id	sid	eid	entity	type
iajs-702	1	1	2012	DATE
iajs-702	1	2	25	CARDINAL
iajs-702	1	3	1	CARDINAL
iajs-702	1	4	al-haitham	ORG
iajs-702	1	5	1	CARDINAL
iajs-702	2	1	25 year	DATE
iajs-702	2	2	2012	DATE
iajs-702	2	3	i. m. a. hadi	PERSON
iajs-702	3	1	n. majeed	PERSON
iajs-702	3	2	ibn-al-haitham	PERSON
iajs-702	3	3	university of baghdad	ORG
iajs-702	3	4	august 2011	DATE
iajs-702	3	5	september 2011	DATE
iajs-702	6	1	one	CARDINAL
iajs-702	6	2	max	PERSON
iajs-702	7	1	max-cs	PERSON
iajs-702	8	1	1introduction	CARDINAL
iajs-702	9	1		PRODUCT
iajs-702	10	1	1	CARDINAL
iajs-702	12	1	1.1	CARDINAL
iajs-702	12	2	2	CARDINAL
iajs-702	12	3	min-cs	FAC
iajs-702	13	1	1.2	CARDINAL
iajs-702	13	2	2	CARDINAL
iajs-702	13	3	max-cs	PERSON
iajs-702	13	4	nonzero annihilator	PERSON
iajs-702	13	5	max	PERSON
iajs-702	13	6	max-cs r-module	PERSON
iajs-702	15	1	c3	PERSON
iajs-702	15	2	two	CARDINAL
iajs-702	15	3	zero	CARDINAL
iajs-702	16	1	3	CARDINAL
iajs-702	16	2	1.3	CARDINAL
iajs-702	16	3	1	CARDINAL
iajs-702	17	1	max-cs	PERSON
iajs-702	17	2	1	CARDINAL
iajs-702	18	1	2	CARDINAL
iajs-702	18	2	max-cs	PERSON
iajs-702	18	3	ℤ2	CARDINAL
iajs-702	18	4	ℤ3, ℤ6,	ORG
iajs-702	18	5	ℤ10	ORG
iajs-702	18	6	ℤ30	ORG
iajs-702	18	7	ℤ-module	ORG
iajs-702	18	8	max-cs	PERSON
iajs-702	18	9	1	CARDINAL
iajs-702	18	10	1	CARDINAL
iajs-702	19	1	2012	DATE
iajs-702	19	2	25	CARDINAL
iajs-702	19	3	1	CARDINAL
iajs-702	19	4	al-haitham	ORG
iajs-702	19	5	1	CARDINAL
iajs-702	20	1	25 year 2012 3	DATE
iajs-702	21	1	max-cs	PERSON
iajs-702	22	1	ℤ-module ℤ	ORG
iajs-702	22	2	ℤ4	ORG
iajs-702	22	3	ℤ8	CARDINAL
iajs-702	22	4	ℤ16	ORG
iajs-702	22	5	max-cs	PERSON
iajs-702	22	6	4.	CARDINAL
iajs-702	23	1	4	CARDINAL
iajs-702	23	2	1.18	CARDINAL
iajs-702	24	1	max	PERSON
iajs-702	24	2	1	CARDINAL
iajs-702	25	1	5	CARDINAL
iajs-702	25	2	max-cs	PERSON
iajs-702	26	1	ℤ12	PRODUCT
iajs-702	26	2	2	CARDINAL
iajs-702	26	3	3	DATE
iajs-702	26	4	4	DATE
iajs-702	26	5	6	DATE
iajs-702	26	6	0	CARDINAL
iajs-702	27	1		ORG
iajs-702	28	1		ORG
iajs-702	29	1		ORG
iajs-702	30	1		PRODUCT
iajs-702	31	1	ℤ12	ORG
iajs-702	32	1	123	CARDINAL
iajs-702	32	2	  	PRODUCT
iajs-702	34	1	3	CARDINAL
iajs-702	34	2	4	CARDINAL
iajs-702	36	1	2	CARDINAL
iajs-702	36	2		CARDINAL
iajs-702	36	3	3	CARDINAL
iajs-702	36	4		PRODUCT
iajs-702	37	1	2	CARDINAL
iajs-702	37	2	6	CARDINAL
iajs-702	38	1	max-cs	PERSON
iajs-702	38	2	6	CARDINAL
iajs-702	39	1	ℤ24	PERSON
iajs-702	39	2	max-cs	PERSON
iajs-702	40	1	2 1 2 m	QUANTITY
iajs-702	42	1		PRODUCT
iajs-702	42	2	max	PERSON
iajs-702	42	3	max	PERSON
