id sid tid token lemma pos iajs-200 1 1 179 179 NUM iajs-200 1 2 | | NOUN iajs-200 1 3 mathematics mathematic NOUN iajs-200 1 4 2015 2015 NUM iajs-200 1 5 ) ) PUNCT iajs-200 1 6 عام عام ADP iajs-200 1 7 1(العدد 1(العدد NUM iajs-200 1 8 28المجلد 28المجلد NUM iajs-200 1 9 مجلة مجلة PROPN iajs-200 1 10 إبن إبن VERB iajs-200 1 11 الھيثم الھيثم NOUN iajs-200 1 12 للعلوم للعلوم NOUN iajs-200 1 13 الصرفة الصرفة NOUN iajs-200 2 1 و و PRON iajs-200 2 2 التطبيقية التطبيقية ADJ iajs-200 2 3 ibn ibn PROPN iajs-200 2 4 al al PROPN iajs-200 2 5 - - PUNCT iajs-200 2 6 haitham haitham PROPN iajs-200 2 7 j. j. PROPN iajs-200 2 8 for for ADP iajs-200 2 9 pure pure PROPN iajs-200 2 10 & & CCONJ iajs-200 2 11 appl appl PROPN iajs-200 2 12 . . PUNCT iajs-200 3 1 sci sci PROPN iajs-200 3 2 . . PUNCT iajs-200 3 3 vol vol NOUN iajs-200 3 4 . . PROPN iajs-200 4 1 28 28 NUM iajs-200 4 2 ( ( PUNCT iajs-200 4 3 1 1 NUM iajs-200 4 4 ) ) PUNCT iajs-200 4 5 2015 2015 NUM iajs-200 4 6 on on ADP iajs-200 4 7 semi semi ADJ iajs-200 4 8 - - ADJ iajs-200 4 9 essential essential ADJ iajs-200 4 10 submodules submodule NOUN iajs-200 4 11 muna muna PROPN iajs-200 4 12 a. a. PROPN iajs-200 4 13 ahmed ahmed PROPN iajs-200 4 14 math.200600986@yahoo.com math.200600986@yahoo.com PROPN iajs-200 4 15 maysaa maysaa PROPN iajs-200 4 16 r. r. PROPN iajs-200 4 17 abbas abbas PROPN iajs-200 4 18 maysaa.alsaher@yahoo.com maysaa.alsaher@yahoo.com PROPN iajs-200 4 19     SPACE iajs-200 4 20 department department NOUN iajs-200 4 21 of of ADP iajs-200 4 22 mathematics mathematics PROPN iajs-200 4 23 , , PUNCT iajs-200 4 24 college college NOUN iajs-200 4 25 of of ADP iajs-200 4 26 science science NOUN iajs-200 4 27 for for ADP iajs-200 4 28 women woman NOUN iajs-200 4 29 , , PUNCT iajs-200 4 30 university university NOUN iajs-200 4 31 of of ADP iajs-200 4 32 baghdad baghdad PROPN iajs-200 4 33 , , PUNCT iajs-200 4 34 iraq iraq PROPN iajs-200 4 35 - - PUNCT iajs-200 4 36 baghdad baghdad PROPN iajs-200 4 37 . . PUNCT iajs-200 5 1 received receive VERB iajs-200 5 2 in in ADP iajs-200 5 3 : : PUNCT iajs-200 5 4 20 20 NUM iajs-200 5 5 october october NOUN iajs-200 5 6 2014 2014 NUM iajs-200 5 7 , , PUNCT iajs-200 5 8 accepted accept VERB iajs-200 5 9 in in ADP iajs-200 5 10 : : PUNCT iajs-200 5 11 5 5 NUM iajs-200 5 12 january january NOUN iajs-200 5 13 2015 2015 NUM iajs-200 5 14 abstract abstract ADV iajs-200 5 15 let let VERB iajs-200 5 16 r r PRON iajs-200 5 17 be be AUX iajs-200 5 18 a a DET iajs-200 5 19 commutative commutative ADJ iajs-200 5 20 ring ring NOUN iajs-200 5 21 with with ADP iajs-200 5 22 identity identity NOUN iajs-200 5 23 and and CCONJ iajs-200 5 24 let let VERB iajs-200 5 25 m m PRON iajs-200 5 26 be be AUX iajs-200 5 27 a a DET iajs-200 5 28 unitary unitary ADJ iajs-200 5 29 left left ADJ iajs-200 5 30 r r NOUN iajs-200 5 31 - - PUNCT iajs-200 5 32 module module NOUN iajs-200 5 33 . . PUNCT iajs-200 6 1 the the DET iajs-200 6 2 purpose purpose NOUN iajs-200 6 3 of of ADP iajs-200 6 4 this this DET iajs-200 6 5 paper paper NOUN iajs-200 6 6 is be AUX iajs-200 6 7 to to PART iajs-200 6 8 investigate investigate VERB iajs-200 6 9 some some DET iajs-200 6 10 new new ADJ iajs-200 6 11 results result NOUN iajs-200 6 12 ( ( PUNCT iajs-200 6 13 up up ADP iajs-200 6 14 to to ADP iajs-200 6 15 our our PRON iajs-200 6 16 knowledge knowledge NOUN iajs-200 6 17 ) ) PUNCT iajs-200 6 18 on on ADP iajs-200 6 19 the the DET iajs-200 6 20 concept concept NOUN iajs-200 6 21 of of ADP iajs-200 6 22 semi semi ADJ iajs-200 6 23 - - ADJ iajs-200 6 24 essential essential ADJ iajs-200 6 25 submodules submodule NOUN iajs-200 6 26 which which PRON iajs-200 6 27 introduced introduce VERB iajs-200 6 28 by by ADP iajs-200 6 29 ali ali PROPN iajs-200 6 30 s. s. PROPN iajs-200 6 31 mijbass mijbass PROPN iajs-200 6 32 and and CCONJ iajs-200 6 33 nada nada PROPN iajs-200 6 34 k. k. PROPN iajs-200 6 35 abdullah abdullah PROPN iajs-200 6 36 , , PUNCT iajs-200 6 37 and and CCONJ iajs-200 6 38 we we PRON iajs-200 6 39 make make VERB iajs-200 6 40 simple simple ADJ iajs-200 6 41 changes change NOUN iajs-200 6 42 to to ADP iajs-200 6 43 the the DET iajs-200 6 44 definition definition NOUN iajs-200 6 45 relate relate VERB iajs-200 6 46 with with ADP iajs-200 6 47 the the DET iajs-200 6 48 zero zero NUM iajs-200 6 49 submodule submodule NOUN iajs-200 6 50 , , PUNCT iajs-200 6 51 so so SCONJ iajs-200 6 52 we we PRON iajs-200 6 53 say say VERB iajs-200 6 54 that that SCONJ iajs-200 6 55 a a DET iajs-200 6 56 submodule submodule NOUN iajs-200 6 57 n n PROPN iajs-200 6 58 of of ADP iajs-200 6 59 an an DET iajs-200 6 60 r r NOUN iajs-200 6 61 - - PUNCT iajs-200 6 62 module module NOUN iajs-200 6 63 m m NOUN iajs-200 6 64 is be AUX iajs-200 6 65 called call VERB iajs-200 6 66 semi semi ADJ iajs-200 6 67 - - ADJ iajs-200 6 68 essential essential ADJ iajs-200 6 69 , , PUNCT iajs-200 6 70 if if SCONJ iajs-200 6 71 whenever whenever SCONJ iajs-200 6 72 n n X iajs-200 6 73 ∩ ∩ NOUN iajs-200 6 74 p p X iajs-200 6 75 = = X iajs-200 6 76 ( ( PUNCT iajs-200 6 77 0 0 NUM iajs-200 6 78 ) ) PUNCT iajs-200 6 79 , , PUNCT iajs-200 6 80 then then ADV iajs-200 6 81 p p NOUN iajs-200 6 82 = = PUNCT iajs-200 6 83 ( ( PUNCT iajs-200 6 84 0 0 NUM iajs-200 6 85 ) ) PUNCT iajs-200 6 86 for for ADP iajs-200 6 87 each each DET iajs-200 6 88 prime prime PROPN iajs-200 6 89 submodule submodule PROPN iajs-200 6 90 p p PROPN iajs-200 6 91 of of ADP iajs-200 6 92 m. m. NOUN iajs-200 6 93 various various ADJ iajs-200 6 94 properties property NOUN iajs-200 6 95 of of ADP iajs-200 6 96 semi semi ADJ iajs-200 6 97 - - ADJ iajs-200 6 98 essential essential ADJ iajs-200 6 99 submodules submodule NOUN iajs-200 6 100 are be AUX iajs-200 6 101 considered consider VERB iajs-200 6 102 . . PUNCT iajs-200 7 1 keywords keyword NOUN iajs-200 7 2 : : PUNCT iajs-200 7 3 essential essential ADJ iajs-200 7 4 submodules submodule NOUN iajs-200 7 5 , , PUNCT iajs-200 7 6 semi semi ADJ iajs-200 7 7 - - ADJ iajs-200 7 8 essential essential ADJ iajs-200 7 9 submodules submodule NOUN iajs-200 7 10 , , PUNCT iajs-200 7 11 uniform uniform ADJ iajs-200 7 12 modules module NOUN iajs-200 7 13 , , PUNCT iajs-200 7 14 semiuniform semiuniform NOUN iajs-200 7 15 modules module NOUN iajs-200 7 16 , , PUNCT iajs-200 7 17 fully fully ADV iajs-200 7 18 prime prime ADJ iajs-200 7 19 modules module NOUN iajs-200 7 20 and and CCONJ iajs-200 7 21 fully fully ADV iajs-200 7 22 essential essential ADJ iajs-200 7 23 modules module NOUN iajs-200 7 24 . . 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PROPN iajs-200 9 8 for for ADP iajs-200 9 9 pure pure PROPN iajs-200 9 10 & & CCONJ iajs-200 9 11 appl appl PROPN iajs-200 9 12 . . PUNCT iajs-200 10 1 sci sci PROPN iajs-200 10 2 . . PUNCT iajs-200 10 3 vol vol NOUN iajs-200 10 4 . . PROPN iajs-200 11 1 28 28 NUM iajs-200 11 2 ( ( PUNCT iajs-200 11 3 1 1 NUM iajs-200 11 4 ) ) PUNCT iajs-200 11 5 2015 2015 NUM iajs-200 11 6 1 1 NUM iajs-200 11 7 . . PUNCT iajs-200 11 8 introduction introduction NOUN iajs-200 11 9 throughout throughout ADP iajs-200 11 10 this this DET iajs-200 11 11 paper paper NOUN iajs-200 11 12 , , PUNCT iajs-200 11 13 r r NOUN iajs-200 11 14 represents represent VERB iajs-200 11 15 a a DET iajs-200 11 16 commutative commutative ADJ iajs-200 11 17 ring ring NOUN iajs-200 11 18 with with ADP iajs-200 11 19 identity identity NOUN iajs-200 11 20 and and CCONJ iajs-200 11 21 m m NOUN iajs-200 11 22 is be AUX iajs-200 11 23 a a DET iajs-200 11 24 unitary unitary ADJ iajs-200 11 25 left left ADJ iajs-200 11 26 r r NOUN iajs-200 11 27 - - PUNCT iajs-200 11 28 module module NOUN iajs-200 11 29 . . PUNCT iajs-200 12 1 assume assume VERB iajs-200 12 2 that that SCONJ iajs-200 12 3 all all DET iajs-200 12 4 r r NOUN iajs-200 12 5 - - PUNCT iajs-200 12 6 modules module NOUN iajs-200 12 7 under under ADP iajs-200 12 8 study study NOUN iajs-200 12 9 contain contain VERB iajs-200 12 10 prime prime ADJ iajs-200 12 11 submodules submodule NOUN iajs-200 12 12 . . PUNCT iajs-200 13 1 it it PRON iajs-200 13 2 is be AUX iajs-200 13 3 well well ADV iajs-200 13 4 known know VERB iajs-200 13 5 that that SCONJ iajs-200 13 6 a a DET iajs-200 13 7 submodule submodule NOUN iajs-200 13 8 n n PROPN iajs-200 13 9 of of ADP iajs-200 13 10 m m PROPN iajs-200 13 11 is be AUX iajs-200 13 12 called call VERB iajs-200 13 13 essential essential ADJ iajs-200 13 14 , , PUNCT iajs-200 13 15 if if SCONJ iajs-200 13 16 whenever whenever SCONJ iajs-200 13 17 n n X iajs-200 13 18 ∩ ∩ ADJ iajs-200 13 19 l l NOUN iajs-200 13 20 = = SYM iajs-200 13 21 ( ( PUNCT iajs-200 13 22 0 0 NUM iajs-200 13 23 ) ) PUNCT iajs-200 13 24 , , PUNCT iajs-200 13 25 then then ADV iajs-200 13 26 l l NOUN iajs-200 13 27 = = SYM iajs-200 13 28 ( ( PUNCT iajs-200 13 29 0 0 NUM iajs-200 13 30 ) ) PUNCT iajs-200 13 31 for for ADP iajs-200 13 32 each each DET iajs-200 13 33 submodule submodule NOUN iajs-200 13 34 l l NOUN iajs-200 13 35 of of ADP iajs-200 13 36 m m PROPN iajs-200 13 37 [ [ X iajs-200 13 38 7 7 X iajs-200 13 39 ] ] PUNCT iajs-200 13 40 and and CCONJ iajs-200 13 41 [ [ X iajs-200 13 42 9 9 NUM iajs-200 13 43 ] ] PUNCT iajs-200 13 44 . . PUNCT iajs-200 14 1 ali ali PROPN iajs-200 14 2 and and CCONJ iajs-200 14 3 nada nada PROPN iajs-200 14 4 in in ADP iajs-200 14 5 [ [ X iajs-200 14 6 1 1 NUM iajs-200 14 7 ] ] PUNCT iajs-200 14 8 introduced introduce VERB iajs-200 14 9 the the DET iajs-200 14 10 concept concept NOUN iajs-200 14 11 of of ADP iajs-200 14 12 semi semi ADJ iajs-200 14 13 - - ADJ iajs-200 14 14 essential essential ADJ iajs-200 14 15 submodules submodule NOUN iajs-200 14 16 as as ADP iajs-200 14 17 a a DET iajs-200 14 18 generalization generalization NOUN iajs-200 14 19 of of ADP iajs-200 14 20 the the DET iajs-200 14 21 class class NOUN iajs-200 14 22 of of ADP iajs-200 14 23 essential essential ADJ iajs-200 14 24 submodules submodule NOUN iajs-200 14 25 , , PUNCT iajs-200 14 26 where where SCONJ iajs-200 14 27 they they PRON iajs-200 14 28 say say VERB iajs-200 14 29 that that SCONJ iajs-200 14 30 a a DET iajs-200 14 31 nonzero nonzero PROPN iajs-200 14 32 submodule submodule PROPN iajs-200 14 33 n n PROPN iajs-200 14 34 of of ADP iajs-200 14 35 m m PROPN iajs-200 14 36 is be AUX iajs-200 14 37 called call VERB iajs-200 14 38 semi semi ADJ iajs-200 14 39 - - ADJ iajs-200 14 40 essential essential ADJ iajs-200 14 41 , , PUNCT iajs-200 14 42 if if SCONJ iajs-200 14 43 n n ADP iajs-200 14 44 ∩ ∩ NOUN iajs-200 14 45 p p X iajs-200 14 46 ≠ ≠ PROPN iajs-200 14 47 ( ( PUNCT iajs-200 14 48 0 0 NUM iajs-200 14 49 ) ) PUNCT iajs-200 14 50 for for ADP iajs-200 14 51 each each DET iajs-200 14 52 nonzero nonzero NOUN iajs-200 14 53 prime prime ADJ iajs-200 14 54 rsubmodule rsubmodule NOUN iajs-200 14 55 p p NOUN iajs-200 14 56 of of ADP iajs-200 14 57 m m PROPN iajs-200 14 58 [ [ X iajs-200 14 59 1 1 NUM iajs-200 14 60 ] ] PUNCT iajs-200 14 61 , , PUNCT iajs-200 14 62 where where SCONJ iajs-200 14 63 a a DET iajs-200 14 64 submodule submodule NOUN iajs-200 14 65 p p NOUN iajs-200 14 66 of of ADP iajs-200 14 67 m m PROPN iajs-200 14 68 is be AUX iajs-200 14 69 called call VERB iajs-200 14 70 prime prime ADJ iajs-200 14 71 , , PUNCT iajs-200 14 72 if if SCONJ iajs-200 14 73 whenever whenever SCONJ iajs-200 14 74 rm rm PROPN iajs-200 14 75   PROPN iajs-200 14 76 p p X iajs-200 14 77 for for ADP iajs-200 14 78 r r NOUN iajs-200 14 79 r r PROPN iajs-200 14 80 and and CCONJ iajs-200 14 81 m m NOUN iajs-200 14 82 m m ADJ iajs-200 14 83 , , PUNCT iajs-200 14 84 then then ADV iajs-200 14 85 either either CCONJ iajs-200 14 86 m m VERB iajs-200 14 87   NOUN iajs-200 14 88 p p NOUN iajs-200 14 89 or or CCONJ iajs-200 14 90 r r NOUN iajs-200 14 91   NOUN iajs-200 14 92 ( ( PUNCT iajs-200 14 93 p p X iajs-200 14 94 : : PUNCT iajs-200 14 95 m m VERB iajs-200 14 96 ) ) PUNCT iajs-200 15 1 [ [ X iajs-200 15 2 12 12 NUM iajs-200 15 3 ] ] PUNCT iajs-200 15 4 . . PUNCT iajs-200 16 1 in in ADP iajs-200 16 2 this this DET iajs-200 16 3 paper paper NOUN iajs-200 16 4 we we PRON iajs-200 16 5 rewrite rewrite VERB iajs-200 16 6 the the DET iajs-200 16 7 definition definition NOUN iajs-200 16 8 of of ADP iajs-200 16 9 the the DET iajs-200 16 10 semi semi ADJ iajs-200 16 11 - - ADJ iajs-200 16 12 essential essential ADJ iajs-200 16 13 submodules submodule NOUN iajs-200 16 14 which which PRON iajs-200 16 15 introduced introduce VERB iajs-200 16 16 [ [ X iajs-200 16 17 1 1 X iajs-200 16 18 ] ] PUNCT iajs-200 16 19 in in ADP iajs-200 16 20 another another DET iajs-200 16 21 formula formula NOUN iajs-200 16 22 , , PUNCT iajs-200 16 23 in in ADP iajs-200 16 24 fact fact NOUN iajs-200 16 25 we we PRON iajs-200 16 26 did do AUX iajs-200 16 27 n't not PART iajs-200 16 28 find find VERB iajs-200 16 29 any any DET iajs-200 16 30 reasonable reasonable ADJ iajs-200 16 31 reason reason NOUN iajs-200 16 32 to to PART iajs-200 16 33 exclude exclude VERB iajs-200 16 34 the the DET iajs-200 16 35 zero zero NUM iajs-200 16 36 submodule submodule NOUN iajs-200 16 37 from from ADP iajs-200 16 38 the the DET iajs-200 16 39 definition definition NOUN iajs-200 16 40 of of ADP iajs-200 16 41 semi semi ADJ iajs-200 16 42 - - ADJ iajs-200 16 43 essential essential ADJ iajs-200 16 44 submodules submodule NOUN iajs-200 16 45 . . 