206	1	university of baghdad	ORG
iajs-1999	207	1	2009	DATE
iajs-1999	208	1	7	CARDINAL
iajs-1999	208	2	macdonald	PERSON
iajs-1999	208	3	l.g.	PERSON
iajs-1999	211	1	1973	DATE
iajs-1999	211	2	33	CARDINAL