iajs-702	43	1	8	CARDINAL
iajs-702	44	1	max-cs	PERSON
iajs-702	44	2	1.3	CARDINAL
iajs-702	44	3	1	CARDINAL
iajs-702	45	1	9	CARDINAL
iajs-702	45	2		PRODUCT
iajs-702	46	1	2	CARDINAL
iajs-702	46	2	1	CARDINAL
iajs-702	46	3	4	CARDINAL
iajs-702	46	4	0	DATE
iajs-702	46	5	6	CARDINAL
iajs-702	48	1	max	PERSON
iajs-702	48	2	ℤ8 	PRODUCT
iajs-702	48	3	0	CARDINAL
iajs-702	49	1		PERSON
iajs-702	50	1		PRODUCT
iajs-702	50	2	0	CARDINAL
iajs-702	50	3	 ℤ2	PERSON
iajs-702	51	1	max	PERSON
iajs-702	51	2	10	CARDINAL
iajs-702	52	1	1	CARDINAL
iajs-702	52	2	2	CARDINAL
iajs-702	52	3	two	CARDINAL
iajs-702	52	4	1	CARDINAL
iajs-702	52	5	2	CARDINAL
iajs-702	52	6	1≅m 2	DATE
iajs-702	54	1	mahmoud	PERSON
iajs-702	54	2	5	CARDINAL
iajs-702	55	1	1.1	CARDINAL
iajs-702	55	2	ℤ-module	ORG
iajs-702	55	3	ℤ8  ℤ2	PRODUCT
iajs-702	56	1	kamal	PERSON
iajs-702	56	2	ℤ8	PRODUCT
iajs-702	56	3	kamal	PERSON
iajs-702	56	4	ℤ2	ORG
iajs-702	57	1	2012	DATE
iajs-702	58	1	25	CARDINAL
iajs-702	58	2	1	CARDINAL
iajs-702	58	3	al-haitham	ORG
iajs-702	58	4	1	CARDINAL
iajs-702	59	1	25 year 2012	DATE
iajs-702	59	2	5	CARDINAL
iajs-702	59	3	3	CARDINAL
iajs-702	59	4	kamal	PERSON
iajs-702	60	1	1.4	CARDINAL
iajs-702	60	2	⊆	CARDINAL
iajs-702	61	1	max	PERSON
iajs-702	61	2	≠ annn	PERSON
iajs-702	61	3	submodule n ≨	ORG
iajs-702	61	4	m. proof	PERSON
iajs-702	61	5	annr	PERSON
iajs-702	63	1	i.	PERSON
iajs-702	64	1	annr	PERSON
iajs-702	64	2	0r	CARDINAL
iajs-702	67	1	0	CARDINAL
iajs-702	68	1	≠ 0	PERSON
iajs-702	69	1	m. conversely	PERSON
iajs-702	71	1	ann m	PERSON
iajs-702	71	2	ann n	PERSON
iajs-702	71	3	ann m.	PERSON
iajs-702	71	4	0r	CARDINAL
iajs-702	76	1	ann r	PERSON
iajs-702	76	2	0r	CARDINAL
iajs-702	76	3	max	PERSON
iajs-702	77	1	1.5	CARDINAL
iajs-702	77	2	ann m.	PERSON
iajs-702	80	1	1	CARDINAL
iajs-702	81	1	al-hazmi	PERSON
iajs-702	81	2	2,p.24	CARDINAL
iajs-702	82	1	first	ORDINAL
iajs-702	83	1	1.6 lemma	QUANTITY
iajs-702	83	2	m. n	PERSON
iajs-702	84	1	w	ORG
iajs-702	84	2	two	CARDINAL
iajs-702	84	3	0	CARDINAL
iajs-702	85	1	4	CARDINAL
iajs-702	85	2	1.5	CARDINAL
iajs-702	85	3	n.	PERSON
iajs-702	87	1		ORG
iajs-702	90	1	1.7	CARDINAL
iajs-702	90	2	u e k  m.	ORG
iajs-702	91	1	2012	DATE
iajs-702	92	1	25	CARDINAL
iajs-702	92	2	1	CARDINAL
iajs-702	92	3	al-haitham	ORG
iajs-702	92	4	1	CARDINAL
iajs-702	93	1	25 year 2012	DATE
iajs-702	93	2	w	ORG
iajs-702	93	3	two	CARDINAL
iajs-702	93	4	k.	PERSON
iajs-702	93	5	w ≠	PERSON
iajs-702	94	1	m.	PERSON
iajs-702	95	1	≠	PERSON
iajs-702	96	1	u 	PERSON
iajs-702	96	2	≠	PERSON
iajs-702	97	1	w ≠	PERSON