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NOUN iajs-200 19 42 we we PRON iajs-200 19 43 see see VERB iajs-200 19 44 it it PRON iajs-200 19 45 is be AUX iajs-200 19 46 necessary necessary ADJ iajs-200 19 47 to to PART iajs-200 19 48 put put VERB iajs-200 19 49 some some DET iajs-200 19 50 simple simple ADJ iajs-200 19 51 remarks remark NOUN iajs-200 19 52 about about ADP iajs-200 19 53 the the DET iajs-200 19 54 class class NOUN iajs-200 19 55 of of ADP iajs-200 19 56 semi semi ADJ iajs-200 19 57 - - ADJ iajs-200 19 58 essential essential ADJ iajs-200 19 59 submodules submodule NOUN iajs-200 19 60 which which PRON iajs-200 19 61 not not PART iajs-200 19 62 mentioned mention VERB iajs-200 19 63 in in ADP iajs-200 19 64 [ [ X iajs-200 19 65 1 1 NUM iajs-200 19 66 ] ] PUNCT iajs-200 19 67 . . PUNCT iajs-200 20 1 remarks remark NOUN iajs-200 20 2 ( ( PUNCT iajs-200 20 3 1.2 1.2 NUM iajs-200 20 4 ): ): PUNCT iajs-200 20 5 1 1 X iajs-200 20 6 . . X iajs-200 20 7 consider consider VERB iajs-200 20 8 the the DET iajs-200 20 9 z z NOUN iajs-200 20 10 - - PUNCT iajs-200 20 11 module module NOUN iajs-200 20 12 m m NOUN iajs-200 20 13 = = PROPN iajs-200 20 14 z8 z8 PROPN iajs-200 20 15 ⊕ ⊕ PROPN iajs-200 20 16 z2 z2 PROPN iajs-200 20 17 . . PUNCT iajs-200 21 1 in in ADP iajs-200 21 2 this this DET iajs-200 21 3 module module NOUN iajs-200 21 4 there there PRON iajs-200 21 5 are be VERB iajs-200 21 6 eleven eleven NUM iajs-200 21 7 submodules submodule NOUN iajs-200 21 8 which which PRON iajs-200 21 9 are be AUX iajs-200 21 10 < < X iajs-200 21 11 ( ( PUNCT iajs-200 21 12 0 0 NUM iajs-200 21 13 , , PUNCT iajs-200 21 14 0 0 NUM iajs-200 21 15 ) ) PUNCT iajs-200 21 16 > > PUNCT iajs-200 21 17 , , PUNCT iajs-200 21 18 < < X iajs-200 21 19 ( ( PUNCT iajs-200 21 20 1 1 NUM iajs-200 21 21 , , PUNCT iajs-200 21 22 0 0 NUM iajs-200 21 23 ) ) PUNCT iajs-200 21 24 > > PUNCT iajs-200 21 25 , , PUNCT iajs-200 21 26 < < X iajs-200 21 27 ( ( PUNCT iajs-200 21 28 0 0 NUM iajs-200 21 29 , , PUNCT iajs-200 21 30 1 1 NUM iajs-200 21 31 ) ) PUNCT iajs-200 21 32 > > PUNCT iajs-200 21 33 , , PUNCT iajs-200 21 34 < < X iajs-200 21 35 ( ( PUNCT iajs-200 21 36 1 1 NUM iajs-200 21 37 , , PUNCT iajs-200 21 38 1 1 NUM iajs-200 21 39 ) ) PUNCT iajs-200 21 40 > > PUNCT iajs-200 21 41 , , PUNCT iajs-200 21 42 < < X iajs-200 21 43 ( ( PUNCT iajs-200 21 44 2 2 NUM iajs-200 21 45 , , PUNCT iajs-200 21 46 0 0 NUM iajs-200 21 47 ) ) PUNCT iajs-200 21 48 > > PUNCT iajs-200 21 49 , , PUNCT iajs-200 21 50 < < X iajs-200 21 51 ( ( PUNCT iajs-200 21 52 2 2 NUM iajs-200 21 53 , , PUNCT iajs-200 21 54 1 1 NUM iajs-200 21 55 ) ) PUNCT iajs-200 21 56 > > PUNCT iajs-200 21 57 , , PUNCT iajs-200 21 58 < < X iajs-200 21 59 ( ( PUNCT iajs-200 21 60 4 4 NUM iajs-200 21 61 , , PUNCT iajs-200 21 62 0 0 NUM iajs-200 21 63 ) ) PUNCT iajs-200 21 64 > > PUNCT iajs-200 21 65 , , PUNCT iajs-200 21 66 < < X iajs-200 21 67 ( ( PUNCT iajs-200 21 68 4 4 NUM iajs-200 21 69 , , PUNCT iajs-200 21 70 1 1 NUM iajs-200 21 71 ) ) PUNCT iajs-200 21 72 > > PUNCT iajs-200 21 73 , , PUNCT iajs-200 21 74 < < X iajs-200 21 75 ( ( PUNCT iajs-200 21 76 0 0 NUM iajs-200 21 77 , , PUNCT iajs-200 21 78 1 1 NUM iajs-200 21 79 ) ) PUNCT iajs-200 21 80 , , PUNCT iajs-200 21 81 ( ( PUNCT iajs-200 21 82 4 4 NUM iajs-200 21 83 , , PUNCT iajs-200 21 84 0 0 NUM iajs-200 21 85 ) ) PUNCT iajs-200 21 86 > > PUNCT iajs-200 21 87 , , PUNCT iajs-200 21 88 < < X iajs-200 21 89 ( ( PUNCT iajs-200 21 90 2 2 NUM iajs-200 21 91 , , PUNCT iajs-200 21 92 0 0 NUM iajs-200 21 93 ) ) PUNCT iajs-200 21 94 , , PUNCT iajs-200 21 95 ( ( PUNCT iajs-200 21 96 4 4 NUM iajs-200 21 97 , , PUNCT iajs-200 21 98 1 1 NUM iajs-200 21 99 ) ) PUNCT iajs-200 21 100 > > PUNCT iajs-200 21 101 , , PUNCT iajs-200 21 102 and and CCONJ iajs-200 21 103 m. m. VERB iajs-200 21 104 the the DET iajs-200 21 105 semi semi ADJ iajs-200 21 106 - - ADJ iajs-200 21 107 essential essential ADJ iajs-200 21 108 submodules submodule NOUN iajs-200 21 109 of of ADP iajs-200 21 110 m m PROPN iajs-200 21 111 are be AUX iajs-200 21 112 < < X iajs-200 21 113 ( ( PUNCT iajs-200 21 114 1 1 NUM iajs-200 21 115 , , PUNCT iajs-200 21 116 1 1 NUM iajs-200 21 117 ) ) PUNCT iajs-200 21 118 > > PUNCT iajs-200 21 119 , , PUNCT iajs-200 21 120 < < X iajs-200 21 121 ( ( PUNCT iajs-200 21 122 1 1 NUM iajs-200 21 123 , , PUNCT iajs-200 21 124 0 0 NUM iajs-200 21 125 ) ) PUNCT iajs-200 21 126 > > PUNCT iajs-200 21 127 , , PUNCT iajs-200 21 128 < < X iajs-200 21 129 ( ( PUNCT iajs-200 21 130 2 2 NUM iajs-200 21 131 , , PUNCT iajs-200 21 132 0 0 NUM iajs-200 21 133 ) ) PUNCT iajs-200 21 134 > > PUNCT iajs-200 21 135 , , PUNCT iajs-200 21 136 < < X iajs-200 21 137 ( ( PUNCT iajs-200 21 138 2 2 NUM iajs-200 21 139 , , PUNCT iajs-200 21 140 1 1 NUM iajs-200 21 141 ) ) PUNCT iajs-200 21 142 > > PUNCT iajs-200 21 143 , , PUNCT iajs-200 21 144 < < X iajs-200 21 145 ( ( PUNCT iajs-200 21 146 4 4 NUM iajs-200 21 147 , , PUNCT iajs-200 21 148 0 0 NUM iajs-200 21 149 ) ) PUNCT iajs-200 21 150 > > PUNCT iajs-200 21 151 , , PUNCT iajs-200 21 152 < < X iajs-200 21 153 ( ( PUNCT iajs-200 21 154 0 0 NUM iajs-200 21 155 , , PUNCT iajs-200 21 156 1 1 NUM iajs-200 21 157 ) ) PUNCT iajs-200 21 158 , , PUNCT iajs-200 21 159 ( ( PUNCT iajs-200 21 160 4 4 NUM iajs-200 21 161 , , PUNCT iajs-200 21 162 0 0 NUM iajs-200 21 163 ) ) PUNCT iajs-200 21 164 > > PUNCT iajs-200 21 165 , , PUNCT iajs-200 21 166 < < X iajs-200 21 167 ( ( PUNCT iajs-200 21 168 2 2 NUM iajs-200 21 169 , , PUNCT iajs-200 21 170 0 0 NUM iajs-200 21 171 ) ) PUNCT iajs-200 21 172 , , PUNCT iajs-200 21 173 ( ( PUNCT iajs-200 21 174 4 4 NUM iajs-200 21 175 , , PUNCT iajs-200 21 176 1 1 NUM iajs-200 21 177 ) ) PUNCT iajs-200 21 178 > > X iajs-200 21 179 and and CCONJ iajs-200 21 180 m. m. NOUN iajs-200 21 181 in in ADP iajs-200 21 182 fact fact NOUN iajs-200 21 183 each each DET iajs-200 21 184 one one NUM iajs-200 21 185 of of ADP iajs-200 21 186 them they PRON iajs-200 21 187 intersects intersect VERB iajs-200 21 188 with with ADP iajs-200 21 189 each each DET iajs-200 21 190 nonzero nonzero ADJ iajs-200 21 191 prime prime PROPN iajs-200 21 192 submodule submodule NOUN iajs-200 21 193 of of ADP iajs-200 21 194 m m PROPN iajs-200 21 195 is be AUX iajs-200 21 196 nonzero nonzero ADJ iajs-200 21 197 , , PUNCT iajs-200 21 198 where where SCONJ iajs-200 21 199 the the DET iajs-200 21 200 prime prime ADJ iajs-200 21 201 submodules submodule NOUN iajs-200 21 202 of of ADP iajs-200 21 203 m m PROPN iajs-200 21 204 are be AUX iajs-200 21 205 < < X iajs-200 21 206 ( ( PUNCT iajs-200 21 207 2 2 NUM iajs-200 21 208 , , PUNCT iajs-200 21 209 0 0 NUM iajs-200 21 210 ) ) PUNCT iajs-200 21 211 , , PUNCT iajs-200 21 212 ( ( PUNCT iajs-200 21 213 4 4 NUM iajs-200 21 214 , , PUNCT iajs-200 21 215 1 1 NUM iajs-200 21 216 ) ) PUNCT iajs-200 21 217 > > PUNCT iajs-200 21 218 , , PUNCT iajs-200 21 219 < < X iajs-200 21 220 ( ( PUNCT iajs-200 21 221 1 1 NUM iajs-200 21 222 , , PUNCT iajs-200 21 223 1 1 NUM iajs-200 21 224 ) ) PUNCT iajs-200 21 225 > > PUNCT iajs-200 21 226 , , PUNCT iajs-200 21 227 < < X iajs-200 21 228 ( ( PUNCT iajs-200 21 229 1 1 NUM iajs-200 21 230 , , PUNCT iajs-200 21 231 0 0 NUM iajs-200 21 232 ) ) PUNCT iajs-200 21 233 > > PUNCT iajs-200 21 234 , , PUNCT iajs-200 21 235 and and CCONJ iajs-200 21 236 < < X iajs-200 21 237 ( ( PUNCT iajs-200 21 238 2 2 NUM iajs-200 21 239 , , PUNCT iajs-200 21 240 0 0 NUM iajs-200 21 241 ) ) PUNCT iajs-200 21 242 > > PUNCT iajs-200 21 243 . . PUNCT iajs-200 22 1 2 2 NUM iajs-200 22 2 . . X iajs-200 22 3 when when SCONJ iajs-200 22 4 a a DET iajs-200 22 5 submodule submodule NOUN iajs-200 22 6 n n PROPN iajs-200 22 7 of of ADP iajs-200 22 8 an an DET iajs-200 22 9 r r NOUN iajs-200 22 10 - - PUNCT iajs-200 22 11 module module NOUN iajs-200 22 12 m m NOUN iajs-200 22 13 is be AUX iajs-200 22 14 nonzero nonzero NOUN iajs-200 22 15 in in ADP iajs-200 22 16 the the DET iajs-200 22 17 def def NOUN iajs-200 22 18 ( ( PUNCT iajs-200 22 19 1.1 1.1 NUM iajs-200 22 20 ) ) PUNCT iajs-200 22 21 , , PUNCT iajs-200 22 22 then then ADV iajs-200 22 23 n n PRON iajs-200 22 24 is be AUX iajs-200 22 25 a a DET iajs-200 22 26 semiessential semiessential ADJ iajs-200 22 27 submodule submodule NOUN iajs-200 22 28 if if SCONJ iajs-200 22 29 n n NOUN iajs-200 22 30 ∩ ∩ NOUN iajs-200 22 31 p p X iajs-200 22 32 ≠ ≠ PROPN iajs-200 22 33 ( ( PUNCT iajs-200 22 34 0 0 NUM iajs-200 22 35 ) ) PUNCT iajs-200 22 36 for for ADP iajs-200 22 37 each each DET iajs-200 22 38 prime prime PROPN iajs-200 22 39 submodule submodule PROPN iajs-200 22 40 p p PROPN iajs-200 22 41 of of ADP iajs-200 22 42 m m PROPN iajs-200 22 43 , , PUNCT iajs-200 22 44 and and CCONJ iajs-200 22 45 this this PRON iajs-200 22 46 is be AUX iajs-200 22 47 the the DET iajs-200 22 48 same same ADJ iajs-200 22 49 definition definition NOUN iajs-200 22 50 which which PRON iajs-200 22 51 is be AUX iajs-200 22 52 said say VERB iajs-200 22 53 by by ADP iajs-200 22 54 ali ali PROPN iajs-200 22 55 and and CCONJ iajs-200 22 56 nada nada PROPN iajs-200 22 57 in in ADP iajs-200 22 58 [ [ X iajs-200 22 59 1 1 NUM iajs-200 22 60 ] ] PUNCT iajs-200 22 61 . . PUNCT iajs-200 23 1 3 3 X iajs-200 23 2 . . X iajs-200 23 3 every every DET iajs-200 23 4 module module NOUN iajs-200 23 5 is be AUX iajs-200 23 6 a a DET iajs-200 23 7 semi semi ADJ iajs-200 23 8 - - ADJ iajs-200 23 9 essential essential ADJ iajs-200 23 10 submodule submodule NOUN iajs-200 23 11 of of ADP iajs-200 23 12 itself itself PRON iajs-200 23 13 . . PUNCT iajs-200 24 1 4 4 X iajs-200 24 2 . . X iajs-200 24 3 for for ADP iajs-200 24 4 the the DET iajs-200 24 5 concept concept NOUN iajs-200 24 6 of of ADP iajs-200 24 7 the the DET iajs-200 24 8 essential essential ADJ iajs-200 24 9 submodules submodule NOUN iajs-200 24 10 , , PUNCT iajs-200 24 11 ( ( PUNCT iajs-200 24 12 0 0 NUM iajs-200 24 13 ) ) PUNCT iajs-200 24 14 is be AUX iajs-200 24 15 an an DET iajs-200 24 16 essential essential ADJ iajs-200 24 17 submodule submodule NOUN iajs-200 24 18 of of ADP iajs-200 24 19 an an DET iajs-200 24 20 rmodule rmodule NOUN iajs-200 24 21 m m NOUN iajs-200 24 22 if if SCONJ iajs-200 24 23 and and CCONJ iajs-200 24 24 only only ADV iajs-200 24 25 if if SCONJ iajs-200 24 26 m m VERB iajs-200 24 27 = = SYM iajs-200 24 28 ( ( PUNCT iajs-200 24 29 0 0 NUM iajs-200 24 30 ) ) PUNCT iajs-200 24 31 , , PUNCT iajs-200 24 32 but but CCONJ iajs-200 24 33 ( ( PUNCT iajs-200 24 34 0 0 X iajs-200 24 35 ) ) PUNCT iajs-200 24 36 may may AUX iajs-200 24 37 be be AUX iajs-200 24 38 semi semi ADJ iajs-200 24 39 - - ADJ iajs-200 24 40 essential essential ADJ iajs-200 24 41 submodule submodule NOUN iajs-200 24 42 in in ADP iajs-200 24 43 a a DET iajs-200 24 44 nonzero nonzero NOUN iajs-200 24 45 module module NOUN iajs-200 24 46 . . PUNCT iajs-200 25 1 in in ADP iajs-200 25 2 fact fact NOUN iajs-200 25 3 ( ( PUNCT iajs-200 25 4 0 0 NUM iajs-200 25 5 ) ) PUNCT iajs-200 25 6 ≤sem ≤sem NOUN iajs-200 25 7 m m VERB iajs-200 25 8 if if SCONJ iajs-200 25 9 and and CCONJ iajs-200 25 10 only only ADV iajs-200 25 11 if if SCONJ iajs-200 25 12 m m NOUN iajs-200 25 13 has have VERB iajs-200 25 14 only only ADV iajs-200 25 15 one one NUM iajs-200 25 16 prime prime ADJ iajs-200 25 17 submodule submodule NOUN iajs-200 25 18 which which PRON iajs-200 25 19 is be AUX iajs-200 25 20 ( ( PUNCT iajs-200 25 21 0 0 NUM iajs-200 25 22 ) ) PUNCT iajs-200 25 23 , , PUNCT iajs-200 25 24 for for ADP iajs-200 25 25 example example NOUN iajs-200 25 26 ( ( PUNCT iajs-200 25 27 0 0 NUM iajs-200 25 28 ) ) PUNCT iajs-200 25 29 is be AUX iajs-200 25 30 a a DET iajs-200 25 31 semi semi ADJ iajs-200 25 32 - - ADJ iajs-200 25 33 essential essential ADJ iajs-200 25 34 submodule submodule NOUN iajs-200 25 35 of of ADP iajs-200 25 36 the the DET iajs-200 25 37 z z NOUN iajs-200 25 38 - - PUNCT iajs-200 25 39 module module NOUN iajs-200 25 40 , , PUNCT iajs-200 25 41 z2 z2 PROPN iajs-200 25 42 , , PUNCT iajs-200 25 43 while while SCONJ iajs-200 25 44 ( ( PUNCT iajs-200 25 45 0 0 NUM iajs-200 25 46 ) ) PUNCT iajs-200 25 47 is be AUX iajs-200 25 48 not not PART iajs-200 25 49 semi semi ADJ iajs-200 25 50 - - ADJ iajs-200 25 51 essential essential ADJ iajs-200 25 52 submodule submodule NOUN iajs-200 25 53 of of ADP iajs-200 25 54 z. z. PROPN iajs-200 25 55 5 5 NUM iajs-200 25 56 . . PUNCT iajs-200 26 1 the the DET iajs-200 26 2 sum sum NOUN iajs-200 26 3 of of ADP iajs-200 26 4 two two NUM iajs-200 26 5 semi semi ADJ iajs-200 26 6 - - ADJ iajs-200 26 7 essential essential ADJ iajs-200 26 8 submodules submodule NOUN iajs-200 26 9 is be AUX iajs-200 26 10 also also ADV iajs-200 26 11 semi semi ADJ iajs-200 26 12 - - ADJ iajs-200 26 13 essential essential ADJ iajs-200 26 14 submodule submodule NOUN iajs-200 26 15 . . PUNCT iajs-200 27 1 proof proof NOUN iajs-200 27 2 ( ( PUNCT iajs-200 27 3 5 5 NUM iajs-200 27 4 ): ): PUNCT iajs-200 27 5 let let VERB iajs-200 27 6 m m PRON iajs-200 27 7 be be AUX iajs-200 27 8 an an DET iajs-200 27 9 r r NOUN iajs-200 27 10 - - PUNCT iajs-200 27 11 module module NOUN iajs-200 27 12 and and CCONJ iajs-200 27 13 let let VERB iajs-200 27 14 l l NOUN iajs-200 27 15 and and CCONJ iajs-200 27 16 k k PROPN iajs-200 27 17 be be AUX iajs-200 27 18 two two NUM iajs-200 27 19 essential essential ADJ iajs-200 27 20 submodules submodule NOUN iajs-200 27 21 of of ADP iajs-200 27 22 m. m. NOUN iajs-200 27 23 note note NOUN iajs-200 27 24 that that SCONJ iajs-200 27 25 l l NOUN iajs-200 27 26 ≤ ≤ NOUN iajs-200 27 27 l+k l+k PROPN iajs-200 27 28 , , PUNCT iajs-200 27 29 since since SCONJ iajs-200 27 30 l l PROPN iajs-200 27 31 ≤sem ≤sem PROPN iajs-200 27 32 m m PROPN iajs-200 27 33 , , PUNCT iajs-200 27 34 so so ADV iajs-200 27 35 by by ADP iajs-200 27 36 [ [ X iajs-200 27 37 1 1 NUM iajs-200 27 38 ] ] PUNCT iajs-200 27 39 , , PUNCT iajs-200 27 40 l+k l+k PROPN iajs-200 27 41 ≤sem ≤sem PROPN iajs-200 27 42 m. m. NOUN iajs-200 27 43 6 6 NUM iajs-200 27 44 . . PUNCT iajs-200 28 1 let let VERB iajs-200 28 2 m m PRON iajs-200 28 3 be be AUX iajs-200 28 4 an an DET iajs-200 28 5 r r NOUN iajs-200 28 6 - - PUNCT iajs-200 28 7 module module NOUN iajs-200 28 8 , , PUNCT iajs-200 28 9 and and CCONJ iajs-200 28 10 let let VERB iajs-200 28 11 n n PRON iajs-200 28 12 ≤ ≤ NUM iajs-200 28 13 m. m. NOUN iajs-200 28 14 then then ADV iajs-200 28 15 for for ADP iajs-200 28 16 each each DET iajs-200 28 17 r r NOUN iajs-200 28 18 - - PUNCT iajs-200 28 19 module module NOUN iajs-200 28 20 m m NOUN iajs-200 28 21 ' ' PUNCT iajs-200 28 22 and and CCONJ iajs-200 28 23 for for ADP iajs-200 28 24 each each DET iajs-200 28 25 homomorphism homomorphism NOUN iajs-200 29 1 f f X iajs-200 29 2 : : PUNCT iajs-200 29 3 m m PROPN iajs-200 29 4 → → SYM iajs-200 29 5 m m NOUN iajs-200 29 6 ' ' PUNCT iajs-200 29 7 with with ADP iajs-200 29 8 ker ker PROPN iajs-200 29 9 f f PROPN iajs-200 29 10 ∩ ∩ PROPN iajs-200 29 11 n n PROPN iajs-200 29 12 ≠ ≠ PROPN iajs-200 29 13 ( ( PUNCT iajs-200 29 14 0 0 NUM iajs-200 29 15 ) ) PUNCT iajs-200 29 16 , , PUNCT iajs-200 29 17 implies imply VERB iajs-200 29 18 that that SCONJ iajs-200 29 19 n n PROPN iajs-200 29 20 ≤sem ≤sem PROPN iajs-200 29 21 m. m. NOUN iajs-200 29 22 181 181 NUM iajs-200 30 1 | | NOUN iajs-200 30 2 mathematics mathematic NOUN iajs-200 30 3 2015 2015 NUM iajs-200 30 4 ) ) PUNCT iajs-200 30 5 عام عام ADP iajs-200 30 6 1(العدد 1(العدد NUM iajs-200 30 7 28المجلد 28المجلد NUM iajs-200 30 8 مجلة مجلة PROPN iajs-200 30 9 إبن إبن VERB iajs-200 30 10 الھيثم الھيثم NOUN iajs-200 30 11 للعلوم للعلوم NOUN iajs-200 30 12 الصرفة الصرفة NOUN iajs-200 31 1 و و PRON iajs-200 31 2 التطبيقية التطبيقية ADJ iajs-200 31 3 ibn ibn PROPN iajs-200 31 4 al al PROPN iajs-200 31 5 - - PUNCT iajs-200 31 6 haitham haitham PROPN iajs-200 31 7 j. j. PROPN iajs-200 31 8 for for ADP iajs-200 31 9 pure pure PROPN iajs-200 31 10 & & CCONJ iajs-200 31 11 appl appl PROPN iajs-200 31 12 . . PUNCT iajs-200 32 1 sci sci PROPN iajs-200 32 2 . . PUNCT iajs-200 32 3 vol vol NOUN iajs-200 32 4 . . PROPN iajs-200 33 1 28 28 NUM iajs-200 33 2 ( ( PUNCT iajs-200 33 3 1 1 NUM iajs-200 33 4 ) ) PUNCT iajs-200 33 5 2015 2015 NUM iajs-200 33 6 proof proof NOUN iajs-200 33 7 ( ( PUNCT iajs-200 33 8 6 6 NUM iajs-200 33 9 ): ): PUNCT iajs-200 33 10 let let VERB iajs-200 33 11 p p PRON iajs-200 33 12 be be AUX iajs-200 33 13 a a DET iajs-200 33 14 nonzero nonzero ADJ iajs-200 33 15 prime prime ADJ iajs-200 33 16 submodule submodule NOUN iajs-200 33 17 of of ADP iajs-200 33 18 m m PROPN iajs-200 33 19 , , PUNCT iajs-200 33 20 and and CCONJ iajs-200 33 21 let let VERB iajs-200 33 22 π π NOUN iajs-200 33 23 : : PUNCT iajs-200 33 24 m m VERB iajs-200 33 25 → → NOUN iajs-200 33 26 be be AUX iajs-200 33 27 the the DET iajs-200 33 28 natural natural ADJ iajs-200 33 29 epimorphism epimorphism NOUN iajs-200 33 30 . . PUNCT iajs-200 34 1 by by ADP iajs-200 34 2 assumption assumption NOUN iajs-200 34 3 ker ker PROPN iajs-200 34 4 π π PROPN iajs-200 34 5 ∩ ∩ PROPN iajs-200 34 6 n n PROPN iajs-200 34 7 ≠ ≠ PROPN iajs-200 34 8 ( ( PUNCT iajs-200 34 9 0 0 NUM iajs-200 34 10 ) ) PUNCT iajs-200 34 11 . . PUNCT iajs-200 35 1 but but CCONJ iajs-200 35 2 ker ker NOUN iajs-200 35 3 π π NOUN iajs-200 35 4 = = SYM iajs-200 35 5 p p X iajs-200 35 6 , , PUNCT iajs-200 35 7 then then ADV iajs-200 35 8 p p X iajs-200 35 9 ∩ ∩ NOUN iajs-200 35 10 n n PRON iajs-200 35 11 ≠ ≠ PROPN iajs-200 35 12 ( ( PUNCT iajs-200 35 13 0 0 NUM iajs-200 35 14 ) ) PUNCT iajs-200 35 15 , , PUNCT iajs-200 35 16 hence hence ADV iajs-200 35 17 n n CCONJ iajs-200 35 18 ≤sem ≤sem PROPN iajs-200 35 19 m. m. NOUN iajs-200 35 20 proposition proposition NOUN iajs-200 35 21 ( ( PUNCT iajs-200 35 22 1.3 1.3 NUM iajs-200 35 23 ): ): PUNCT iajs-200 35 24 let let VERB iajs-200 35 25 f f X iajs-200 35 26 : : PUNCT iajs-200 35 27 m m PROPN iajs-200 35 28 → → SYM iajs-200 35 29 m m PART iajs-200 35 30 ' ' PUNCT iajs-200 35 31 be be VERB iajs-200 35 32 an an DET iajs-200 35 33 isomorphism isomorphism NOUN iajs-200 35 34 . . PUNCT iajs-200 36 1 if if SCONJ iajs-200 36 2 n n PROPN iajs-200 36 3 ≤sem ≤sem PROPN iajs-200 36 4 m m PROPN iajs-200 36 5 , , PUNCT iajs-200 36 6 then then ADV iajs-200 36 7 f(n f(n PROPN iajs-200 36 8 ) ) PUNCT iajs-200 37 1 ≤sem ≤sem PROPN iajs-200 37 2 m m NOUN iajs-200 37 3 ' ' PUNCT iajs-200 37 4 . . PUNCT iajs-200 38 1 proof proof NOUN iajs-200 38 2 : : PUNCT iajs-200 38 3 let let VERB iajs-200 38 4 p p PRON iajs-200 38 5 be be AUX iajs-200 38 6 a a DET iajs-200 38 7 nonzero nonzero ADJ iajs-200 38 8 prime prime ADJ iajs-200 38 9 submodule submodule NOUN iajs-200 38 10 of of ADP iajs-200 38 11 m m PROPN iajs-200 38 12 ' ' PUNCT iajs-200 38 13 . . PUNCT iajs-200 39 1 since since SCONJ iajs-200 39 2 f f PROPN iajs-200 39 3 is be AUX iajs-200 39 4 an an DET iajs-200 39 5 epimorphism epimorphism NOUN iajs-200 39 6 , , PUNCT iajs-200 39 7 then then ADV iajs-200 39 8 f-1(p f-1(p PROPN iajs-200 39 9 ) ) PUNCT iajs-200 39 10 is be AUX iajs-200 39 11 a a DET iajs-200 39 12 prime prime ADJ iajs-200 39 13 submodule submodule NOUN iajs-200 39 14 of of ADP iajs-200 39 15 m m PROPN iajs-200 39 16 [ [ X iajs-200 39 17 12 12 NUM iajs-200 39 18 , , PUNCT iajs-200 39 19 prop prop NOUN iajs-200 39 20 . . PUNCT iajs-200 39 21 3.8 3.8 NUM iajs-200 39 22 , , PUNCT iajs-200 39 23 p.10 p.10 ADP iajs-200 39 24 ] ] PUNCT iajs-200 39 25 . . PUNCT iajs-200 40 1 but but CCONJ iajs-200 40 2 n n PRON iajs-200 40 3 ≤sem ≤sem NOUN iajs-200 40 4 m m PROPN iajs-200 40 5 , , PUNCT iajs-200 40 6 then then ADV iajs-200 40 7 n n NUM iajs-200 40 8 ∩ ∩ ADJ iajs-200 40 9 f-1(p f-1(p NOUN iajs-200 40 10 ) ) PUNCT iajs-200 40 11 ≠ ≠ PROPN iajs-200 40 12 ( ( PUNCT iajs-200 40 13 0 0 NUM iajs-200 40 14 ) ) PUNCT iajs-200 40 15 , , PUNCT iajs-200 40 16 on on ADP iajs-200 40 17 the the DET iajs-200 40 18 other other ADJ iajs-200 40 19 hand hand NOUN iajs-200 40 20 f f PROPN iajs-200 40 21 is be AUX iajs-200 40 22 a a DET iajs-200 40 23 monomorphism monomorphism NOUN iajs-200 40 24 thus thus ADV iajs-200 40 25 f(n f(n PROPN iajs-200 40 26 ) ) PUNCT iajs-200 40 27 ∩ ∩ NOUN iajs-200 40 28 p p X iajs-200 40 29 ≠ ≠ PROPN iajs-200 40 30 ( ( PUNCT iajs-200 40 31 0 0 NUM iajs-200 40 32 ) ) PUNCT iajs-200 40 33 , , PUNCT iajs-200 40 34 and and CCONJ iajs-200 40 35 we we PRON iajs-200 40 36 are be AUX iajs-200 40 37 done do VERB iajs-200 40 38 . . PUNCT iajs-200 41 1 in in ADP iajs-200 41 2 [ [ X iajs-200 41 3 1 1 NUM iajs-200 41 4 ] ] PUNCT iajs-200 41 5 , , PUNCT iajs-200 41 6 ali ali PROPN iajs-200 41 7 and and CCONJ iajs-200 41 8 nada nada PROPN iajs-200 41 9 gave give VERB iajs-200 41 10 an an DET iajs-200 41 11 example example NOUN iajs-200 41 12 verified verify VERB iajs-200 41 13 , , PUNCT iajs-200 41 14 that that SCONJ iajs-200 41 15 the the DET iajs-200 41 16 class class NOUN iajs-200 41 17 of of ADP iajs-200 41 18 semi semi ADJ iajs-200 41 19 - - ADJ iajs-200 41 20 essential essential ADJ iajs-200 41 21 submodules submodule NOUN iajs-200 41 22 was be AUX iajs-200 41 23 did do AUX iajs-200 41 24 n't not PART iajs-200 41 25 satisfy satisfy VERB iajs-200 41 26 the the DET iajs-200 41 27 transitive transitive ADJ iajs-200 41 28 property property NOUN iajs-200 41 29 for for ADP iajs-200 41 30 nonzero nonzero PROPN iajs-200 41 31 submodules submodule NOUN iajs-200 41 32 . . PUNCT iajs-200 42 1 but but CCONJ iajs-200 42 2 in in ADP iajs-200 42 3 this this DET iajs-200 42 4 work work NOUN iajs-200 42 5 , , PUNCT iajs-200 42 6 we we PRON iajs-200 42 7 show show VERB iajs-200 42 8 that that SCONJ iajs-200 42 9 the the DET iajs-200 42 10 example example NOUN iajs-200 42 11 which which PRON iajs-200 42 12 they they PRON iajs-200 42 13 gave give VERB iajs-200 42 14 it it PRON iajs-200 42 15 in in ADP iajs-200 42 16 [ [ X iajs-200 42 17 1 1 X iajs-200 42 18 ] ] PUNCT iajs-200 42 19 is be AUX iajs-200 42 20 not not PART iajs-200 42 21 true true ADJ iajs-200 42 22 , , PUNCT iajs-200 42 23 and and CCONJ iajs-200 42 24 we we PRON iajs-200 42 25 prove prove VERB iajs-200 42 26 that that SCONJ iajs-200 42 27 the the DET iajs-200 42 28 class class NOUN iajs-200 42 29 of of ADP iajs-200 42 30 semi semi ADJ iajs-200 42 31 - - ADJ iajs-200 42 32 essential essential ADJ iajs-200 42 33 submodules submodule NOUN iajs-200 42 34 satisfies satisfy VERB iajs-200 42 35 the the DET iajs-200 42 36 transitive transitive ADJ iajs-200 42 37 property property NOUN iajs-200 42 38 . . PUNCT iajs-200 43 1 in in ADP iajs-200 43 2 fact fact NOUN iajs-200 43 3 ali ali PROPN iajs-200 43 4 and and CCONJ iajs-200 43 5 nada nada PROPN iajs-200 43 6 said say VERB iajs-200 43 7 that that SCONJ iajs-200 43 8 4 4 NUM iajs-200 43 9 ≤sem ≤sem NOUN iajs-200 43 10 2 2 NUM iajs-200 43 11 and and CCONJ iajs-200 43 12 2 2 NUM iajs-200 43 13 ≤sem ≤sem PROPN iajs-200 43 14 z12 z12 NUM iajs-200 43 15 , , PUNCT iajs-200 43 16 but but CCONJ iajs-200 43 17 4 4 NUM iajs-200 43 18 ≰sem ≰sem NOUN iajs-200 43 19 z12 z12 NUM iajs-200 43 20 . . PUNCT iajs-200 44 1 in in ADP iajs-200 44 2 fact fact NOUN iajs-200 44 3 4 4 NUM iajs-200 44 4 ≰sem ≰sem NOUN iajs-200 44 5 2 2 NUM iajs-200 44 6 since since SCONJ iajs-200 44 7 6 6 NUM iajs-200 44 8 is be AUX iajs-200 44 9 a a DET iajs-200 44 10 prime prime ADJ iajs-200 44 11 submodule submodule NOUN iajs-200 44 12 of of ADP iajs-200 44 13 2 2 NUM iajs-200 44 14 and and CCONJ iajs-200 44 15 4 4 NUM iajs-200 44 16 ∩ ∩ NOUN iajs-200 44 17 6 6 NUM iajs-200 44 18 = = SYM iajs-200 44 19 ( ( PUNCT iajs-200 44 20 0 0 NUM iajs-200 44 21 ) ) PUNCT iajs-200 44 22 . . PUNCT iajs-200 45 1 however however ADV iajs-200 45 2 , , PUNCT iajs-200 45 3 in in ADP iajs-200 45 4 the the DET iajs-200 45 5 following follow VERB iajs-200 45 6 proposition proposition NOUN iajs-200 45 7 we we PRON iajs-200 45 8 give give VERB iajs-200 45 9 the the DET iajs-200 45 10 proof proof NOUN iajs-200 45 11 of of ADP iajs-200 45 12 the the DET iajs-200 45 13 transitive transitive ADJ iajs-200 45 14 property property NOUN iajs-200 45 15 for for ADP iajs-200 45 16 nonzero nonzero PROPN iajs-200 45 17 semi semi ADJ iajs-200 45 18 - - ADJ iajs-200 45 19 essential essential ADJ iajs-200 45 20 submodules submodule NOUN iajs-200 45 21 . . PUNCT iajs-200 46 1 before before ADP iajs-200 46 2 that that SCONJ iajs-200 46 3 we we PRON iajs-200 46 4 need need VERB iajs-200 46 5 the the DET iajs-200 46 6 following follow VERB iajs-200 46 7 lemma lemma PROPN iajs-200 46 8 which which PRON iajs-200 46 9 appeared appear VERB iajs-200 46 10 in in ADP iajs-200 46 11 [ [ X iajs-200 46 12 3 3 NUM iajs-200 46 13 , , PUNCT iajs-200 46 14 prop prop NOUN iajs-200 46 15 ( ( PUNCT iajs-200 46 16 1.7 1.7 NUM iajs-200 46 17 ) ) PUNCT iajs-200 46 18 , , PUNCT iajs-200 46 19 p.11 p.11 PROPN iajs-200 46 20 ] ] PUNCT iajs-200 46 21 . . PUNCT iajs-200 47 1 lemma lemma PROPN iajs-200 47 2 ( ( PUNCT iajs-200 47 3 1.4 1.4 NUM iajs-200 47 4 ): ): PUNCT iajs-200 47 5 let let VERB iajs-200 47 6 c c PRON iajs-200 47 7 be be AUX iajs-200 47 8 an an DET iajs-200 47 9 r r NOUN iajs-200 47 10 - - PUNCT iajs-200 47 11 module module NOUN iajs-200 47 12 , , PUNCT iajs-200 47 13 if if SCONJ iajs-200 47 14 p p NOUN iajs-200 47 15 is be AUX iajs-200 47 16 a a DET iajs-200 47 17 prime prime ADJ iajs-200 47 18 submodule submodule NOUN iajs-200 47 19 of of ADP iajs-200 47 20 c c PROPN iajs-200 47 21 and and CCONJ iajs-200 47 22 b b PROPN iajs-200 47 23 is be AUX iajs-200 47 24 a a DET iajs-200 47 25 submodule submodule NOUN iajs-200 47 26 of of ADP iajs-200 47 27 c c PROPN iajs-200 47 28 , , PUNCT iajs-200 47 29 such such ADJ iajs-200 47 30 that that SCONJ iajs-200 47 31 b b PROPN iajs-200 47 32 ≰ ≰ PROPN iajs-200 47 33 p p X iajs-200 47 34 , , PUNCT iajs-200 47 35 then then ADV iajs-200 47 36 p p X iajs-200 47 37 ∩ ∩ PROPN iajs-200 47 38 b b NOUN iajs-200 47 39 is be AUX iajs-200 47 40 a a DET iajs-200 47 41 prime prime ADJ iajs-200 47 42 submodule submodule NOUN iajs-200 47 43 in in ADP iajs-200 47 44 b. b. PROPN iajs-200 47 45 proposition proposition NOUN iajs-200 47 46 ( ( PUNCT iajs-200 47 47 1.5 1.5 NUM iajs-200 47 48 ): ): PUNCT iajs-200 47 49 let let VERB iajs-200 47 50 a a DET iajs-200 47 51 , , PUNCT iajs-200 47 52 b b NOUN iajs-200 47 53 , , PUNCT iajs-200 47 54 c c AUX iajs-200 47 55 be be AUX iajs-200 47 56 r r NOUN iajs-200 47 57 - - PUNCT iajs-200 47 58 modules module NOUN iajs-200 47 59 such such ADJ iajs-200 47 60 that that SCONJ iajs-200 47 61 a a DET iajs-200 47 62 ≤ ≤ NUM iajs-200 47 63 b b PRON iajs-200 47 64 ≤ ≤ PROPN iajs-200 47 65 c. c. NOUN iajs-200 47 66 suppose suppose VERB iajs-200 47 67 that that SCONJ iajs-200 47 68 a a PRON iajs-200 47 69 is be AUX iajs-200 47 70 a a DET iajs-200 47 71 nonzero nonzero ADJ iajs-200 47 72 submodules submodule NOUN iajs-200 47 73 of of ADP iajs-200 47 74 m. m. NOUN iajs-200 47 75 if if SCONJ iajs-200 47 76 a a DET iajs-200 47 77 ≤sem ≤sem PROPN iajs-200 47 78 b b PROPN iajs-200 47 79 and and