iajs-702	98	1	1.8	CARDINAL
iajs-702	102	1		ORG
iajs-702	103	1		PRODUCT
iajs-702	105	1	1.6	CARDINAL
iajs-702	105	2	1.8	CARDINAL
iajs-702	105	3	1.9	CARDINAL
iajs-702	106	1	1	CARDINAL
iajs-702	107	1	2	CARDINAL
iajs-702	108	1	3	CARDINAL
iajs-702	110	1	1.10	CARDINAL
iajs-702	111	1	2	CARDINAL
iajs-702	114	1	1.7	CARDINAL
iajs-702	117	1	lemma 1.6.	ORG
iajs-702	119	1		ORG
iajs-702	119	2	4	CARDINAL
iajs-702	119	3	1.7	CARDINAL
iajs-702	120	1	1.6	CARDINAL
iajs-702	124	1	2	CARDINAL
iajs-702	124	2	3.1.1	CARDINAL
iajs-702	125	1	1.11	CARDINAL
iajs-702	127	1	2012	DATE
iajs-702	128	1	25	CARDINAL
iajs-702	128	2	1	CARDINAL
iajs-702	128	3	al-haitham	ORG
iajs-702	128	4	1	CARDINAL
iajs-702	129	1	25 year 2012	DATE
iajs-702	129	2	4	CARDINAL
iajs-702	129	3	 e k. hence	PERSON
iajs-702	129	4	1.7	CARDINAL
iajs-702	129	5	{k: k	PERSON
iajs-702	130	1	zorn	ORG
iajs-702	130	2	w.	PERSON
iajs-702	130	3	w	GPE
iajs-702	131	1	w	GPE
iajs-702	132	1	w 	PERSON
iajs-702	132	2	0	CARDINAL
iajs-702	134	1	1.12	CARDINAL
iajs-702	136	1	1.13	CARDINAL
iajs-702	137	1	1	CARDINAL
iajs-702	139	1	2	CARDINAL
iajs-702	139	2	1 	QUANTITY
iajs-702	139	3	2	CARDINAL
iajs-702	139	4	m1 and m2	PRODUCT
iajs-702	139	5	1	CARDINAL
iajs-702	139	6	2	CARDINAL
iajs-702	139	7	m. therefore	PERSON
iajs-702	140	1		PRODUCT
iajs-702	140	2	2	CARDINAL
iajs-702	140	3	1	CARDINAL
iajs-702	141	1	1 	QUANTITY
iajs-702	141	2	2	CARDINAL
iajs-702	141	3	m1 and m2	PERSON
iajs-702	141	4	two	CARDINAL
iajs-702	141	5	m1 and m2	PRODUCT
iajs-702	141	6		PRODUCT
iajs-702	141	7	2 	QUANTITY
iajs-702	141	8	e m.	PERSON
iajs-702	141	9	1	DATE
iajs-702	142	1		PRODUCT
iajs-702	142	2	2	CARDINAL
iajs-702	142	3	2	CARDINAL
iajs-702	142	4	4	CARDINAL
iajs-702	143	1		PRODUCT
iajs-702	143	2	2	CARDINAL
iajs-702	144	1	m. hence m	GPE
iajs-702	145	1	1.14	CARDINAL
iajs-702	147	1	4	CARDINAL
iajs-702	147	2	1.5	CARDINAL
iajs-702	147	3	4	CARDINAL
iajs-702	149	1	 w	PERSON
iajs-702	149	2	 w	PERSON
iajs-702	149	3		PERSON
iajs-702	150	1	2012	DATE
iajs-702	151	1	25	CARDINAL
iajs-702	151	2	1	CARDINAL
iajs-702	151	3	al-haitham	ORG
iajs-702	151	4	1	CARDINAL
iajs-702	152	1	25 year	DATE
iajs-702	152	2	2012	DATE
iajs-702	152	3	1.15	CARDINAL
iajs-702	152	4	 ℤ2	PRODUCT
iajs-702	152	5	≅ ℤ8	CARDINAL
iajs-702	152	6	1.16	CARDINAL
iajs-702	152	7	4	CARDINAL
iajs-702	152	8	m. hence	PERSON
iajs-702	152	9	14	CARDINAL
iajs-702	153	1	1.17	CARDINAL
iajs-702	154	1	 m	PERSON
iajs-702	155	1	1.16	CARDINAL
iajs-702	156	1	1.16	CARDINAL
iajs-702	157	1		PRODUCT
iajs-702	157	2	ℤ2	ORG