CCONJ iajs-200 47 80 b b PROPN iajs-200 47 81 ≤sem ≤sem PROPN iajs-200 48 1 c c PROPN iajs-200 48 2 then then ADV iajs-200 48 3 a a DET iajs-200 48 4 ≤sem ≤sem PROPN iajs-200 48 5 c. c. NOUN iajs-200 48 6 proof proof NOUN iajs-200 48 7 : : PUNCT iajs-200 48 8 let let VERB iajs-200 48 9 p p PRON iajs-200 48 10 be be AUX iajs-200 48 11 a a DET iajs-200 48 12 prime prime ADJ iajs-200 48 13 submodule submodule NOUN iajs-200 48 14 of of ADP iajs-200 48 15 c c PROPN iajs-200 48 16 such such ADJ iajs-200 48 17 that that SCONJ iajs-200 48 18 a a DET iajs-200 48 19 ∩ ∩ ADJ iajs-200 48 20 p p X iajs-200 48 21 = = X iajs-200 48 22 ( ( PUNCT iajs-200 48 23 0 0 NUM iajs-200 48 24 ) ) PUNCT iajs-200 48 25 . . PUNCT iajs-200 49 1 note note VERB iajs-200 49 2 that that SCONJ iajs-200 49 3 ( ( PUNCT iajs-200 49 4 0 0 NUM iajs-200 49 5 ) ) PUNCT iajs-200 49 6 = = PUNCT iajs-200 49 7 a a DET iajs-200 49 8 ∩ ∩ ADJ iajs-200 49 9 p p X iajs-200 49 10 = = X iajs-200 49 11 ( ( PUNCT iajs-200 49 12 a a DET iajs-200 49 13 ∩ ∩ ADJ iajs-200 49 14 p p NOUN iajs-200 49 15 ) ) PUNCT iajs-200 49 16 ∩ ∩ NOUN iajs-200 49 17 b b X iajs-200 49 18 = = SYM iajs-200 49 19 a a DET iajs-200 49 20 ∩ ∩ NOUN iajs-200 49 21 ( ( PUNCT iajs-200 49 22 p p X iajs-200 49 23 ∩ ∩ ADJ iajs-200 49 24 b b NOUN iajs-200 49 25 ) ) PUNCT iajs-200 49 26 . . PUNCT iajs-200 50 1 but but CCONJ iajs-200 50 2 p p NOUN iajs-200 50 3 is be AUX iajs-200 50 4 a a DET iajs-200 50 5 prime prime ADJ iajs-200 50 6 submodule submodule NOUN iajs-200 50 7 of of ADP iajs-200 50 8 c c PROPN iajs-200 50 9 , , PUNCT iajs-200 50 10 so so ADV iajs-200 50 11 we we PRON iajs-200 50 12 have have VERB iajs-200 50 13 two two NUM iajs-200 50 14 cases case NOUN iajs-200 50 15 . . PUNCT iajs-200 51 1 if if SCONJ iajs-200 51 2 b b X iajs-200 51 3 ≤ ≤ X iajs-200 51 4 p p NOUN iajs-200 51 5 then then ADV iajs-200 51 6 ( ( PUNCT iajs-200 51 7 0 0 NUM iajs-200 51 8 ) ) PUNCT iajs-200 51 9 = = NOUN iajs-200 52 1 a a DET iajs-200 52 2 ∩ ∩ NOUN iajs-200 52 3 ( ( PUNCT iajs-200 52 4 p p X iajs-200 52 5 ∩ ∩ ADJ iajs-200 52 6 b b NOUN iajs-200 52 7 ) ) PUNCT iajs-200 52 8 = = PUNCT iajs-200 52 9 a a DET iajs-200 52 10 ∩ ∩ ADJ iajs-200 52 11 b b NOUN iajs-200 52 12 , , PUNCT iajs-200 52 13 hence hence ADV iajs-200 52 14 a a DET iajs-200 52 15 ∩ ∩ ADJ iajs-200 52 16 b b NOUN iajs-200 52 17 = = SYM iajs-200 52 18 ( ( PUNCT iajs-200 52 19 0 0 NUM iajs-200 52 20 ) ) PUNCT iajs-200 52 21 , , PUNCT iajs-200 52 22 but but CCONJ iajs-200 52 23 a a DET iajs-200 52 24 ≤ ≤ PROPN iajs-200 52 25 b b NOUN iajs-200 52 26 , , PUNCT iajs-200 52 27 so so SCONJ iajs-200 52 28 a a DET iajs-200 52 29 ∩ ∩ ADJ iajs-200 52 30 b b NOUN iajs-200 52 31 = = SYM iajs-200 52 32 a a NOUN iajs-200 52 33 , , PUNCT iajs-200 52 34 which which PRON iajs-200 52 35 is be AUX iajs-200 52 36 implies imply VERB iajs-200 52 37 that that SCONJ iajs-200 52 38 a a PRON iajs-200 52 39 = = X iajs-200 52 40 ( ( PUNCT iajs-200 52 41 0 0 NUM iajs-200 52 42 ) ) PUNCT iajs-200 52 43 . . PUNCT iajs-200 53 1 but but CCONJ iajs-200 53 2 this this PRON iajs-200 53 3 is be AUX iajs-200 53 4 a a DET iajs-200 53 5 contradiction contradiction NOUN iajs-200 53 6 with with ADP iajs-200 53 7 our our PRON iajs-200 53 8 assumption assumption NOUN iajs-200 53 9 . . PUNCT iajs-200 54 1 thus thus ADV iajs-200 54 2 b b X iajs-200 54 3 ≰ ≰ PROPN iajs-200 54 4 p p X iajs-200 54 5 , , PUNCT iajs-200 54 6 and and CCONJ iajs-200 54 7 by by ADP iajs-200 54 8 lemma lemma PROPN iajs-200 54 9 ( ( PUNCT iajs-200 54 10 1.4 1.4 NUM iajs-200 54 11 ) ) PUNCT iajs-200 54 12 , , PUNCT iajs-200 54 13 p p PROPN iajs-200 54 14 ∩ ∩ PROPN iajs-200 54 15 b b NOUN iajs-200 54 16 is be AUX iajs-200 54 17 a a DET iajs-200 54 18 prime prime ADJ iajs-200 54 19 submodule submodule NOUN iajs-200 54 20 of of ADP iajs-200 54 21 b. b. PROPN iajs-200 55 1 but but CCONJ iajs-200 55 2 a a DET iajs-200 55 3 ≤sem ≤sem PROPN iajs-200 55 4 b b PROPN iajs-200 55 5 , , PUNCT iajs-200 55 6 therefore therefore ADV iajs-200 55 7 p p X iajs-200 55 8 ∩ ∩ ADJ iajs-200 55 9 b b NOUN iajs-200 55 10 = = SYM iajs-200 55 11 ( ( PUNCT iajs-200 55 12 0 0 NUM iajs-200 55 13 ) ) PUNCT iajs-200 55 14 , , PUNCT iajs-200 55 15 and and CCONJ iajs-200 55 16 since since SCONJ iajs-200 55 17 b b PROPN iajs-200 55 18 ≤sem ≤sem PROPN iajs-200 55 19 c c PROPN iajs-200 55 20 , , PUNCT iajs-200 55 21 then then ADV iajs-200 55 22 p p NOUN iajs-200 55 23 = = PUNCT iajs-200 55 24 ( ( PUNCT iajs-200 55 25 0 0 NUM iajs-200 55 26 ) ) PUNCT iajs-200 55 27 , , PUNCT iajs-200 55 28 that that PRON iajs-200 55 29 is be AUX iajs-200 55 30 a a DET iajs-200 55 31 ≤sem ≤sem PROPN iajs-200 55 32 c. c. PROPN iajs-200 55 33 remark remark NOUN iajs-200 55 34 ( ( PUNCT iajs-200 55 35 1.6 1.6 NUM iajs-200 55 36 ): ): PUNCT iajs-200 56 1 the the DET iajs-200 56 2 condition condition NOUN iajs-200 56 3 a a DET iajs-200 56 4 ≠ ≠ PROPN iajs-200 56 5 ( ( PUNCT iajs-200 56 6 0 0 NUM iajs-200 56 7 ) ) PUNCT iajs-200 56 8 in in ADP iajs-200 56 9 prop prop NOUN iajs-200 56 10 ( ( PUNCT iajs-200 56 11 1.5 1.5 NUM iajs-200 56 12 ) ) PUNCT iajs-200 56 13 is be AUX iajs-200 56 14 necessary necessary ADJ iajs-200 56 15 . . PUNCT iajs-200 57 1 in in ADP iajs-200 57 2 fact fact NOUN iajs-200 57 3 in in ADP iajs-200 57 4 the the DET iajs-200 57 5 z z NOUN iajs-200 57 6 - - PUNCT iajs-200 57 7 module module NOUN iajs-200 57 8 z12 z12 NOUN iajs-200 57 9 , , PUNCT iajs-200 57 10 ( ( PUNCT iajs-200 57 11 0 0 NUM iajs-200 57 12 ) ) PUNCT iajs-200 57 13 is be AUX iajs-200 57 14 a a DET iajs-200 57 15 semi semi ADJ iajs-200 57 16 - - ADJ iajs-200 57 17 essential essential ADJ iajs-200 57 18 submodule submodule NOUN iajs-200 57 19 of of ADP iajs-200 57 20 { { PUNCT iajs-200 57 21 0 0 NUM iajs-200 57 22 , , PUNCT iajs-200 57 23 6 6 NUM iajs-200 57 24 } } PUNCT iajs-200 57 25 and and CCONJ iajs-200 57 26 { { PUNCT iajs-200 57 27 0 0 NUM iajs-200 57 28 , , PUNCT iajs-200 57 29 6 6 NUM iajs-200 57 30 } } PUNCT iajs-200 57 31 is be AUX iajs-200 57 32 a a DET iajs-200 57 33 semi semi ADJ iajs-200 57 34 - - ADJ iajs-200 57 35 essential essential ADJ iajs-200 57 36 submodule submodule NOUN iajs-200 57 37 of of ADP iajs-200 57 38 z12 z12 PROPN iajs-200 57 39 , , PUNCT iajs-200 57 40 but but CCONJ iajs-200 57 41 ( ( PUNCT iajs-200 57 42 0 0 X iajs-200 57 43 ) ) PUNCT iajs-200 57 44 not not PART iajs-200 57 45 semi semi ADV iajs-200 57 46 - - ADJ iajs-200 57 47 essential essential ADJ iajs-200 57 48 in in ADP iajs-200 57 49 z12 z12 PROPN iajs-200 57 50 . . PUNCT iajs-200 58 1 the the DET iajs-200 58 2 converse converse NOUN iajs-200 58 3 of of ADP iajs-200 58 4 prop prop NOUN iajs-200 58 5 ( ( PUNCT iajs-200 58 6 1.5 1.5 NUM iajs-200 58 7 ) ) PUNCT iajs-200 58 8 is be AUX iajs-200 58 9 not not PART iajs-200 58 10 true true ADJ iajs-200 58 11 in in ADP iajs-200 58 12 general general ADJ iajs-200 58 13 , , PUNCT iajs-200 58 14 as as SCONJ iajs-200 58 15 the the DET iajs-200 58 16 following follow VERB iajs-200 58 17 example example NOUN iajs-200 58 18 shows show NOUN iajs-200 58 19 . . PUNCT iajs-200 59 1 example example NOUN iajs-200 59 2 ( ( PUNCT iajs-200 59 3 1.7 1.7 NUM iajs-200 59 4 ): ): PUNCT iajs-200 59 5 consider consider VERB iajs-200 59 6 the the DET iajs-200 59 7 z z NOUN iajs-200 59 8 - - PUNCT iajs-200 59 9 module module NOUN iajs-200 59 10 , , PUNCT iajs-200 59 11 z36 z36 NUM iajs-200 59 12 , , PUNCT iajs-200 59 13 the the DET iajs-200 59 14 submodule submodule NOUN iajs-200 59 15 ( ( PUNCT iajs-200 59 16 18 18 NUM iajs-200 59 17 ) ) PUNCT iajs-200 59 18 is be AUX iajs-200 59 19 a a DET iajs-200 59 20 semi semi ADJ iajs-200 59 21 - - ADJ iajs-200 59 22 essential essential ADJ iajs-200 59 23 submodule submodule NOUN iajs-200 59 24 of of ADP iajs-200 59 25 z36 z36 PROPN iajs-200 59 26 . . PUNCT iajs-200 60 1 but but CCONJ iajs-200 60 2 ( ( PUNCT iajs-200 60 3 18 18 NUM iajs-200 60 4 ) ) PUNCT iajs-200 60 5 is be AUX iajs-200 60 6 not not PART iajs-200 60 7 semi semi ADJ iajs-200 60 8 - - ADJ iajs-200 60 9 essential essential ADJ iajs-200 60 10 submodule submodule NOUN iajs-200 60 11 of of ADP iajs-200 60 12 ( ( PUNCT iajs-200 60 13 2 2 NUM iajs-200 60 14 ) ) PUNCT iajs-200 60 15 . . PUNCT iajs-200 61 1 2 2 X iajs-200 61 2 . . X iajs-200 61 3 other other ADJ iajs-200 61 4 results result NOUN iajs-200 61 5 on on ADP iajs-200 61 6 semi semi ADJ iajs-200 61 7 - - ADJ iajs-200 61 8 essential essential ADJ iajs-200 61 9 submodules submodule NOUN iajs-200 61 10 in in ADP iajs-200 61 11 this this DET iajs-200 61 12 section section NOUN iajs-200 61 13 , , PUNCT iajs-200 61 14 we we PRON iajs-200 61 15 introduce introduce VERB iajs-200 61 16 other other ADJ iajs-200 61 17 properties property NOUN iajs-200 61 18 of of ADP iajs-200 61 19 semi semi ADJ iajs-200 61 20 - - ADJ iajs-200 61 21 essential essential ADJ iajs-200 61 22 submodules submodule NOUN iajs-200 61 23 . . PUNCT iajs-200 62 1 recall recall VERB iajs-200 62 2 that that SCONJ iajs-200 62 3 an an DET iajs-200 62 4 r r NOUN iajs-200 62 5 - - PUNCT iajs-200 62 6 module module NOUN iajs-200 62 7 m m NOUN iajs-200 62 8 is be AUX iajs-200 62 9 called call VERB iajs-200 62 10 fully fully ADV iajs-200 62 11 prime prime ADJ iajs-200 62 12 , , PUNCT iajs-200 62 13 if if SCONJ iajs-200 62 14 every every DET iajs-200 62 15 proper proper ADJ iajs-200 62 16 submodule submodule NOUN iajs-200 62 17 of of ADP iajs-200 62 18 m m PROPN iajs-200 62 19 is be AUX iajs-200 62 20 a a DET iajs-200 62 21 prime prime ADJ iajs-200 62 22 submodule submodule NOUN iajs-200 63 1 [ [ X iajs-200 63 2 5 5 NUM iajs-200 63 3 ] ] PUNCT iajs-200 63 4 , , PUNCT iajs-200 63 5 and and CCONJ iajs-200 63 6 a a DET iajs-200 63 7 nonzero nonzero ADJ iajs-200 63 8 r r NOUN iajs-200 63 9 - - PUNCT iajs-200 63 10 module module NOUN iajs-200 63 11 is be AUX iajs-200 63 12 called call VERB iajs-200 63 13 fully fully ADV iajs-200 63 14 essential essential ADJ iajs-200 63 15 , , PUNCT iajs-200 63 16 if if SCONJ iajs-200 63 17 every every DET iajs-200 63 18 nonzero nonzero ADJ iajs-200 63 19 semi semi ADJ iajs-200 63 20 - - ADJ iajs-200 63 21 essential essential ADJ iajs-200 63 22 submodule submodule NOUN iajs-200 63 23 of of ADP iajs-200 63 24 m m PROPN iajs-200 63 25 is be AUX iajs-200 63 26 an an DET iajs-200 63 27 essential essential ADJ iajs-200 63 28 submodule submodule NOUN iajs-200 63 29 of of ADP iajs-200 63 30 m m PROPN iajs-200 63 31 [ [ X iajs-200 63 32 11 11 NUM iajs-200 63 33 ] ] PUNCT iajs-200 63 34 . . PUNCT iajs-200 64 1 tamadher tamadher NOUN iajs-200 64 2 in in ADP iajs-200 64 3 [ [ X iajs-200 64 4 8 8 NUM iajs-200 64 5 , , PUNCT iajs-200 64 6 lemma lemma PROPN iajs-200 64 7 3.7 3.7 NUM iajs-200 64 8 ] ] PUNCT iajs-200 64 9 , , PUNCT iajs-200 64 10 proved prove VERB iajs-200 64 11 that that SCONJ iajs-200 64 12 if if SCONJ iajs-200 64 13 a a PRON iajs-200 64 14 and and CCONJ iajs-200 64 15 b b NOUN iajs-200 64 16 are be AUX iajs-200 64 17 prime prime ADJ iajs-200 64 18 submodules submodule NOUN iajs-200 64 19 of of ADP iajs-200 64 20 an an DET iajs-200 64 21 rmodule rmodule NOUN iajs-200 64 22 m m PROPN iajs-200 64 23 and and CCONJ iajs-200 64 24 a a DET iajs-200 64 25 ≤ ≤ NUM iajs-200 64 26 b b NOUN iajs-200 64 27 , , PUNCT iajs-200 64 28 then then ADV iajs-200 64 29 a a PRON iajs-200 64 30 is be AUX iajs-200 64 31 a a DET iajs-200 64 32 prime prime ADJ iajs-200 64 33 submodule submodule NOUN iajs-200 64 34 in in ADP iajs-200 64 35 b. b. PROPN iajs-200 64 36 in in ADP iajs-200 64 37 fact fact NOUN iajs-200 64 38 b b NOUN iajs-200 64 39 need need AUX iajs-200 64 40 not not PART iajs-200 64 41 be be AUX iajs-200 64 42 necessary necessary ADJ iajs-200 64 43 prime prime ADJ iajs-200 64 44 submodule submodule NOUN iajs-200 64 45 in in ADP iajs-200 64 46 m. m. NOUN iajs-200 64 47 we we PRON iajs-200 64 48 use use VERB iajs-200 64 49 this this DET iajs-200 64 50 statement statement NOUN iajs-200 64 51 to to PART iajs-200 64 52 prove prove VERB iajs-200 64 53 the the DET iajs-200 64 54 following follow VERB iajs-200 64 55 proposition proposition NOUN iajs-200 64 56 , , PUNCT iajs-200 64 57 which which PRON iajs-200 64 58 is be AUX iajs-200 64 59 forming form VERB iajs-200 64 60 a a DET iajs-200 64 61 generalization generalization NOUN iajs-200 64 62 of of ADP iajs-200 64 63 the the DET iajs-200 64 64 result result NOUN iajs-200 64 65 which which PRON iajs-200 64 66 was be AUX iajs-200 64 67 given give VERB iajs-200 64 68 in in ADP iajs-200 64 69 [ [ X iajs-200 64 70 11 11 NUM iajs-200 64 71 , , PUNCT iajs-200 64 72 lemma lemma PROPN iajs-200 64 73 ( ( PUNCT iajs-200 64 74 1.4 1.4 NUM iajs-200 64 75 ) ) PUNCT iajs-200 64 76 ] ] PUNCT iajs-200 64 77 . . PUNCT iajs-200 65 1 proposition proposition NOUN iajs-200 65 2 ( ( PUNCT iajs-200 65 3 2.1 2.1 NUM iajs-200 65 4 ): ): PUNCT iajs-200 65 5 let let VERB iajs-200 65 6 m m PRON iajs-200 65 7 be be AUX iajs-200 65 8 a a DET iajs-200 65 9 fully fully ADV iajs-200 65 10 prime prime ADJ iajs-200 65 11 r r NOUN iajs-200 65 12 - - PUNCT iajs-200 65 13 module module NOUN iajs-200 65 14 , , PUNCT iajs-200 65 15 and and CCONJ iajs-200 65 16 let let VERB iajs-200 65 17 ( ( PUNCT iajs-200 65 18 0 0 NUM iajs-200 65 19 ) ) PUNCT iajs-200 65 20 ≠ ≠ PROPN iajs-200 65 21 n n PRON iajs-200 65 22 ≤ ≤ NOUN iajs-200 65 23 m. m. NOUN iajs-200 65 24 then then ADV iajs-200 65 25 n n CCONJ iajs-200 65 26 ≤sem ≤sem NOUN iajs-200 66 1 l l NOUN iajs-200 66 2 if if SCONJ iajs-200 66 3 and and CCONJ iajs-200 66 4 only only ADV iajs-200 66 5 if if SCONJ iajs-200 66 6 n n PRON iajs-200 66 7 ≤e ≤e VERB iajs-200 66 8 l l NOUN iajs-200 66 9 for for ADP iajs-200 66 10 every every DET iajs-200 66 11 submodule submodule NOUN iajs-200 66 12 l l NOUN iajs-200 66 13 of of ADP iajs-200 66 14 m. m. NOUN iajs-200 66 15 proof proof NOUN iajs-200 66 16 ⇒ ⇒ NOUN iajs-200 66 17 ): ): PUNCT iajs-200 66 18 assume assume VERB iajs-200 66 19 that that SCONJ iajs-200 66 20 n n PRON iajs-200 66 21 is be AUX iajs-200 66 22 a a DET iajs-200 66 23 semi semi ADJ iajs-200 66 24 essential essential ADJ iajs-200 66 25 submodule submodule NOUN iajs-200 66 26 of of ADP iajs-200 66 27 l l NOUN iajs-200 66 28 , , PUNCT iajs-200 66 29 and and CCONJ iajs-200 66 30 let let VERB iajs-200 66 31 a a PRON iajs-200 66 32 be be AUX iajs-200 66 33 a a DET iajs-200 66 34 submodule submodule NOUN iajs-200 66 35 of of ADP iajs-200 66 36 l l NOUN iajs-200 66 37 such such ADJ iajs-200 66 38 that that SCONJ iajs-200 66 39 n n NOUN iajs-200 66 40 ∩ ∩ NOUN iajs-200 66 41 a a X iajs-200 66 42 = = X iajs-200 66 43 ( ( PUNCT iajs-200 66 44 0 0 NUM iajs-200 66 45 ) ) PUNCT iajs-200 66 46 . . PUNCT iajs-200 67 1 since since SCONJ iajs-200 67 2 m m PROPN iajs-200 67 3 is be AUX iajs-200 67 4 a a DET iajs-200 67 5 fully fully ADV iajs-200 67 6 prime prime ADJ iajs-200 67 7 module module NOUN iajs-200 67 8 then then ADV iajs-200 67 9 both both PRON iajs-200 67 10 of of ADP iajs-200 67 11 n n PROPN iajs-200 67 12 and and CCONJ iajs-200 67 13 a a PRON iajs-200 67 14 are be AUX iajs-200 67 15 prime prime ADJ iajs-200 67 16 submodules submodule NOUN iajs-200 67 17 of of ADP iajs-200 67 18 m m PROPN iajs-200 67 19 , , PUNCT iajs-200 67 20 and and CCONJ iajs-200 67 21 by by ADP iajs-200 67 22 [ [ X iajs-200 67 23 8 8 NUM iajs-200 67 24 , , PUNCT iajs-200 67 25 lemma lemma PROPN iajs-200 67 26 3.7 3.7 NUM iajs-200 67 27 ] ] PUNCT iajs-200 67 28 a a PRON iajs-200 67 29 is be AUX iajs-200 67 30 a a DET iajs-200 67 31 prime prime ADJ iajs-200 67 32 submodule submodule NOUN iajs-200 67 33 of of ADP iajs-200 67 34 l. l. PROPN iajs-200 67 35 but but CCONJ iajs-200 67 36 n n PROPN iajs-200 67 37 is be AUX iajs-200 67 38 a a DET iajs-200 67 39 semiessential semiessential ADJ iajs-200 67 40 submodule submodule NOUN iajs-200 67 41 of of ADP iajs-200 67 42 l l NOUN iajs-200 67 43 , , PUNCT iajs-200 67 44 therefore therefore ADV iajs-200 67 45 a a X iajs-200 67 46 = = X iajs-200 67 47 ( ( PUNCT iajs-200 67 48 0 0 NUM iajs-200 67 49 ) ) PUNCT iajs-200 67 50 , , PUNCT iajs-200 67 51 that that PRON iajs-200 67 52 is be AUX iajs-200 67 53 n n PRON iajs-200 67 54 is be AUX iajs-200 67 55 an an DET iajs-200 67 56 essential essential ADJ iajs-200 67 57 submodule submodule NOUN iajs-200 67 58 of of ADP iajs-200 67 59 l. l. PROPN iajs-200 67 60 ⇐ ⇐ PROPN iajs-200 67 61 ): ): PUNCT iajs-200 67 62 it it PRON iajs-200 67 63 is be AUX iajs-200 67 64 clear clear ADJ iajs-200 67 65 . . PUNCT iajs-200 68 1 corollary corollary ADJ iajs-200 68 2 ( ( PUNCT iajs-200 68 3 2.2 2.2 NUM iajs-200 68 4 ): ): PUNCT iajs-200 68 5 every every DET iajs-200 68 6 fully fully ADV iajs-200 68 7 prime prime ADJ iajs-200 68 8 module module NOUN iajs-200 68 9 is be AUX iajs-200 68 10 a a DET iajs-200 68 11 fully fully ADV iajs-200 68 12 essential essential ADJ iajs-200 68 13 module module NOUN iajs-200 68 14 . . PUNCT iajs-200 69 1 182 182 NUM iajs-200 69 2 | | ADV iajs-200 69 3 mathematics mathematic NOUN iajs-200 69 4 2015 2015 NUM iajs-200 69 5 ) ) PUNCT iajs-200 69 6 عام عام ADP iajs-200 69 7 1(العدد 1(العدد NUM iajs-200 69 8 28المجلد 28المجلد NUM iajs-200 69 9 مجلة مجلة PROPN iajs-200 69 10 إبن إبن VERB iajs-200 69 11 الھيثم الھيثم NOUN iajs-200 69 12 للعلوم للعلوم NOUN iajs-200 69 13 الصرفة الصرفة NOUN iajs-200 70 1 و و PRON iajs-200 70 2 التطبيقية التطبيقية ADJ iajs-200 70 3 ibn ibn PROPN iajs-200 70 4 al al PROPN iajs-200 70 5 - - PUNCT iajs-200 70 6 haitham haitham PROPN iajs-200 70 7 j. j. PROPN iajs-200 70 8 for for ADP iajs-200 70 9 pure pure PROPN iajs-200 70 10 & & CCONJ iajs-200 70 11 appl appl PROPN iajs-200 70 12 . . PUNCT iajs-200 71 1 sci sci PROPN iajs-200 71 2 . . PUNCT iajs-200 71 3 vol vol NOUN iajs-200 71 4 . . PROPN iajs-200 72 1 28 28 NUM iajs-200 72 2 ( ( PUNCT iajs-200 72 3 1 1 NUM iajs-200 72 4 ) ) PUNCT iajs-200 72 5 2015 2015 NUM iajs-200 72 6 recall recall VERB iajs-200 72 7 that that SCONJ iajs-200 72 8 a a DET iajs-200 72 9 nonzero nonzero ADJ iajs-200 72 10 r r NOUN iajs-200 72 11 - - PUNCT iajs-200 72 12 module module NOUN iajs-200 72 13 m m NOUN iajs-200 72 14 is be AUX iajs-200 72 15 called call VERB iajs-200 72 16 semi semi ADJ iajs-200 72 17 - - ADJ iajs-200 72 18 uniform uniform ADJ iajs-200 72 19 if if SCONJ iajs-200 72 20 every every DET iajs-200 72 21 nonzero nonzero ADJ iajs-200 72 22 r r NOUN iajs-200 72 23 - - PUNCT iajs-200 72 24 submodule submodule NOUN iajs-200 72 25 of of ADP iajs-200 72 26 m m PROPN iajs-200 72 27 is be AUX iajs-200 72 28 semi semi ADJ iajs-200 72 29 - - ADJ iajs-200 72 30 essential essential ADJ iajs-200 72 31 . . PUNCT iajs-200 73 1 a a DET iajs-200 73 2 ring ring NOUN iajs-200 73 3 r r NOUN iajs-200 73 4 is be AUX iajs-200 73 5 called call VERB iajs-200 73 6 semi semi ADJ iajs-200 73 7 - - ADJ iajs-200 73 8 uniform uniform ADJ iajs-200 73 9 if if SCONJ iajs-200 73 10 r r NOUN iajs-200 73 11 is be AUX iajs-200 73 12 a a DET iajs-200 73 13 semi semi ADJ iajs-200 73 14 - - ADJ iajs-200 73 15 uniform uniform ADJ iajs-200 73 16 r r NOUN iajs-200 73 17 - - PUNCT iajs-200 73 18 module module NOUN iajs-200 73 19 , , PUNCT iajs-200 73 20 [ [ X iajs-200 73 21 1 1 NUM iajs-200 73 22 ] ] PUNCT iajs-200 73 23 . . PUNCT iajs-200 74 1 proposition proposition NOUN iajs-200 74 2 ( ( PUNCT iajs-200 74 3 2.3 2.3 NUM iajs-200 74 4 ): ): PUNCT iajs-200 74 5 let let VERB iajs-200 74 6 m m PRON iajs-200 74 7 be be AUX iajs-200 74 8 an an DET iajs-200 74 9 r r NOUN iajs-200 74 10 - - PUNCT iajs-200 74 11 module module NOUN iajs-200 74 12 . . PUNCT iajs-200 75 1 then then ADV iajs-200 75 2 m m PROPN iajs-200 75 3 is be AUX iajs-200 75 4 uniform uniform ADJ iajs-200 75 5 if if SCONJ iajs-200 76 1 and and CCONJ iajs-200 76 2 only only ADV iajs-200 76 3 if if SCONJ iajs-200 76 4 m m NOUN iajs-200 76 5 is be AUX iajs-200 76 6 semiuniform semiuniform ADJ iajs-200 76 7 and and CCONJ iajs-200 76 8 fully fully ADV iajs-200 76 9 essential essential ADJ iajs-200 76 10 . . PUNCT iajs-200 77 1 proof proof ADJ iajs-200 77 2 ⇒ ⇒ NOUN iajs-200 77 3 ): ): PUNCT iajs-200 77 4 it it PRON iajs-200 77 5 is be AUX iajs-200 77 6 clear clear ADJ iajs-200 77 7 . . PUNCT iajs-200 78 1 ⇐ ⇐ ADJ iajs-200 78 2 ): ): PUNCT iajs-200 78 3 let let VERB iajs-200 78 4 n n PRON iajs-200 78 5 be be AUX iajs-200 78 6 a a DET iajs-200 78 7 nonzero nonzero ADJ iajs-200 78 8 submodule submodule NOUN iajs-200 78 9 of of ADP iajs-200 78 10 m m PROPN iajs-200 78 11 , , PUNCT iajs-200 78 12 since since SCONJ iajs-200 78 13 m m PROPN iajs-200 78 14 is be AUX iajs-200 78 15 a a DET iajs-200 78 16 semi semi ADJ iajs-200 78 17 - - ADJ iajs-200 78 18 uniform uniform ADJ iajs-200 78 19 module module NOUN iajs-200 78 20 , , PUNCT iajs-200 79 1 then then ADV iajs-200 79 2 n n CCONJ iajs-200 79 3 ≤sem ≤sem PROPN iajs-200 79 4 m. m. NOUN iajs-200 80 1 but but CCONJ iajs-200 80 2 m m NOUN iajs-200 80 3 is be AUX iajs-200 80 4 a a DET iajs-200 80 5 fully fully ADV iajs-200 80 6 essential essential ADJ iajs-200 80 7 module module NOUN iajs-200 80 8 , , PUNCT iajs-200 80 9 then then ADV iajs-200 80 10 n n CCONJ iajs-200 80 11 ≤e ≤e VERB iajs-200 80 12 m. m. NOUN iajs-200 80 13 corollary corollary NOUN iajs-200 80 14 ( ( PUNCT iajs-200 80 15 2.4 2.4 NUM iajs-200 80 16 ): ): PUNCT iajs-200 80 17 let let VERB iajs-200 80 18 m m PRON iajs-200 80 19 be be AUX iajs-200 80 20 a a DET iajs-200 80 21 fully fully ADV iajs-200 80 22 prime prime ADJ iajs-200 80 23 module module NOUN iajs-200 80 24 , , PUNCT iajs-200 80 25 then then ADV iajs-200 80 26 a a DET iajs-200 80 27 module module NOUN iajs-200 80 28 m m NOUN iajs-200 80 29 is be AUX iajs-200 80 30 uniform uniform ADJ iajs-200 81 1 if if SCONJ iajs-200 81 2 and and CCONJ iajs-200 81 3 if if SCONJ iajs-200 81 4 m m NOUN iajs-200 81 5 is be AUX iajs-200 81 6 a a DET iajs-200 81 7 semi semi ADJ iajs-200 81 8 - - ADJ iajs-200 81 9 uniform uniform ADJ iajs-200 81 10 module module NOUN iajs-200 81 11 . . PUNCT iajs-200 82 1 the the DET iajs-200 82 2 following follow VERB iajs-200 82 3 proposition proposition NOUN iajs-200 82 4 appeared appear VERB iajs-200 82 5 in in ADP iajs-200 82 6 [ [ X iajs-200 82 7 11 11 NUM iajs-200 82 8 ] ] PUNCT iajs-200 82 9 , , PUNCT iajs-200 82 10 it it PRON iajs-200 82 11 deals deal VERB iajs-200 82 12 with with ADP iajs-200 82 13 the the DET iajs-200 82 14 direct direct ADJ iajs-200 82 15 sum sum NOUN iajs-200 82 16 of of ADP iajs-200 82 17 semi semi ADJ iajs-200 82 18 - - ADJ iajs-200 82 19 essential essential ADJ iajs-200 82 20 submodules submodule NOUN iajs-200 82 21 , , PUNCT iajs-200 82 22 and and CCONJ iajs-200 82 23 we we PRON iajs-200 82 24 give give VERB iajs-200 82 25 the the DET iajs-200 82 26 proof proof NOUN iajs-200 82 27 for for ADP iajs-200 82 28 completeness completeness NOUN iajs-200 82 29 . . PUNCT iajs-200 83 1 are be AUX iajs-200 83 2 2and 2and NUM iajs-200 83 3 m m PROPN iajs-200 83 4 1module 1module NUM iajs-200 83 5 where where SCONJ iajs-200 83 6 m m VERB iajs-200 83 7 - - VERB iajs-200 83 8 be be AUX iajs-200 83 9 a a DET iajs-200 83 10 fully fully ADV iajs-200 83 11 prime prime ADJ iajs-200 83 12 r r NOUN iajs-200 83 13 2 2 NUM iajs-200 83 14 m m NOUN iajs-200 83 15 ⨁ ⨁ PROPN iajs-200 83 16 1let 1let PROPN iajs-200 83 17 m m NOUN iajs-200 83 18 = = VERB iajs-200 83 19 mproposition mproposition NOUN iajs-200 83 20 ( ( PUNCT iajs-200 83 21 2.5 2.5 NUM iajs-200 83 22 ): ): PUNCT iajs-200 83 23 -is -is ADP iajs-200 83 24 a a DET iajs-200 83 25 semi2 semi2 NOUN iajs-200 83 26 k k PROPN iajs-200 83 27 ⊕ ⊕ PROPN iajs-200 83 28 1 1 NUM iajs-200 83 29 . . PUNCT iajs-200 84 1 then then ADV iajs-200 85 1 k2≤ k2≤ NUM iajs-200 85 2 m m VERB iajs-200 85 3 2k 2k NOUN iajs-200 85 4 and and CCONJ iajs-200 85 5 ( ( PUNCT iajs-200 85 6 0 0 NUM iajs-200 85 7 ) ) SYM iajs-200 85 8 1 1 NUM iajs-200 85 9 ≤ ≤ NUM iajs-200 85 10 m m VERB iajs-200 85 11 1k 1k NUM iajs-200 85 12 submodules submodule NOUN iajs-200 85 13 of of ADP iajs-200 85 14 m m PROPN iajs-200 85 15 , , PUNCT iajs-200 85 16 and and CCONJ iajs-200 85 17 let let VERB iajs-200 85 18 ( ( PUNCT iajs-200 85 19 0 0 NUM iajs-200 85 20 ) ) PUNCT iajs-200 85 21 and and CCONJ iajs-200 85 22 1essential 1essential NUM iajs-200 85 23 submodule submodule NOUN iajs-200 85 24 of of ADP iajs-200 85 25 m m PROPN iajs-200 85 26 - - PUNCT iajs-200 85 27 is be AUX iajs-200 85 28 a a DET iajs-200 85 29 semi semi ADJ iajs-200 85 30 1if 1if NOUN iajs-200 85 31 and and CCONJ iajs-200 85 32 only only ADV iajs-200 85 33 if if SCONJ iajs-200 85 34 k k PROPN iajs-200 85 35 2 2 NUM iajs-200 85 36 m m NOUN iajs-200 85 37 ⊕ ⊕ PROPN iajs-200 85 38 1essential 1essential PROPN iajs-200 85 39 submodule submodule NOUN iajs-200 85 40 of of ADP iajs-200 85 41 m m PROPN iajs-200 85 42 .2essential .2essential PROPN iajs-200 85 43 submodule submodule NOUN iajs-200 85 44 of of ADP iajs-200 85 45 m m PROPN iajs-200 85 46 - - PUNCT iajs-200 85 47 is be AUX iajs-200 85 48 a a DET iajs-200 85 49 semi semi ADJ iajs-200 85 50 2k 2k NOUN iajs-200 85 51 proof proof NOUN iajs-200 85 52 ⇒ ⇒ NOUN iajs-200 85 53 ): ): PUNCT iajs-200 85 54 since since SCONJ iajs-200 85 55 m m PROPN iajs-200 85 56 is be AUX iajs-200 85 57 a a DET iajs-200 85 58 fully fully ADV iajs-200 85 59 prime prime ADJ iajs-200 85 60 module module NOUN iajs-200 85 61 , , PUNCT iajs-200 85 62 then then ADV iajs-200 85 63 by by ADP iajs-200 85 64 [ [ PUNCT iajs-200 85 65 11 11 NUM iajs-200 85 66 , , PUNCT iajs-200 85 67 lemma lemma PROPN iajs-200 85 68 ( ( PUNCT iajs-200 85 69 1.14 1.14 NUM iajs-200 85 70 ) ) PUNCT iajs-200 85 71 ] ] PUNCT iajs-200 85 72 k1 k1 PROPN iajs-200 85 73 ⊕ ⊕ PROPN iajs-200 85 74 k2 k2 PROPN iajs-200 85 75 is be AUX iajs-200 85 76 an an DET iajs-200 85 77 essential essential ADJ iajs-200 85 78 submodule submodule NOUN iajs-200 85 79 of of ADP iajs-200 85 80 m1 m1 PROPN iajs-200 85 81 ⊕ ⊕ PROPN iajs-200 85 82 m2 m2 PROPN iajs-200 85 83 , , PUNCT iajs-200 85 84 and and CCONJ iajs-200 85 85 by by ADP iajs-200 85 86 [ [ X iajs-200 85 87 2 2 NUM iajs-200 85 88 ] ] PUNCT iajs-200 85 89 , , PUNCT iajs-200 85 90 k1 k1 PROPN iajs-200 85 91 is be AUX iajs-200 85 92 an an DET iajs-200 85 93 essential essential ADJ iajs-200 85 94 submodule submodule NOUN iajs-200 85 95 of of ADP iajs-200 85 96 m1 m1 PROPN iajs-200 85 97 and and CCONJ iajs-200 85 98 k2 k2 PROPN iajs-200 85 99 is be AUX iajs-200 85 100 an an DET iajs-200 85 101 essential essential ADJ iajs-200 85 102 submodule submodule NOUN iajs-200 85 103 of of ADP iajs-200 85 104 m2 m2 PROPN iajs-200 85 105 . . PUNCT iajs-200 86 1 but but CCONJ iajs-200 86 2 every every DET iajs-200 86 3 essential essential ADJ iajs-200 86 4 submodule submodule NOUN iajs-200 86 5 is be AUX iajs-200 86 6 a a DET iajs-200 86 7 semi semi ADJ iajs-200 86 8 - - ADJ iajs-200 86 9 essential essential ADJ iajs-200 86 10 , , PUNCT iajs-200 86 11 so so SCONJ iajs-200 86 12 we we PRON iajs-200 86 13 are be AUX iajs-200 86 14 done do VERB