iajs-702	157	3	ℤ3	ORG
iajs-702	157	4	ℤ-module	ORG
iajs-702	158	1		PRODUCT
iajs-702	158	2	1.16	CARDINAL
iajs-702	159	1	1.18	CARDINAL
iajs-702	159	2	1.14	CARDINAL
iajs-702	161	1	2	CARDINAL
iajs-702	161	2	 ℤ2	FAC
iajs-702	162	1	ℤ8  ℤ2	PRODUCT
iajs-702	163	1	1.19	CARDINAL
iajs-702	164	1	max	PERSON
iajs-702	166	1	6	CARDINAL
iajs-702	166	2	2.3.11	DATE
iajs-702	166	3	7	CARDINAL
iajs-702	166	4	2.5	CARDINAL
iajs-702	166	5	1	CARDINAL
iajs-702	167	1	4	CARDINAL
iajs-702	168	1	m. hence m	ORG
iajs-702	168	2	max	PERSON
iajs-702	169	1	1.20	CARDINAL
iajs-702	169	2	ℤ	ORG
iajs-702	169	3	ℤ-module	ORG
iajs-702	169	4	max	PERSON
iajs-702	169	5	ℤ	ORG
iajs-702	169	6	2012	DATE
iajs-702	170	1	25	CARDINAL
iajs-702	171	1	1	CARDINAL
iajs-702	171	2	al-haitham	ORG
iajs-702	171	3	1	CARDINAL
iajs-702	172	1	25 year 2012	DATE
iajs-702	172	2	2ℤ	CARDINAL
iajs-702	172	3	ℤ-module	ORG
iajs-702	172	4	ℤ	ORG
iajs-702	173	1	1.16	CARDINAL
iajs-702	173	2	max-cs	PERSON
iajs-702	173	3	max-cs	PERSON
iajs-702	173	4	max-cs	PERSON
iajs-702	173	5	first	ORDINAL
iajs-702	173	6	1.21	CARDINAL
iajs-702	173	7	max	PERSON
iajs-702	173	8	max	PERSON
iajs-702	174	1	0	CARDINAL
iajs-702	175	1	m.	PERSON
iajs-702	175	2	first	ORDINAL
iajs-702	175	3	4	CARDINAL
iajs-702	175	4	1.4	CARDINAL
iajs-702	177	1	4	CARDINAL
iajs-702	179	1	annb ≠ 0	PERSON
iajs-702	180	1	max	PERSON
iajs-702	180	2	 k	PERSON
iajs-702	182	1	max	PERSON
iajs-702	183	1	1.22	CARDINAL
iajs-702	183	2	max	PERSON
iajs-702	183	3	max	PERSON
iajs-702	184	1	m. hence	PERSON
iajs-702	184	2	second	ORDINAL
iajs-702	185	1	max	PERSON
iajs-702	185	2	1.21	CARDINAL
iajs-702	186	1	max	PERSON
iajs-702	186	2	1.3	CARDINAL
iajs-702	186	3	10	CARDINAL
iajs-702	187	1	1.23	CARDINAL
iajs-702	188	1	 m	PERSON
iajs-702	188	2	max	PERSON
iajs-702	189	1	max	PERSON
iajs-702	190	1	1.22	CARDINAL
iajs-702	194	1	8	CARDINAL
iajs-702	195	1	1.24	CARDINAL
iajs-702	195	2	max-cs r-module	PERSON
iajs-702	196	1	max	PERSON
iajs-702	197	1	max	PERSON
iajs-702	198	1	≅	CARDINAL
iajs-702	198	2	1	CARDINAL
iajs-702	200	1	m.	PERSON
iajs-702	200	2	0 ≠ x	PERSON
iajs-702	200	3	 ker f.	PERSON
iajs-702	200	4	2012	DATE
iajs-702	201	1	25	CARDINAL
iajs-702	201	2	1	CARDINAL
iajs-702	201	3	al-haitham	ORG
iajs-702	201	4	1	CARDINAL
iajs-702	202	1	25 year 2012	DATE
iajs-702	202	2	0 ≠ r 	PERSON
iajs-702	203	1	ker f. hence rf(x	PERSON
iajs-702	204	1	0	CARDINAL
iajs-702	205	1	f(x	ORG
iajs-702	206	1	0	CARDINAL
iajs-702	207	1	f(x	ORG
iajs-702	208	1	0	CARDINAL
iajs-702	209	1	ker f = l	PERSON
iajs-702	210	1	m. since annm	PERSON