iajs-200 86 15 . . PUNCT iajs-200 87 1 ⇐ ⇐ ADJ iajs-200 87 2 ): ): PUNCT iajs-200 87 3 it it PRON iajs-200 87 4 follows follow VERB iajs-200 87 5 similarly similarly ADV iajs-200 87 6 . . PUNCT iajs-200 88 1 in in ADP iajs-200 88 2 the the DET iajs-200 88 3 following follow VERB iajs-200 88 4 proposition proposition NOUN iajs-200 88 5 , , PUNCT iajs-200 88 6 we we PRON iajs-200 88 7 give give VERB iajs-200 88 8 another another DET iajs-200 88 9 result result NOUN iajs-200 88 10 for for ADP iajs-200 88 11 the the DET iajs-200 88 12 direct direct ADJ iajs-200 88 13 sum sum NOUN iajs-200 88 14 of of ADP iajs-200 88 15 semi semi ADJ iajs-200 88 16 - - ADJ iajs-200 88 17 essential essential ADJ iajs-200 88 18 submodules submodule NOUN iajs-200 88 19 . . PUNCT iajs-200 89 1 proposition proposition NOUN iajs-200 89 2 ( ( PUNCT iajs-200 89 3 2.6 2.6 NUM iajs-200 89 4 ): ): PUNCT iajs-200 89 5 let let VERB iajs-200 89 6 m m NOUN iajs-200 89 7 = = VERB iajs-200 89 8 m1 m1 PROPN iajs-200 89 9 ⨁ ⨁ PROPN iajs-200 89 10 m2 m2 PROPN iajs-200 89 11 be be VERB iajs-200 89 12 an an DET iajs-200 89 13 r r NOUN iajs-200 89 14 - - PUNCT iajs-200 89 15 module module NOUN iajs-200 89 16 where where SCONJ iajs-200 89 17 m1 m1 PROPN iajs-200 89 18 and and CCONJ iajs-200 89 19 m2 m2 PROPN iajs-200 89 20 are be AUX iajs-200 89 21 submodules submodule NOUN iajs-200 89 22 of of ADP iajs-200 89 23 m m PROPN iajs-200 89 24 , , PUNCT iajs-200 89 25 and and CCONJ iajs-200 89 26 let let VERB iajs-200 89 27 k1 k1 NOUN iajs-200 89 28 ≤ ≤ ADJ iajs-200 89 29 m1 m1 PROPN iajs-200 89 30 and and CCONJ iajs-200 89 31 k2 k2 PROPN iajs-200 89 32 ≤ ≤ PROPN iajs-200 89 33 m2 m2 PROPN iajs-200 89 34 . . PUNCT iajs-200 90 1 if if SCONJ iajs-200 90 2 k1 k1 PROPN iajs-200 90 3 ⨁ ⨁ PROPN iajs-200 90 4 k2 k2 PROPN iajs-200 90 5 is be AUX iajs-200 90 6 a a DET iajs-200 90 7 semi semi ADJ iajs-200 90 8 - - ADJ iajs-200 90 9 essential essential ADJ iajs-200 90 10 submodule submodule NOUN iajs-200 90 11 of of ADP iajs-200 90 12 m1 m1 PROPN iajs-200 90 13 ⨁ ⨁ PROPN iajs-200 90 14 m2 m2 PROPN iajs-200 90 15 , , PUNCT iajs-200 90 16 then then ADV iajs-200 90 17 k1 k1 PROPN iajs-200 90 18 is be AUX iajs-200 90 19 a a DET iajs-200 90 20 semi semi ADJ iajs-200 90 21 - - ADJ iajs-200 90 22 essential essential ADJ iajs-200 90 23 submodule submodule NOUN iajs-200 90 24 of of ADP iajs-200 90 25 m1 m1 NOUN iajs-200 90 26 , , PUNCT iajs-200 90 27 provided provide VERB iajs-200 90 28 that that SCONJ iajs-200 90 29 every every DET iajs-200 90 30 prime prime ADJ iajs-200 90 31 submodule submodule NOUN iajs-200 90 32 of of ADP iajs-200 90 33 m1 m1 PROPN iajs-200 90 34 is be AUX iajs-200 90 35 a a DET iajs-200 90 36 prime prime ADJ iajs-200 90 37 submodule submodule NOUN iajs-200 90 38 of of ADP iajs-200 90 39 m. m. NOUN iajs-200 90 40 proof proof NOUN iajs-200 90 41 : : PUNCT iajs-200 90 42 let let VERB iajs-200 90 43 p1 p1 PROPN iajs-200 90 44 be be AUX iajs-200 90 45 a a DET iajs-200 90 46 prime prime ADJ iajs-200 90 47 submodule submodule NOUN iajs-200 90 48 of of ADP iajs-200 90 49 m1 m1 PROPN iajs-200 90 50 such such ADJ iajs-200 90 51 that that SCONJ iajs-200 90 52 k1 k1 NOUN iajs-200 90 53 ∩ ∩ ADJ iajs-200 90 54 p1 p1 NOUN iajs-200 90 55 = = SYM iajs-200 90 56 ( ( PUNCT iajs-200 90 57 0 0 NUM iajs-200 90 58 ) ) PUNCT iajs-200 90 59 . . PUNCT iajs-200 91 1 we we PRON iajs-200 91 2 can can AUX iajs-200 91 3 easily easily ADV iajs-200 91 4 prove prove VERB iajs-200 91 5 that that SCONJ iajs-200 91 6 ( ( PUNCT iajs-200 91 7 k1 k1 PROPN iajs-200 91 8 ⨁ ⨁ PROPN iajs-200 91 9 k2 k2 PROPN iajs-200 91 10 ) ) PUNCT iajs-200 91 11 ∩ ∩ ADJ iajs-200 91 12 p1 p1 NOUN iajs-200 91 13 = = SYM iajs-200 91 14 ( ( PUNCT iajs-200 91 15 0 0 NUM iajs-200 91 16 ) ) PUNCT iajs-200 91 17 . . PUNCT iajs-200 92 1 by by ADP iajs-200 92 2 assumption assumption NOUN iajs-200 92 3 p1 p1 NOUN iajs-200 92 4 is be AUX iajs-200 92 5 a a DET iajs-200 92 6 prime prime ADJ iajs-200 92 7 submodule submodule NOUN iajs-200 92 8 of of ADP iajs-200 92 9 m m PROPN iajs-200 92 10 and and CCONJ iajs-200 92 11 k1 k1 PROPN iajs-200 92 12 ⨁ ⨁ PROPN iajs-200 92 13 k2 k2 PROPN iajs-200 92 14 ≤sem ≤sem PROPN iajs-200 92 15 m m PROPN iajs-200 92 16 , , PUNCT iajs-200 92 17 thus thus ADV iajs-200 92 18 p1 p1 NOUN iajs-200 92 19 = = SYM iajs-200 92 20 ( ( PUNCT iajs-200 92 21 0 0 NUM iajs-200 92 22 ) ) PUNCT iajs-200 92 23 . . PUNCT iajs-200 93 1 recall recall VERB iajs-200 93 2 that that SCONJ iajs-200 93 3 the the DET iajs-200 93 4 prime prime ADJ iajs-200 93 5 radical radical NOUN iajs-200 93 6 of of ADP iajs-200 93 7 an an DET iajs-200 93 8 r r NOUN iajs-200 93 9 - - PUNCT iajs-200 93 10 module module NOUN iajs-200 93 11 m m NOUN iajs-200 93 12 is be AUX iajs-200 93 13 denoted denote VERB iajs-200 93 14 by by ADP iajs-200 93 15 rad(m rad(m PROPN iajs-200 93 16 ) ) PUNCT iajs-200 93 17 , , PUNCT iajs-200 93 18 and and CCONJ iajs-200 93 19 it it PRON iajs-200 93 20 is be AUX iajs-200 93 21 the the DET iajs-200 93 22 intersection intersection NOUN iajs-200 93 23 of of ADP iajs-200 93 24 all all DET iajs-200 93 25 prime prime ADJ iajs-200 93 26 modules module NOUN iajs-200 93 27 of of ADP iajs-200 93 28 m m PROPN iajs-200 93 29 [ [ X iajs-200 93 30 10 10 NUM iajs-200 93 31 ] ] PUNCT iajs-200 93 32 . . PUNCT iajs-200 94 1 proposition proposition NOUN iajs-200 94 2 ( ( PUNCT iajs-200 94 3 2.7 2.7 NUM iajs-200 94 4 ): ): PUNCT iajs-200 94 5 let let VERB iajs-200 94 6 m m PRON iajs-200 94 7 be be AUX iajs-200 94 8 an an DET iajs-200 94 9 r r NOUN iajs-200 94 10 - - PUNCT iajs-200 94 11 module module NOUN iajs-200 94 12 and and CCONJ iajs-200 94 13 let let VERB iajs-200 94 14 ( ( PUNCT iajs-200 94 15 0 0 NUM iajs-200 94 16 ) ) PUNCT iajs-200 94 17 ≠ ≠ PROPN iajs-200 94 18 n n PRON iajs-200 94 19 ≤ ≤ NOUN iajs-200 94 20 m. m. NOUN iajs-200 94 21 if if SCONJ iajs-200 94 22 n n CCONJ iajs-200 94 23 ' ' PUNCT iajs-200 94 24 is be AUX iajs-200 94 25 a a DET iajs-200 94 26 semi semi ADJ iajs-200 94 27 relative relative ADJ iajs-200 94 28 complement complement NOUN iajs-200 94 29 of of ADP iajs-200 94 30 n n PROPN iajs-200 94 31 in in ADP iajs-200 94 32 m m PROPN iajs-200 94 33 , , PUNCT iajs-200 94 34 and and CCONJ iajs-200 94 35 n n CCONJ iajs-200 94 36 ' ' CCONJ iajs-200 94 37 ≤ ≤ NUM iajs-200 94 38 rad(m rad(m PROPN iajs-200 94 39 ) ) PUNCT iajs-200 94 40 , , PUNCT iajs-200 94 41 then then ADV iajs-200 94 42 n n PROPN iajs-200 94 43 ⨁ ⨁ PROPN iajs-200 94 44 n n CCONJ iajs-200 94 45 ' ' CCONJ iajs-200 94 46 ≤sem ≤sem PROPN iajs-200 94 47 m. m. NOUN iajs-200 94 48 proof proof NOUN iajs-200 94 49 : : PUNCT iajs-200 94 50 consider consider VERB iajs-200 94 51 the the DET iajs-200 94 52 natural natural ADJ iajs-200 94 53 epimorphism epimorphism NOUN iajs-200 94 54 π π NOUN iajs-200 94 55 : : PUNCT iajs-200 94 56 m m PROPN iajs-200 94 57 → → PUNCT iajs-200 94 58 . . PUNCT iajs-200 95 1 since since SCONJ iajs-200 95 2 n n CCONJ iajs-200 95 3 ' ' PUNCT iajs-200 95 4 is be AUX iajs-200 95 5 a a DET iajs-200 95 6 semi semi ADJ iajs-200 95 7 relative relative ADJ iajs-200 95 8 complement complement NOUN iajs-200 95 9 of of ADP iajs-200 95 10 n n PROPN iajs-200 95 11 in in ADP iajs-200 95 12 m m PROPN iajs-200 95 13 , , PUNCT iajs-200 95 14 so so ADV iajs-200 95 15 by by ADP iajs-200 95 16 [ [ X iajs-200 95 17 1 1 NUM iajs-200 95 18 ] ] PUNCT iajs-200 95 19 , , PUNCT iajs-200 95 20 ⊕ ⊕ PROPN iajs-200 95 21 ≤sem ≤sem PROPN iajs-200 95 22 . . PUNCT iajs-200 96 1 but but CCONJ iajs-200 96 2 ker ker PROPN iajs-200 96 3 π π PROPN iajs-200 96 4 = = PUNCT iajs-200 96 5 n n CCONJ iajs-200 96 6 ' ' PUNCT iajs-200 96 7 and and CCONJ iajs-200 96 8 n n CCONJ iajs-200 96 9 ' ' CCONJ iajs-200 96 10 ≤ ≤ NUM iajs-200 96 11 rad(m rad(m PROPN iajs-200 96 12 ) ) PUNCT iajs-200 96 13 , , PUNCT iajs-200 96 14 then then ADV iajs-200 96 15 by by ADP iajs-200 96 16 [ [ X iajs-200 96 17 1 1 NUM iajs-200 96 18 ] ] PUNCT iajs-200 96 19 , , PUNCT iajs-200 96 20 π-1 π-1 PROPN iajs-200 96 21 ( ( PUNCT iajs-200 96 22 ⊕ ⊕ PROPN iajs-200 96 23 ) ) PUNCT iajs-200 96 24 ≤sem ≤sem PROPN iajs-200 96 25 m. m. NOUN iajs-200 96 26 hence hence ADV iajs-200 96 27 n n PROPN iajs-200 96 28 ⨁ ⨁ PROPN iajs-200 96 29 n n CCONJ iajs-200 96 30 ' ' CCONJ iajs-200 96 31 ≤sem ≤sem PROPN iajs-200 96 32 m. m. PROPN iajs-200 96 33 ali ali PROPN iajs-200 96 34 and and CCONJ iajs-200 96 35 nada nada PROPN iajs-200 96 36 in in ADP iajs-200 96 37 [ [ X iajs-200 96 38 1 1 NUM iajs-200 96 39 ] ] PUNCT iajs-200 96 40 showed show VERB iajs-200 96 41 by by ADP iajs-200 96 42 an an DET iajs-200 96 43 example example NOUN iajs-200 96 44 that that SCONJ iajs-200 96 45 the the DET iajs-200 96 46 intersection intersection NOUN iajs-200 96 47 of of ADP iajs-200 96 48 two two NUM iajs-200 96 49 semi semi ADJ iajs-200 96 50 - - ADJ iajs-200 96 51 essential essential ADJ iajs-200 96 52 submodules submodule NOUN iajs-200 96 53 need need AUX iajs-200 96 54 not not PART iajs-200 96 55 be be AUX iajs-200 96 56 semi semi ADJ iajs-200 96 57 - - ADJ iajs-200 96 58 essential essential ADJ iajs-200 96 59 submodule submodule NOUN iajs-200 96 60 , , PUNCT iajs-200 96 61 and and CCONJ iajs-200 96 62 they they PRON iajs-200 96 63 satisfied satisfy VERB iajs-200 96 64 that that SCONJ iajs-200 96 65 under under ADP iajs-200 96 66 certain certain ADJ iajs-200 96 67 condition condition NOUN iajs-200 96 68 , , PUNCT iajs-200 96 69 see see VERB iajs-200 96 70 [ [ X iajs-200 96 71 1 1 NUM iajs-200 96 72 ] ] PUNCT iajs-200 96 73 . . PUNCT iajs-200 97 1 in in ADP iajs-200 97 2 this this DET iajs-200 97 3 work work NOUN iajs-200 97 4 we we PRON iajs-200 97 5 give give VERB iajs-200 97 6 a a DET iajs-200 97 7 deferent deferent ADJ iajs-200 97 8 condition condition NOUN iajs-200 97 9 . . PUNCT iajs-200 98 1 proposition proposition NOUN iajs-200 98 2 ( ( PUNCT iajs-200 98 3 2.8 2.8 NUM iajs-200 98 4 ): ): PUNCT iajs-200 98 5 let let VERB iajs-200 98 6 m m PRON iajs-200 98 7 be be AUX iajs-200 98 8 an an DET iajs-200 98 9 r r NOUN iajs-200 98 10 - - PUNCT iajs-200 98 11 module module NOUN iajs-200 98 12 and and CCONJ iajs-200 98 13 let let VERB iajs-200 98 14 n1 n1 NOUN iajs-200 98 15 and and CCONJ iajs-200 98 16 n2 n2 ADJ iajs-200 98 17 be be AUX iajs-200 98 18 semi semi ADJ iajs-200 98 19 - - ADJ iajs-200 98 20 essential essential ADJ iajs-200 98 21 submodules submodule NOUN iajs-200 98 22 of of ADP iajs-200 98 23 m m NOUN iajs-200 98 24 such such ADJ iajs-200 98 25 that that SCONJ iajs-200 98 26 n1 n1 PROPN iajs-200 98 27 ∩ ∩ ADJ iajs-200 98 28 n2 n2 ADJ iajs-200 98 29 ≠ ≠ PROPN iajs-200 98 30 ( ( PUNCT iajs-200 98 31 0 0 NUM iajs-200 98 32 ) ) PUNCT iajs-200 98 33 and and CCONJ iajs-200 98 34 all all DET iajs-200 98 35 prime prime ADJ iajs-200 98 36 submodules submodule NOUN iajs-200 98 37 of of ADP iajs-200 98 38 n1 n1 NOUN iajs-200 98 39 are be AUX iajs-200 98 40 prime prime ADJ iajs-200 98 41 submodules submodule NOUN iajs-200 98 42 of of ADP iajs-200 98 43 m m PROPN iajs-200 98 44 , , PUNCT iajs-200 98 45 then then ADV iajs-200 98 46 n1 n1 PROPN iajs-200 98 47 ∩ ∩ ADJ iajs-200 98 48 n2 n2 NOUN iajs-200 98 49 ≤sem ≤sem PROPN iajs-200 98 50 m. m. NOUN iajs-200 98 51 proof proof NOUN iajs-200 98 52 : : PUNCT iajs-200 98 53 let let VERB iajs-200 98 54 p p PRON iajs-200 98 55 be be AUX iajs-200 98 56 a a DET iajs-200 98 57 prime prime ADJ iajs-200 98 58 submodule submodule NOUN iajs-200 98 59 of of ADP iajs-200 98 60 m m PRON iajs-200 99 1 such such ADJ iajs-200 99 2 that that SCONJ iajs-200 99 3 ( ( PUNCT iajs-200 99 4 n1 n1 PROPN iajs-200 99 5 ∩ ∩ ADJ iajs-200 99 6 n2 n2 ADJ iajs-200 99 7 ) ) PUNCT iajs-200 99 8 ∩ ∩ NOUN iajs-200 99 9 p p X iajs-200 99 10 = = X iajs-200 99 11 ( ( PUNCT iajs-200 99 12 0 0 NUM iajs-200 99 13 ) ) PUNCT iajs-200 99 14 . . PUNCT iajs-200 100 1 this this PRON iajs-200 100 2 implies imply VERB iajs-200 100 3 that that SCONJ iajs-200 100 4 n2 n2 ADJ iajs-200 100 5 ∩ ∩ NOUN iajs-200 100 6 ( ( PUNCT iajs-200 100 7 n1∩ n1∩ NOUN iajs-200 100 8 p p NOUN iajs-200 100 9 ) ) PUNCT iajs-200 100 10 = = SYM iajs-200 100 11 ( ( PUNCT iajs-200 100 12 0 0 NUM iajs-200 100 13 ) ) PUNCT iajs-200 100 14 . . PUNCT iajs-200 101 1 if if SCONJ iajs-200 101 2 n1 n1 NOUN iajs-200 101 3 ≤ ≤ PUNCT iajs-200 101 4 p p X iajs-200 101 5 , , PUNCT iajs-200 101 6 then then ADV iajs-200 101 7 we we PRON iajs-200 101 8 have have VERB iajs-200 101 9 a a DET iajs-200 101 10 contradiction contradiction NOUN iajs-200 101 11 with with ADP iajs-200 101 12 the the DET iajs-200 101 13 assumption assumption NOUN iajs-200 101 14 , , PUNCT iajs-200 101 15 thus thus ADV iajs-200 101 16 n1 n1 PROPN iajs-200 101 17 ≰ ≰ PROPN iajs-200 101 18 p. p. NOUN iajs-200 101 19 this this PRON iajs-200 101 20 implies imply VERB iajs-200 101 21 that that SCONJ iajs-200 101 22 n1 n1 PROPN iajs-200 101 23 ∩ ∩ NOUN iajs-200 101 24 p p NOUN iajs-200 101 25 is be AUX iajs-200 101 26 a a DET iajs-200 101 27 prime prime ADJ iajs-200 101 28 submodule submodule NOUN iajs-200 101 29 of of ADP iajs-200 101 30 n1 n1 PROPN iajs-200 101 31 [ [ X iajs-200 101 32 3 3 NUM iajs-200 101 33 , , PUNCT iajs-200 101 34 prop prop NOUN iajs-200 101 35 ( ( PUNCT iajs-200 101 36 1 1 NUM iajs-200 101 37 - - SYM iajs-200 101 38 7 7 NUM iajs-200 101 39 , , PUNCT iajs-200 101 40 p. p. NOUN iajs-200 101 41 11 11 NUM iajs-200 101 42 ) ) PUNCT iajs-200 101 43 ] ] PUNCT iajs-200 101 44 . . PUNCT iajs-200 102 1 since since SCONJ iajs-200 102 2 n2 n2 PROPN iajs-200 102 3 ≤sem ≤sem PROPN iajs-200 102 4 m m PROPN iajs-200 102 5 183 183 NUM iajs-200 102 6 | | NOUN iajs-200 102 7 mathematics mathematic NOUN iajs-200 102 8 2015 2015 NUM iajs-200 102 9 ) ) PUNCT iajs-200 102 10 عام عام ADP iajs-200 102 11 1(العدد 1(العدد NUM iajs-200 102 12 28المجلد 28المجلد NUM iajs-200 102 13 مجلة مجلة PROPN iajs-200 102 14 إبن إبن VERB iajs-200 102 15 الھيثم الھيثم NOUN iajs-200 102 16 للعلوم للعلوم NOUN iajs-200 102 17 الصرفة الصرفة NOUN iajs-200 103 1 و و PRON iajs-200 103 2 التطبيقية التطبيقية ADJ iajs-200 103 3 ibn ibn PROPN iajs-200 103 4 al al PROPN iajs-200 103 5 - - PUNCT iajs-200 103 6 haitham haitham PROPN iajs-200 103 7 j. j. PROPN iajs-200 103 8 for for ADP iajs-200 103 9 pure pure PROPN iajs-200 103 10 & & CCONJ iajs-200 103 11 appl appl PROPN iajs-200 103 12 . . PUNCT iajs-200 104 1 sci sci PROPN iajs-200 104 2 . . PUNCT iajs-200 104 3 vol vol NOUN iajs-200 104 4 . . PROPN iajs-200 105 1 28 28 NUM iajs-200 105 2 ( ( PUNCT iajs-200 105 3 1 1 NUM iajs-200 105 4 ) ) PUNCT iajs-200 105 5 2015 2015 NUM iajs-200 105 6 and and CCONJ iajs-200 105 7 by by ADP iajs-200 105 8 our our PRON iajs-200 105 9 assumption assumption NOUN iajs-200 105 10 n1 n1 PROPN iajs-200 105 11 ∩ ∩ NOUN iajs-200 105 12 p p NOUN iajs-200 105 13 is be AUX iajs-200 105 14 a a DET iajs-200 105 15 prime prime ADJ iajs-200 105 16 submodule submodule NOUN iajs-200 105 17 of of ADP iajs-200 105 18 m m PROPN iajs-200 105 19 , , PUNCT iajs-200 105 20 then then ADV iajs-200 105 21 n1 n1 PROPN iajs-200 105 22 ∩ ∩ NOUN iajs-200 105 23 p p X iajs-200 105 24 = = X iajs-200 105 25 ( ( PUNCT iajs-200 105 26 0 0 NUM iajs-200 105 27 ) ) PUNCT iajs-200 105 28 . . PUNCT iajs-200 106 1 but but CCONJ iajs-200 106 2 n1 n1 PROPN iajs-200 106 3 ≤sem ≤sem PROPN iajs-200 106 4 m m PROPN iajs-200 106 5 , , PUNCT iajs-200 106 6 therefore therefore ADV iajs-200 106 7 p p NOUN iajs-200 106 8 = = PUNCT iajs-200 106 9 ( ( PUNCT iajs-200 106 10 0 0 NUM iajs-200 106 11 ) ) PUNCT iajs-200 106 12 , , PUNCT iajs-200 106 13 hence hence ADV iajs-200 106 14 n1 n1 ADJ iajs-200 106 15 ∩ ∩ ADJ iajs-200 106 16 n2 n2 NOUN iajs-200 106 17 ≤sem ≤sem PROPN iajs-200 106 18 m. m. NOUN iajs-200 106 19 note note VERB iajs-200 106 20 that that SCONJ iajs-200 106 21 the the DET iajs-200 106 22 condition condition NOUN iajs-200 106 23 " " PUNCT iajs-200 106 24 all all DET iajs-200 106 25 prime prime ADJ iajs-200 106 26 submodules submodule NOUN iajs-200 106 27 of of ADP iajs-200 106 28 n1 n1 NOUN iajs-200 106 29 are be AUX iajs-200 106 30 prime prime ADJ iajs-200 106 31 submodules submodule NOUN iajs-200 106 32 of of ADP iajs-200 106 33 m m NOUN iajs-200 106 34 " " PUNCT iajs-200 106 35 which which PRON iajs-200 106 36 we we PRON iajs-200 106 37 used use VERB iajs-200 106 38 in in ADP iajs-200 106 39 prop prop NOUN iajs-200 106 40 ( ( PUNCT iajs-200 106 41 2.8 2.8 NUM iajs-200 106 42 ) ) PUNCT iajs-200 106 43 can can AUX iajs-200 106 44 be be AUX iajs-200 106 45 applied apply VERB iajs-200 106 46 also also ADV iajs-200 106 47 for for ADP iajs-200 106 48 n2 n2 ADJ iajs-200 106 49 . . PUNCT iajs-200 107 1 proposition proposition NOUN iajs-200 107 2 ( ( PUNCT iajs-200 107 3 2.9 2.9 NUM iajs-200 107 4 ): ): PUNCT iajs-200 107 5 let let VERB iajs-200 107 6 m m PRON iajs-200 107 7 be be AUX iajs-200 107 8 an an DET iajs-200 107 9 r r NOUN iajs-200 107 10 - - PUNCT iajs-200 107 11 module module NOUN iajs-200 107 12 , , PUNCT iajs-200 107 13 and and CCONJ iajs-200 107 14 let let VERB iajs-200 107 15 n1 n1 NOUN iajs-200 107 16 and and CCONJ iajs-200 107 17 n2 n2 NOUN iajs-200 107 18 are be AUX iajs-200 107 19 semi semi ADJ iajs-200 107 20 - - ADJ iajs-200 107 21 essential essential ADJ iajs-200 107 22 submodules submodule NOUN iajs-200 107 23 of of ADP iajs-200 107 24 m m NOUN iajs-200 107 25 such such ADJ iajs-200 107 26 that that DET iajs-200 107 27 n2 n2 ADJ iajs-200 107 28 ∩ ∩ NOUN iajs-200 107 29 p p NOUN iajs-200 107 30 is be AUX iajs-200 107 31 a a DET iajs-200 107 32 prime prime ADJ iajs-200 107 33 submodules submodule NOUN iajs-200 107 34 of of ADP iajs-200 107 35 m m PRON iajs-200 107 36 for for ADP iajs-200 107 37 all all DET iajs-200 107 38 prime prime ADJ iajs-200 107 39 submodule submodule PROPN iajs-200 107 40 p p PROPN iajs-200 107 41 of of ADP iajs-200 107 42 m m PROPN iajs-200 107 43 , , PUNCT iajs-200 107 44 then then ADV iajs-200 107 45 n1 n1 PROPN iajs-200 107 46 ∩ ∩ ADJ iajs-200 107 47 n2 n2 NOUN iajs-200 107 48 ≤sem ≤sem PROPN iajs-200 107 49 m. m. NOUN iajs-200 107 50 proof proof NOUN iajs-200 107 51 : : PUNCT iajs-200 107 52 let let VERB iajs-200 107 53 p p PRON iajs-200 107 54 be be AUX iajs-200 107 55 a a DET iajs-200 107 56 prime prime ADJ iajs-200 107 57 submodule submodule NOUN iajs-200 107 58 of of ADP iajs-200 107 59 m m PRON iajs-200 108 1 such such ADJ iajs-200 108 2 that that SCONJ iajs-200 108 3 ( ( PUNCT iajs-200 108 4 n1 n1 PROPN iajs-200 108 5 ∩ ∩ ADJ iajs-200 108 6 n2 n2 ADJ iajs-200 108 7 ) ) PUNCT iajs-200 108 8 ∩ ∩ NOUN iajs-200 108 9 p p X iajs-200 108 10 = = X iajs-200 108 11 ( ( PUNCT iajs-200 108 12 0 0 NUM iajs-200 108 13 ) ) PUNCT iajs-200 108 14 . . PUNCT iajs-200 109 1 this this PRON iajs-200 109 2 implies imply VERB iajs-200 109 3 that that SCONJ iajs-200 109 4 n1 n1 PROPN iajs-200 109 5 ∩ ∩ NOUN iajs-200 109 6 ( ( PUNCT iajs-200 109 7 n2 n2 ADJ iajs-200 109 8 ∩ ∩ NOUN iajs-200 109 9 p p X iajs-200 109 10 ) ) PUNCT iajs-200 109 11 = = SYM iajs-200 109 12 ( ( PUNCT iajs-200 109 13 0 0 NUM iajs-200 109 14 ) ) PUNCT iajs-200 109 15 . . PUNCT iajs-200 110 1 but but CCONJ iajs-200 110 2 n2 n2 PROPN iajs-200 110 3 ∩ ∩ NOUN iajs-200 110 4 p p NOUN iajs-200 110 5 is be AUX iajs-200 110 6 a a DET iajs-200 110 7 prime prime ADJ iajs-200 110 8 submodule submodule NOUN iajs-200 110 9 of of ADP iajs-200 110 10 m m PROPN iajs-200 110 11 and and CCONJ iajs-200 110 12 since since SCONJ iajs-200 110 13 n1 n1 PROPN iajs-200 110 14 ≤sem ≤sem PROPN iajs-200 110 15 m m PROPN iajs-200 110 16 , , PUNCT iajs-200 110 17 then then ADV iajs-200 110 18 n2 n2 ADJ iajs-200 110 19 ∩ ∩ NOUN iajs-200 110 20 p p X iajs-200 110 21 = = X iajs-200 110 22 ( ( PUNCT iajs-200 110 23 0 0 NUM iajs-200 110 24 ) ) PUNCT iajs-200 110 25 . . PUNCT iajs-200 111 1 moreover moreover ADV iajs-200 111 2 , , PUNCT iajs-200 111 3 since since SCONJ iajs-200 111 4 n2 n2 PROPN iajs-200 111 5 ≤sem ≤sem PROPN iajs-200 111 6 m m PROPN iajs-200 111 7 , , PUNCT iajs-200 111 8 thus thus ADV iajs-200 111 9 p p X iajs-200 111 10 = = SYM iajs-200 111 11 ( ( PUNCT iajs-200 111 12 0 0 NUM iajs-200 111 13 ) ) PUNCT iajs-200 111 14 , , PUNCT iajs-200 111 15 and and CCONJ iajs-200 111 16 hence hence ADV iajs-200 111 17 n1 n1 ADJ iajs-200 111 18 ∩ ∩ ADJ iajs-200 111 19 n2 n2 NOUN iajs-200 111 20 ≤sem ≤sem PROPN iajs-200 111 21 m. m. NOUN iajs-200 111 22 recall recall VERB iajs-200 111 23 that that SCONJ iajs-200 111 24 , , PUNCT iajs-200 111 25 an an DET iajs-200 111 26 r r NOUN iajs-200 111 27 - - PUNCT iajs-200 111 28 module module NOUN iajs-200 111 29 m m NOUN iajs-200 111 30 is be AUX iajs-200 111 31 called call VERB iajs-200 111 32 multiplication multiplication NOUN iajs-200 111 33 , , PUNCT iajs-200 111 34 if if SCONJ iajs-200 111 35 for for ADP iajs-200 111 36 each each DET iajs-200 111 37 submodule submodule NOUN iajs-200 111 38 n n PROPN iajs-200 111 39 of of ADP iajs-200 111 40 m m PRON iajs-200 111 41 , , PUNCT iajs-200 111 42 there there PRON iajs-200 111 43 exists exist VERB iajs-200 111 44 an an DET iajs-200 111 45 ideal ideal NOUN iajs-200 111 46 i i PRON iajs-200 111 47 of of ADP iajs-200 111 48 r r NOUN iajs-200 112 1 such such ADJ iajs-200 112 2 that that SCONJ iajs-200 112 3 n n NOUN iajs-200 112 4 = = VERB iajs-200 112 5 i i PRON iajs-200 112 6 m m VERB iajs-200 113 1 [ [ X iajs-200 113 2 4 4 NUM iajs-200 113 3 ] ] PUNCT iajs-200 113 4 . . PUNCT iajs-200 114 1 proposition proposition NOUN iajs-200 114 2 ( ( PUNCT iajs-200 114 3 2.10 2.10 NUM iajs-200 114 4 ): ): PUNCT iajs-200 114 5 let let VERB iajs-200 114 6 m m PRON iajs-200 114 7 be be AUX iajs-200 114 8 a a DET iajs-200 114 9 faithful faithful ADJ iajs-200 114 10 and and CCONJ iajs-200 114 11 multiplication multiplication NOUN iajs-200 114 12 module module NOUN iajs-200 114 13 such such ADJ iajs-200 114 14 that that SCONJ iajs-200 114 15 m m PROPN iajs-200 114 16 satisfies satisfy VERB iajs-200 114 17 the the DET iajs-200 114 18 condition condition NOUN iajs-200 114 19 ( ( PUNCT iajs-200 114 20 * * NOUN iajs-200 114 21 ) ) PUNCT iajs-200 114 22 , , PUNCT iajs-200 114 23 and and CCONJ iajs-200 114 24 let let VERB iajs-200 114 25 i i PRON iajs-200 114 26 , , PUNCT iajs-200 114 27 j j PROPN iajs-200 114 28 be be VERB iajs-200 114 29 ideals ideal NOUN iajs-200 114 30 of of ADP iajs-200 114 31 r. r. PROPN iajs-200 114 32 if if SCONJ iajs-200 114 33 i i PRON iajs-200 114 34 m m VERB iajs-200 114 35 ≤sem ≤sem PROPN iajs-200 114 36 jm jm PROPN iajs-200 114 37 , , PUNCT iajs-200 114 38 then then ADV iajs-200 114 39 i i PRON iajs-200 114 40 ≤sem ≤sem PROPN iajs-200 114 41 j. j. PROPN iajs-200 114 42 condition condition PROPN iajs-200 114 43 ( ( PUNCT iajs-200 114 44 * * PUNCT iajs-200 114 45 ): ): PUNCT iajs-200 114 46 for for ADP iajs-200 114 47 any any DET iajs-200 114 48 two two NUM iajs-200 114 49 ideals ideal NOUN iajs-200 114 50 l l NOUN iajs-200 114 51 and and CCONJ iajs-200 114 52 k k PROPN iajs-200 114 53 of of ADP iajs-200 114 54 r r NOUN iajs-200 114 55 , , PUNCT iajs-200 114 56 if if SCONJ iajs-200 114 57 l l NOUN iajs-200 114 58 is be AUX iajs-200 114 59 a a DET iajs-200 114 60 prime prime ADJ iajs-200 114 61 ideal ideal NOUN iajs-200 114 62 of of ADP iajs-200 114 63 k k NOUN iajs-200 114 64 , , PUNCT iajs-200 114 65 then then ADV iajs-200 114 66 lm lm INTJ iajs-200 114 67 is be AUX iajs-200 114 68 a a DET iajs-200 114 69 prime prime ADJ iajs-200 114 70 submodule submodule NOUN iajs-200 114 71 of of ADP iajs-200 114 72 km km PROPN iajs-200 114 73 . . PUNCT iajs-200 115 1 proof proof NOUN iajs-200 115 2 : : PUNCT iajs-200 115 3 let let VERB iajs-200 115 4 p p PRON iajs-200 115 5 be be AUX iajs-200 115 6 a a DET iajs-200 115 7 prime prime ADJ iajs-200 115 8 ideal ideal NOUN iajs-200 115 9 of of ADP iajs-200 115 10 j j PROPN iajs-200 115 11 such such ADJ iajs-200 115 12 that that SCONJ iajs-200 115 13 i i PRON iajs-200 115 14 ∩ ∩ VERB iajs-200 115 15 p p X iajs-200 115 16 = = X iajs-200 115 17 ( ( PUNCT iajs-200 115 18 0 0 NUM iajs-200 115 19 ) ) PUNCT iajs-200 115 20 , , PUNCT iajs-200 115 21 then then ADV iajs-200 115 22 ( ( PUNCT iajs-200 115 23 i i NOUN iajs-200 115 24 ∩ ∩ X iajs-200 115 25 p)m p)m PUNCT iajs-200 115 26 = = SYM iajs-200 115 27 ( ( PUNCT iajs-200 115 28 0)m 0)m NOUN iajs-200 115 29 . . PUNCT iajs-200 116 1 since since SCONJ iajs-200 116 2 m m PROPN iajs-200 116 3 is be AUX iajs-200 116 4 a a DET iajs-200 116 5 faithful faithful ADJ iajs-200 116 6 and and CCONJ iajs-200 116 7 multiplication multiplication NOUN iajs-200 116 8 , , PUNCT iajs-200 116 9 therefore therefore ADV iajs-200 116 10 i i PRON iajs-200 116 11 m m VERB iajs-200 116 12 ∩ ∩ ADJ iajs-200 116 13 pm pm NOUN iajs-200 116 14 = = SYM iajs-200 116 15 ( ( PUNCT iajs-200 116 16 0 0 NUM iajs-200 116 17 ) ) PUNCT iajs-200 117 1 [ [ X iajs-200 117 2 6 6 NUM iajs-200 117 3 , , PUNCT iajs-200 117 4 th th X iajs-200 117 5 ( ( PUNCT iajs-200 117 6 1.7 1.7 NUM iajs-200 117 7 ) ) PUNCT iajs-200 117 8 ] ] PUNCT iajs-200 117 9 . . PUNCT iajs-200 118 1 by by ADP iajs-200 118 2 condition condition NOUN iajs-200 118 3 ( ( PUNCT iajs-200 118 4 * * NOUN iajs-200 118 5 ) ) PUNCT iajs-200 118 6 , , PUNCT iajs-200 118 7 pm pm NOUN iajs-200 118 8 is be AUX iajs-200 118 9 a a DET iajs-200 118 10 prime prime ADJ iajs-200 118 11 submodule submodule NOUN iajs-200 118 12 of of ADP iajs-200 118 13 jm jm PROPN iajs-200 118 14 . . PROPN iajs-200 119 1 but but CCONJ iajs-200 119 2 i i PRON iajs-200 119 3 m m VERB iajs-200 119 4 ≤sem ≤sem PROPN iajs-200 120 1 jm jm PROPN iajs-200 120 2 , , PUNCT iajs-200 120 3 then then ADV iajs-200 120 4 pm pm VERB iajs-200 120 5 = = SYM iajs-200 120 6 ( ( PUNCT iajs-200 120 7 0 0 NUM iajs-200 120 8 ) ) PUNCT iajs-200 120 9 . . PUNCT iajs-200 121 1 since since SCONJ iajs-200 121 2 m m PROPN iajs-200 121 3 is be AUX iajs-200 121 4 a a DET iajs-200 121 5 faithful faithful ADJ iajs-200 121 6 module module NOUN iajs-200 121 7 so so SCONJ iajs-200 121 8 p p NOUN iajs-200 121 9 = = X iajs-200 121 10 ( ( PUNCT iajs-200 121 11 0 0 NUM iajs-200 121 12 ) ) PUNCT iajs-200 121 13 , , PUNCT iajs-200 121 14 thus thus ADV iajs-200 121 15 i i PRON iajs-200 121 16 ≤sem ≤sem PROPN iajs-200 121 17 j. j. PROPN iajs-200 122 1 the the DET iajs-200 122 2 converse converse PROPN iajs-200 122 3 of of ADP iajs-200 122 4 prop prop NOUN iajs-200 122 5 ( ( PUNCT iajs-200 122 6 2.10 2.10 NUM iajs-200 122 7 ) ) PUNCT iajs-200 122 8 is be AUX iajs-200 122 9 true true ADJ iajs-200 122 10 without without ADP iajs-200 122 11 using use VERB iajs-200 122 12 the the DET iajs-200 122 13 condition condition NOUN iajs-200 122 14 ( ( PUNCT iajs-200 122 15 * * NOUN iajs-200 122 16 ) ) PUNCT iajs-200 122 17 , , PUNCT iajs-200 122 18 but but CCONJ iajs-200 122 19 we we PRON iajs-200 122 20 need need VERB iajs-200 122 21 other other ADJ iajs-200 122 22 condition condition NOUN iajs-200 122 23 as as ADP iajs-200 122 24 the the DET iajs-200 122 25 following follow