iajs-702	211	1	1.21	CARDINAL
iajs-702	211	2	max	PERSON
iajs-702	211	3	1.3	CARDINAL
iajs-702	211	4	10	CARDINAL
iajs-702	211	5	max	PERSON
iajs-702	212	1	1.25	CARDINAL
iajs-702	212	2	max	PERSON
iajs-702	215	1	max	PERSON
iajs-702	216	1	8	CARDINAL
iajs-702	217	1	9	CARDINAL
iajs-702	217	2	3.3,p.48	CARDINAL
iajs-702	218	1	1.15	CARDINAL
iajs-702	218	2	max	PERSON
iajs-702	219	1	1.26	CARDINAL
iajs-702	219	2	max	PERSON
iajs-702	219	3	max-cs	PERSON
iajs-702	220	1	9	CARDINAL
iajs-702	220	2	3.3	CARDINAL
iajs-702	221	1	1.21	CARDINAL
iajs-702	223	1	1.27	CARDINAL
iajs-702	224	1	1.28	CARDINAL
iajs-702	224	2	1	CARDINAL
iajs-702	227	1	2	CARDINAL
iajs-702	229	1	0	CARDINAL
iajs-702	230	1	3	CARDINAL
iajs-702	230	2	ℤ-module	ORG
iajs-702	232	1	0	CARDINAL
iajs-702	232	2	2)	DATE
iajs-702	234	1	1.29	CARDINAL
iajs-702	235	1	max	PERSON
iajs-702	235	2	max	PERSON
iajs-702	236	1	max	PERSON
iajs-702	239	1	first	ORDINAL
iajs-702	240	1	10	CARDINAL
iajs-702	240	2	3.31	CARDINAL
iajs-702	241	1	r.	NORP
iajs-702	241	2	7	CARDINAL
iajs-702	241	3	3.1	CARDINAL
iajs-702	244	1	2012	DATE
iajs-702	245	1	25	CARDINAL
iajs-702	245	2	1	CARDINAL
iajs-702	245	3	al-haitham	ORG
iajs-702	245	4	1	CARDINAL
iajs-702	246	1	25 year 2012	DATE
iajs-702	246	2	10	CARDINAL
iajs-702	246	3	3.31	CARDINAL
iajs-702	247	1	submodule w	ORG
iajs-702	250	1	7	CARDINAL
iajs-702	250	2	3.1	CARDINAL
iajs-702	253	1	10	CARDINAL
iajs-702	253	2	3.31	CARDINAL
iajs-702	253	3	chapter three	LAW
iajs-702	254	1	r.	NORP
iajs-702	255	1	r.	NORP
iajs-702	255	2	n = w	ORG
iajs-702	255	3	≠ 0	PERSON
iajs-702	256	1	m.	PERSON
iajs-702	257	1	some l 	TIME
iajs-702	261	1	7	CARDINAL
iajs-702	261	2	1.6	CARDINAL
iajs-702	265	1	0	CARDINAL
iajs-702	266	1	0	CARDINAL
iajs-702	270	1	7	CARDINAL
iajs-702	270	2	6.1	CARDINAL
iajs-702	271	1		ORG
iajs-702	272	1	10	CARDINAL
iajs-702	272	2	3.1	CARDINAL
iajs-702	273	1	r.	NORP
iajs-702	273	2	r.	NORP
iajs-702	273	3	j	PERSON
iajs-702	275	1	jm =	PERSON
iajs-702	276	1	7	CARDINAL
iajs-702	276	2	6.1	CARDINAL
iajs-702	277	1	10	CARDINAL
iajs-702	277	2	3.1	CARDINAL
iajs-702	277	3	jm	ORG
iajs-702	278	1	7	CARDINAL
iajs-702	278	2	3.1	CARDINAL
iajs-702	282	1	max	PERSON
iajs-702	282	2	r.	NORP
iajs-702	284	1		PRODUCT
iajs-702	285	1		PRODUCT
iajs-702	286	1	7	CARDINAL
iajs-702	286	2	1.6	CARDINAL
iajs-702	286	3	0	CARDINAL
iajs-702	288	1	m]m 	PERSON
iajs-702	289	1	1.29	CARDINAL
iajs-702	289	2	1.30	CARDINAL
iajs-702	290	1	max-cs	PERSON
iajs-702	291	1	first	ORDINAL
iajs-702	291	2	2	CARDINAL
iajs-702	291	3	2.1.1	CARDINAL
iajs-702	293	1	1.31	CARDINAL
iajs-702	293	2	r.	NORP
iajs-702	293	3	r.	NORP
iajs-702	293	4	i.	PERSON
iajs-702	293	5	4	CARDINAL
iajs-702	293	6	1.3	CARDINAL
iajs-702	293	7	4	CARDINAL
iajs-702	293	8	1.4	CARDINAL
iajs-702	294	1	r.	NORP
iajs-702	295	1	r.	NORP
iajs-702	296	1	0	CARDINAL
iajs-702	297	1	2012	DATE
iajs-702	298	1	25	CARDINAL
iajs-702	298	2	1	CARDINAL
iajs-702	298	3	al-haitham	ORG
iajs-702	298	4	1	CARDINAL
iajs-702	299	1	25 year 2012	DATE
iajs-702	299	2	lemma 1.6.	ORG
iajs-702	300	1	 e i.	ORG
iajs-702	300	2	j 	PERSON
iajs-702	300	3	 j 	PERSON
iajs-702	301	1	 j  e r	PERSON
iajs-702	301	2	4	CARDINAL
iajs-702	302	1	 j  j*.	PERSON
iajs-702	303	1	j* 	PERSON
iajs-702	304	1		ORG
iajs-702	305	1	lemma 1.6	PERSON
iajs-702	306	1	0	CARDINAL
iajs-702	306	2	some two	CARDINAL
iajs-702	306	3		PRODUCT
iajs-702	306	4	4	CARDINAL
iajs-702	307	1	r.	NORP
iajs-702	308	1	1.32	CARDINAL
iajs-702	308	2	1.31	CARDINAL
iajs-702	309	1	2	CARDINAL
iajs-702	309	2	0	CARDINAL
iajs-702	309	3	0	CARDINAL
iajs-702	309	4	4	CARDINAL
iajs-702	310	1	1.33	CARDINAL
iajs-702	311	1	max	PERSON
iajs-702	312	1	max	PERSON
iajs-702	313	1	r.	NORP
iajs-702	313	2	4	CARDINAL
iajs-702	313	3	2.38	CARDINAL
iajs-702	313	4	ann anni	PERSON
iajs-702	313	5	anni ≠ 0	PERSON
iajs-702	313	6	4	CARDINAL
iajs-702	313	7	1.27(b	CARDINAL
iajs-702	314	1	1.31	CARDINAL
iajs-702	314	2	r.	NORP
iajs-702	314	3	4	CARDINAL
iajs-702	314	4	2.38	CARDINAL
iajs-702	314	5	j = ann	PERSON
iajs-702	315	1	max	PERSON
iajs-702	317	1	r.	NORP
iajs-702	317	2	0	CARDINAL
iajs-702	317	3	j  anni	PERSON
iajs-702	318	1	j = anni	PERSON
iajs-702	318	2	j	PERSON
iajs-702	320	1	0	CARDINAL
iajs-702	321	1	ann anni	PERSON
iajs-702	321	2	1	CARDINAL
iajs-702	321	3	i.	PERSON
iajs-702	321	4	r. (	GPE
iajs-702	322	1	anni ≠ 0	PERSON
iajs-702	323	1	4	CARDINAL
iajs-702	323	2	2.38	CARDINAL
iajs-702	323	3	ann anni	PERSON
iajs-702	324	1	i. so j	ORG
iajs-702	324	2	1.31	CARDINAL
iajs-702	325	1	j	PERSON
iajs-702	327	1	r.	NORP
iajs-702	330	1	1	CARDINAL
iajs-702	331	1	1	CARDINAL
iajs-702	331	2	r.	NORP
iajs-702	332	1	1	CARDINAL
iajs-702	332	2	r.	NORP
iajs-702	332	3	r.	NORP
iajs-702	332	4	4	CARDINAL
iajs-702	333	1	1.34	CARDINAL
iajs-702	334	1	max	PERSON
iajs-702	336	1	4	CARDINAL
iajs-702	336	2	p.36	PERSON
iajs-702	337	1	1.33	CARDINAL
iajs-702	338	1	2012	DATE
iajs-702	339	1	25	CARDINAL
iajs-702	339	2	1	CARDINAL
iajs-702	339	3	al-haitham	ORG
iajs-702	339	4	1	CARDINAL
iajs-702	340	1	25 year 2012	DATE
iajs-702	340	2	von neumann	PERSON
iajs-702	340	3	4	CARDINAL
iajs-702	341	1	1.35	CARDINAL
iajs-702	343	1	max	PERSON
iajs-702	344	1	lemma	ORG
iajs-702	345	1	1.36	CARDINAL
iajs-702	346	1	4	CARDINAL
iajs-702	346	2	p.36	PERSON
iajs-702	347	1	z(r/z(r	ORG
iajs-702	348	1	annr/z(r	ORG
iajs-702	350	1	ann r/z(r	PERSON
iajs-702	350	2	z(r	DATE
iajs-702	352	1	i.	PERSON
iajs-702	352	2	z(r	DATE
iajs-702	352	3	r.	NORP
iajs-702	353	1		CARDINAL
iajs-702	353	2	r.	NORP
iajs-702	353	3		CARDINAL
iajs-702	353	4	j  ann(ax	PERSON
iajs-702	353	5	≠ 0	PERSON
iajs-702	354	1	y ≠ 0	PERSON
iajs-702	356	1	0	CARDINAL
iajs-702	357	1	1	CARDINAL
iajs-702	358	1	2	CARDINAL
iajs-702	358	2	ya ≠ 0	PERSON
iajs-702	358	3	0≠yaann(x)j	CARDINAL
iajs-702	359	1		CARDINAL
iajs-702	360	1	3	CARDINAL
iajs-702	362	1		CARDINAL
iajs-702	363	1	4	CARDINAL
iajs-702	363	2	0≠ yxann(a)j	MONEY
iajs-702	364	1	5	CARDINAL
iajs-702	364	2	0	CARDINAL
iajs-702	365	1		CARDINAL
iajs-702	368	1	1.37	CARDINAL
iajs-702	370	1	max-cs	PERSON
iajs-702	370	2	1.36	CARDINAL
iajs-702	370	3	1.33	CARDINAL
iajs-702	372	1	1.38	CARDINAL
iajs-702	373	1	4	CARDINAL
iajs-702	373	2	r[x1	PERSON
iajs-702	374	1	first	ORDINAL
iajs-702	375	1	f(x	ORG
iajs-702	375	2		CARDINAL
iajs-702	376	1	f(x	ORG
iajs-702	377	1	0	CARDINAL
iajs-702	377	2	1	DATE
iajs-702	377	3	 annr[x]a1x 	PERSON
iajs-702	377	4	annr[x]anx n 	PERSON
iajs-702	379	1	annr(ai	LANGUAGE
iajs-702	379	2	0	CARDINAL
iajs-702	379	3	1	DATE
iajs-702	380	1	j 	PERSON
iajs-702	380	2	j ≠ 0	PERSON
iajs-702	380	3	annra0	ORG
iajs-702	382	1	j ≠ 0	PERSON
iajs-702	383	1	j[x	PERSON
iajs-702	383	2	≠ 0	PERSON
iajs-702	384	1	0 ≠ g(x	PERSON
iajs-702	384	2	j[x	PERSON
iajs-702	385	1	bi  j	PERSON
iajs-702	385	2	0	CARDINAL
iajs-702	385	3	1	DATE
iajs-702	385	4	k 	PERSON
iajs-702	385	5	≠ 0	PERSON
iajs-702	386	1	annr[x](a	PERSON
iajs-702	387	1	2012	DATE
iajs-702	388	1	25	CARDINAL
iajs-702	388	2	1	CARDINAL
iajs-702	388	3	al-haitham	ORG
iajs-702	388	4	1	CARDINAL
iajs-702	389	1	25 year 2012	DATE
iajs-702	390	1	a0 x	PERSON
iajs-702	391	1	0	CARDINAL
iajs-702	391	2	0	CARDINAL
iajs-702	391	3	0	CARDINAL
iajs-702	391	4	0	CARDINAL
iajs-702	391	5	0	CARDINAL
iajs-702	392	1	0	CARDINAL
iajs-702	392	2	0 ≠ bk	PERSON
iajs-702	392	3	j  annra0	PERSON
iajs-702	393	1	annra0 	PERSON
iajs-702	393	2	z(r	DATE
iajs-702	394	1	0	CARDINAL
iajs-702	396	1	f(x	ORG
iajs-702	397	1	r[x1	PERSON
iajs-702	398	1	1.39	CARDINAL
iajs-702	399	1	r[x1	PERSON
iajs-702	400	1	r[x1	PERSON
iajs-702	400	2	max	PERSON
iajs-702	401	1	38	CARDINAL
iajs-702	401	2	r[x1	PERSON
iajs-702	402	1	33	CARDINAL
iajs-702	402	2	1.40	CARDINAL
iajs-702	403	1	1	CARDINAL
iajs-702	403	2	dung,n.v.	ORG
iajs-702	404	1	huynh	PERSON
iajs-702	404	2	d.v.	GPE
iajs-702	404	3	smith	GPE
iajs-702	404	4	p.f.	GPE
iajs-702	404	5	r.	NORP
iajs-702	404	6	1994	DATE
iajs-702	404	7	john wiley	PERSON
iajs-702	404	8	new york	GPE
iajs-702	405	1	2	CARDINAL
iajs-702	405	2	husain suleman.s.al-hazmi	PERSON
iajs-702	405	3	2005	DATE
iajs-702	405	4	ohio university	ORG
iajs-702	406	1	3	CARDINAL
iajs-702	406	2	saad.h.m ohamed	ORG
iajs-702	406	3	bruno j. muller	PERSON
iajs-702	406	4	1990	DATE
iajs-702	406	5	combridge univ.	ORG
iajs-702	407	1	new york	GPE
iajs-702	407	2	chester	GPE
iajs-702	407	3	melbourne	GPE
iajs-702	407	4	sydney	GPE
iajs-702	408	1	4	CARDINAL
iajs-702	408	2	goodearl	PERSON
iajs-702	408	3	k.r.	GPE
iajs-702	408	4	1976	DATE
iajs-702	408	5	marcel dekker	PERSON
iajs-702	408	6	inc.	ORG
iajs-702	408	7	newyork	ORG
iajs-702	408	8	basel	GPE
iajs-702	409	1	mahmoud a. kamal	PERSON
iajs-702	409	2	m. menshawy	PERSON
iajs-702	409	3	2007	DATE
iajs-702	409	4	j. egypt	GPE
iajs-702	410	1	math.soc.	GPE
iajs-702	411	1	157	CARDINAL
iajs-702	412	1	6	CARDINAL
iajs-702	412	2	kasch,f.	ORG
iajs-702	412	3	1982	DATE
iajs-702	412	4	academic press, inc	ORG
iajs-702	412	5	london	GPE
iajs-702	413	1	z.a.el-bast	PERSON
iajs-702	413	2	1988	DATE
iajs-702	413	3	10(4),.755	CARDINAL
iajs-702	413	4	8	CARDINAL
iajs-702	414	1	1984	DATE
iajs-702	415	1	33	DATE
iajs-702	416	1	61-69	CARDINAL
iajs-702	417	1	zeinab talib salman al-zubaidey	PERSON
iajs-702	417	2	2005	DATE
iajs-702	418	1	university of baghdad	ORG
iajs-702	419	1	10	CARDINAL
iajs-702	420	1	ahmed	PERSON
iajs-702	420	2	a.a.	GPE
iajs-702	420	3	1992	DATE
iajs-702	421	1	university of baghdad	ORG
iajs-702	422	1	مقاسات التوسع	GPE
iajs-702	422	2	2012	DATE
iajs-702	422	3	25	CARDINAL
iajs-702	422	4	1	CARDINAL
iajs-702	422	5	al-haitham	ORG
iajs-702	422	6	1	CARDINAL
iajs-702	423	1	25 year	DATE
iajs-702	423	2	2012 ،	DATE
iajs-702	423	3	محمد علي جامعة	PRODUCT
iajs-702	423	4	2011	DATE
iajs-702	423	5	قبل البحث	PERSON
iajs-702	423	6	، 2011	DATE
iajs-702	423	7	25	CARDINAL
iajs-702	423	8	استلم البحث	ORG
iajs-702	423	9	الخالصة	GPE
iajs-702	423	10	ھذا البحث	ORG
iajs-702	423	11	دراسة واسعة	PERSON
iajs-702	423	12	مقاسـات التوسـع مـث	ORG
iajs-702	424	1	مقاس	GPE
iajs-702	425	1	أعظم(ھو أصغر ط	ORG
iajs-702	425	2	فـان الحلقـة	ORG
iajs-702	425	3	غrمقاس	GPE
iajs-702	426	1	واحدة	ORG
iajs-702	427	1	ھذا	ORG
iajs-702	428	1	مقاس	GPE
iajs-702	428	2	مقاس	GPE
iajs-702	428	3	مقاس	GPE
iajs-702	428	4	منتظم	GPE