VERB iajs-200 122 26 proposition proposition NOUN iajs-200 122 27 shows show NOUN iajs-200 122 28 . . PUNCT iajs-200 123 1 proposition proposition NOUN iajs-200 123 2 ( ( PUNCT iajs-200 123 3 2.11 2.11 NUM iajs-200 123 4 ): ): PUNCT iajs-200 123 5 let let VERB iajs-200 123 6 m m PRON iajs-200 123 7 be be AUX iajs-200 123 8 a a DET iajs-200 123 9 finitely finitely ADV iajs-200 123 10 generated generate VERB iajs-200 123 11 , , PUNCT iajs-200 123 12 faithful faithful ADJ iajs-200 123 13 and and CCONJ iajs-200 123 14 multiplication multiplication NOUN iajs-200 123 15 r r NOUN iajs-200 123 16 - - NOUN iajs-200 123 17 module module NOUN iajs-200 123 18 . . PUNCT iajs-200 124 1 if if SCONJ iajs-200 124 2 i i PRON iajs-200 124 3 ≤sem ≤sem PROPN iajs-200 125 1 j j PROPN iajs-200 125 2 then then ADV iajs-200 125 3 i i PRON iajs-200 125 4 m m VERB iajs-200 125 5 ≤sem ≤sem PROPN iajs-200 125 6 jm jm PROPN iajs-200 125 7 for for ADP iajs-200 125 8 every every DET iajs-200 125 9 ideals ideal NOUN iajs-200 126 1 i i PRON iajs-200 126 2 and and CCONJ iajs-200 126 3 j j PROPN iajs-200 126 4 of of ADP iajs-200 126 5 r. r. PROPN iajs-200 126 6 proof proof PROPN iajs-200 126 7 : : PUNCT iajs-200 126 8 let let VERB iajs-200 126 9 p p PRON iajs-200 126 10 be be AUX iajs-200 126 11 a a DET iajs-200 126 12 prime prime ADJ iajs-200 126 13 submodule submodule NOUN iajs-200 126 14 of of ADP iajs-200 126 15 jm jm PROPN iajs-200 126 16 such such ADJ iajs-200 126 17 that that SCONJ iajs-200 127 1 i i PRON iajs-200 127 2 m m VERB iajs-200 127 3 ∩ ∩ ADJ iajs-200 127 4 p p X iajs-200 127 5 = = X iajs-200 127 6 ( ( PUNCT iajs-200 127 7 0 0 NUM iajs-200 127 8 ) ) PUNCT iajs-200 127 9 . . PUNCT iajs-200 128 1 since since SCONJ iajs-200 128 2 m m PROPN iajs-200 128 3 is be AUX iajs-200 128 4 a a DET iajs-200 128 5 multiplication multiplication NOUN iajs-200 128 6 module module NOUN iajs-200 128 7 , , PUNCT iajs-200 128 8 then then ADV iajs-200 128 9 p p NOUN iajs-200 128 10 = = PUNCT iajs-200 128 11 em em PRON iajs-200 128 12 for for ADP iajs-200 128 13 some some DET iajs-200 128 14 prime prime ADJ iajs-200 128 15 ideal ideal NOUN iajs-200 128 16 e e PROPN iajs-200 128 17 of of ADP iajs-200 128 18 r r NOUN iajs-200 128 19 [ [ X iajs-200 128 20 6 6 NUM iajs-200 128 21 , , PUNCT iajs-200 128 22 cor cor X iajs-200 128 23 ( ( PUNCT iajs-200 128 24 2.11 2.11 NUM iajs-200 128 25 ) ) PUNCT iajs-200 128 26 ] ] PUNCT iajs-200 128 27 . . PUNCT iajs-200 129 1 so so ADV iajs-200 129 2 i i PRON iajs-200 129 3 m m VERB iajs-200 129 4 ∩ ∩ VERB iajs-200 129 5 em em PRON iajs-200 129 6 = = SYM iajs-200 129 7 ( ( PUNCT iajs-200 129 8 0 0 NUM iajs-200 129 9 ) ) PUNCT iajs-200 129 10 , , PUNCT iajs-200 129 11 this this PRON iajs-200 129 12 implies imply VERB iajs-200 129 13 that that SCONJ iajs-200 129 14 ( ( PUNCT iajs-200 129 15 i i PRON iajs-200 129 16 ∩ ∩ X iajs-200 129 17 e e NOUN iajs-200 129 18 ) ) PUNCT iajs-200 129 19 m m VERB iajs-200 129 20 = = SYM iajs-200 129 21 ( ( PUNCT iajs-200 129 22 0 0 NUM iajs-200 129 23 ) ) PUNCT iajs-200 129 24 . . PUNCT iajs-200 130 1 since since SCONJ iajs-200 130 2 m m PROPN iajs-200 130 3 is be AUX iajs-200 130 4 a a DET iajs-200 130 5 faithful faithful ADJ iajs-200 130 6 module module NOUN iajs-200 130 7 , , PUNCT iajs-200 130 8 then then ADV iajs-200 130 9 i i PRON iajs-200 130 10 ∩ ∩ NOUN iajs-200 130 11 e e NOUN iajs-200 130 12 = = SYM iajs-200 130 13 ( ( PUNCT iajs-200 130 14 0 0 NUM iajs-200 130 15 ) ) PUNCT iajs-200 130 16 . . PUNCT iajs-200 131 1 since since SCONJ iajs-200 131 2 em em PRON iajs-200 131 3 jm jm PROPN iajs-200 131 4 and and CCONJ iajs-200 131 5 m m PROPN iajs-200 131 6 is be AUX iajs-200 131 7 a a DET iajs-200 131 8 finitely finitely ADV iajs-200 131 9 generated generate VERB iajs-200 131 10 , , PUNCT iajs-200 131 11 faithful faithful ADJ iajs-200 131 12 and and CCONJ iajs-200 131 13 multiplication multiplication NOUN iajs-200 131 14 module module NOUN iajs-200 131 15 so so ADV iajs-200 131 16 by by ADP iajs-200 131 17 [ [ X iajs-200 131 18 6 6 NUM iajs-200 131 19 , , PUNCT iajs-200 131 20 th th X iajs-200 131 21 ( ( PUNCT iajs-200 131 22 3.1 3.1 NUM iajs-200 131 23 ) ) PUNCT iajs-200 131 24 ] ] PUNCT iajs-200 132 1 e e X iajs-200 132 2 j. j. PROPN iajs-200 132 3 but but CCONJ iajs-200 132 4 e e PROPN iajs-200 132 5 is be AUX iajs-200 132 6 a a DET iajs-200 132 7 prime prime ADJ iajs-200 132 8 ideal ideal NOUN iajs-200 132 9 of of ADP iajs-200 132 10 r r NOUN iajs-200 132 11 , , PUNCT iajs-200 132 12 then then ADV iajs-200 132 13 e e PROPN iajs-200 132 14 is be AUX iajs-200 132 15 a a DET iajs-200 132 16 prime prime ADJ iajs-200 132 17 ideal ideal NOUN iajs-200 132 18 of of ADP iajs-200 132 19 j j PROPN iajs-200 133 1 [ [ X iajs-200 133 2 8 8 NUM iajs-200 133 3 , , PUNCT iajs-200 133 4 lemma lemma PROPN iajs-200 133 5 3.7 3.7 NUM iajs-200 133 6 ] ] PUNCT iajs-200 133 7 . . PUNCT iajs-200 134 1 since since SCONJ iajs-200 134 2 i i PRON iajs-200 134 3 is be AUX iajs-200 134 4 a a DET iajs-200 134 5 semi semi ADJ iajs-200 134 6 - - ADJ iajs-200 134 7 essential essential ADJ iajs-200 134 8 ideal ideal NOUN iajs-200 134 9 of of ADP iajs-200 134 10 j j PROPN iajs-200 134 11 , , PUNCT iajs-200 134 12 then then ADV iajs-200 134 13 e e PROPN iajs-200 134 14 = = PUNCT iajs-200 134 15 ( ( PUNCT iajs-200 134 16 0 0 NUM iajs-200 134 17 ) ) PUNCT iajs-200 134 18 , , PUNCT iajs-200 134 19 and and CCONJ iajs-200 134 20 hence hence ADV iajs-200 134 21 p p NOUN iajs-200 134 22 = = X iajs-200 134 23 ( ( PUNCT iajs-200 134 24 0 0 NUM iajs-200 134 25 ) ) PUNCT iajs-200 134 26 . . PUNCT iajs-200 135 1 that that PRON iajs-200 135 2 is be AUX iajs-200 135 3 i i PRON iajs-200 135 4 m m PROPN iajs-200 135 5 ≤sem ≤sem PROPN iajs-200 135 6 jm jm PROPN iajs-200 135 7 . . PROPN iajs-200 135 8 from from ADP iajs-200 135 9 prop prop NOUN iajs-200 135 10 ( ( PUNCT iajs-200 135 11 2.10 2.10 NUM iajs-200 135 12 ) ) PUNCT iajs-200 135 13 and and CCONJ iajs-200 135 14 prop prop NOUN iajs-200 135 15 ( ( PUNCT iajs-200 135 16 2.11 2.11 NUM iajs-200 135 17 ) ) PUNCT iajs-200 135 18 we we PRON iajs-200 135 19 have have VERB iajs-200 135 20 the the DET iajs-200 135 21 following follow VERB iajs-200 135 22 theorem theorem PROPN iajs-200 135 23 . . PUNCT iajs-200 136 1 theorem theorem PROPN iajs-200 136 2 ( ( PUNCT iajs-200 136 3 2.12 2.12 NUM iajs-200 136 4 ): ): PUNCT iajs-200 136 5 let let VERB iajs-200 136 6 m m PRON iajs-200 136 7 be be AUX iajs-200 136 8 a a DET iajs-200 136 9 finitely finitely ADV iajs-200 136 10 generated generate VERB iajs-200 136 11 , , PUNCT iajs-200 136 12 faithful faithful ADJ iajs-200 136 13 and and CCONJ iajs-200 136 14 multiplication multiplication NOUN iajs-200 136 15 module module NOUN iajs-200 136 16 such such ADJ iajs-200 136 17 that that SCONJ iajs-200 136 18 m m PROPN iajs-200 136 19 satisfies satisfy VERB iajs-200 136 20 the the DET iajs-200 136 21 condition condition NOUN iajs-200 136 22 ( ( PUNCT iajs-200 136 23 * * NOUN iajs-200 136 24 ) ) PUNCT iajs-200 136 25 . . PUNCT iajs-200 137 1 then then ADV iajs-200 137 2 i i PRON iajs-200 137 3 ≤sem ≤sem PROPN iajs-200 138 1 j j PROPN iajs-200 138 2 if if SCONJ iajs-200 138 3 and and CCONJ iajs-200 138 4 only only ADV iajs-200 138 5 if if SCONJ iajs-200 138 6 i i PRON iajs-200 138 7 m m VERB iajs-200 138 8 ≤sem ≤sem PROPN iajs-200 138 9 jm jm PROPN iajs-200 138 10 for for ADP iajs-200 138 11 every every DET iajs-200 138 12 two two NUM iajs-200 138 13 ideals ideal NOUN iajs-200 138 14 i i PRON iajs-200 138 15 and and CCONJ iajs-200 138 16 j j PROPN iajs-200 138 17 of of ADP iajs-200 138 18 r. r. PROPN iajs-200 138 19 it it PRON iajs-200 138 20 is be AUX iajs-200 138 21 well well ADV iajs-200 138 22 known know VERB iajs-200 138 23 that that SCONJ iajs-200 138 24 if if SCONJ iajs-200 138 25 a a DET iajs-200 138 26 ring ring NOUN iajs-200 138 27 r r NOUN iajs-200 138 28 has have VERB iajs-200 138 29 only only ADV iajs-200 138 30 one one NUM iajs-200 138 31 maximal maximal ADJ iajs-200 138 32 ideal ideal NOUN iajs-200 139 1 i i PRON iajs-200 139 2 , , PUNCT iajs-200 139 3 then then ADV iajs-200 139 4 i i PRON iajs-200 139 5 is be AUX iajs-200 139 6 an an DET iajs-200 139 7 essential essential ADJ iajs-200 139 8 ideal ideal NOUN iajs-200 139 9 of of ADP iajs-200 139 10 r r NOUN iajs-200 139 11 if if SCONJ iajs-200 140 1 and and CCONJ iajs-200 140 2 only only ADV iajs-200 140 3 if if SCONJ iajs-200 140 4 i i PRON iajs-200 140 5 ≠ ≠ PROPN iajs-200 140 6 ( ( PUNCT iajs-200 140 7 0 0 NUM iajs-200 140 8 ) ) PUNCT iajs-200 140 9 . . PUNCT iajs-200 141 1 in in ADP iajs-200 141 2 the the DET iajs-200 141 3 following follow VERB iajs-200 141 4 proposition proposition NOUN iajs-200 141 5 we we PRON iajs-200 141 6 generalize generalize VERB iajs-200 141 7 this this DET iajs-200 141 8 statement statement NOUN iajs-200 141 9 in in ADP iajs-200 141 10 one one NUM iajs-200 141 11 direction direction NOUN iajs-200 141 12 to to ADP iajs-200 141 13 essential essential ADJ iajs-200 141 14 ( ( PUNCT iajs-200 141 15 hence hence ADV iajs-200 141 16 semi semi ADJ iajs-200 141 17 - - ADJ iajs-200 141 18 essential essential ADJ iajs-200 141 19 ) ) PUNCT iajs-200 141 20 submodules submodule NOUN iajs-200 141 21 . . PUNCT iajs-200 142 1 proposition proposition NOUN iajs-200 142 2 ( ( PUNCT iajs-200 142 3 2.13 2.13 NUM iajs-200 142 4 ): ): PUNCT iajs-200 142 5 let let VERB iajs-200 142 6 m m PRON iajs-200 142 7 be be AUX iajs-200 142 8 a a DET iajs-200 142 9 nonzero nonzero ADJ iajs-200 142 10 multiplication multiplication NOUN iajs-200 142 11 r r NOUN iajs-200 142 12 - - PUNCT iajs-200 142 13 module module NOUN iajs-200 142 14 with with ADP iajs-200 142 15 only only ADV iajs-200 142 16 one one NUM iajs-200 142 17 maximal maximal ADJ iajs-200 142 18 submodule submodule NOUN iajs-200 142 19 n n CCONJ iajs-200 142 20 , , PUNCT iajs-200 142 21 if if SCONJ iajs-200 142 22 n n PRON iajs-200 142 23 ≠ ≠ PROPN iajs-200 142 24 ( ( PUNCT iajs-200 142 25 0 0 NUM iajs-200 142 26 ) ) PUNCT iajs-200 142 27 . . PUNCT iajs-200 143 1 then then ADV iajs-200 143 2 n n PRON iajs-200 143 3 is be AUX iajs-200 143 4 an an DET iajs-200 143 5 essential essential ADJ iajs-200 143 6 ( ( PUNCT iajs-200 143 7 hence hence ADV iajs-200 143 8 semi semi ADJ iajs-200 143 9 - - ADJ iajs-200 143 10 essential essential ADJ iajs-200 143 11 ) ) PUNCT iajs-200 143 12 submodule submodule NOUN iajs-200 143 13 of of ADP iajs-200 143 14 m. m. NOUN iajs-200 143 15 proof proof NOUN iajs-200 143 16 : : PUNCT iajs-200 143 17 let let VERB iajs-200 143 18 p p PRON iajs-200 143 19 be be AUX iajs-200 143 20 a a DET iajs-200 143 21 submodule submodule NOUN iajs-200 143 22 of of ADP iajs-200 143 23 m m PROPN iajs-200 143 24 with with ADP iajs-200 143 25 p p PROPN iajs-200 143 26 ⋂ ⋂ PROPN iajs-200 143 27 n n X iajs-200 143 28 = = SYM iajs-200 143 29 ( ( PUNCT iajs-200 143 30 0 0 NUM iajs-200 143 31 ) ) PUNCT iajs-200 143 32 . . PUNCT iajs-200 144 1 if if SCONJ iajs-200 144 2 p p NOUN iajs-200 144 3 = = NOUN iajs-200 144 4 m m PROPN iajs-200 144 5 , , PUNCT iajs-200 144 6 then then ADV iajs-200 144 7 m m VERB iajs-200 144 8 ⋂ ⋂ PROPN iajs-200 144 9 n n NOUN iajs-200 144 10 = = SYM iajs-200 144 11 ( ( PUNCT iajs-200 144 12 0 0 NUM iajs-200 144 13 ) ) PUNCT iajs-200 144 14 , , PUNCT iajs-200 144 15 hence hence ADV iajs-200 144 16 n n NOUN iajs-200 144 17 = = SYM iajs-200 144 18 ( ( PUNCT iajs-200 144 19 0 0 NUM iajs-200 144 20 ) ) PUNCT iajs-200 144 21 which which PRON iajs-200 144 22 is be AUX iajs-200 144 23 a a DET iajs-200 144 24 contradiction contradiction NOUN iajs-200 144 25 . . PUNCT iajs-200 145 1 thus thus ADV iajs-200 145 2 p p X iajs-200 145 3 is be AUX iajs-200 145 4 a a DET iajs-200 145 5 proper proper ADJ iajs-200 145 6 submodule submodule NOUN iajs-200 145 7 of of ADP iajs-200 145 8 m m PROPN iajs-200 145 9 , , PUNCT iajs-200 145 10 and and CCONJ iajs-200 145 11 since since SCONJ iajs-200 145 12 m m PROPN iajs-200 145 13 is be AUX iajs-200 145 14 a a DET iajs-200 145 15 nonzero nonzero ADJ iajs-200 145 16 multiplication multiplication NOUN iajs-200 145 17 module module NOUN iajs-200 145 18 , , PUNCT iajs-200 145 19 so so ADV iajs-200 145 20 by by ADP iajs-200 145 21 [ [ X iajs-200 145 22 6 6 NUM iajs-200 145 23 , , PUNCT iajs-200 145 24 th th X iajs-200 145 25 ( ( PUNCT iajs-200 145 26 2.5 2.5 NUM iajs-200 145 27 ) ) PUNCT iajs-200 145 28 ] ] PUNCT iajs-200 145 29 , , PUNCT iajs-200 145 30 p p PRON iajs-200 145 31 contained contain VERB iajs-200 145 32 in in ADP iajs-200 145 33 some some DET iajs-200 145 34 maximal maximal ADJ iajs-200 145 35 submodule submodule NOUN iajs-200 145 36 of of ADP iajs-200 145 37 m. m. NOUN iajs-200 145 38 but but CCONJ iajs-200 145 39 m m PRON iajs-200 145 40 has have VERB iajs-200 145 41 only only ADV iajs-200 145 42 one one NUM iajs-200 145 43 maximal maximal ADJ iajs-200 145 44 submodule submodule NOUN iajs-200 145 45 which which PRON iajs-200 145 46 is be AUX iajs-200 145 47 n. n. NOUN iajs-200 145 48 thus thus ADV iajs-200 145 49 p p ADJ iajs-200 145 50 ⊆ ⊆ NUM iajs-200 145 51 n n CCONJ iajs-200 145 52 , , PUNCT iajs-200 145 53 this this PRON iajs-200 145 54 implies imply VERB iajs-200 145 55 that that SCONJ iajs-200 145 56 p p X iajs-200 145 57 = = X iajs-200 145 58 ( ( PUNCT iajs-200 145 59 0 0 NUM iajs-200 145 60 ) ) PUNCT iajs-200 145 61 , , PUNCT iajs-200 145 62 that that PRON iajs-200 145 63 is be AUX iajs-200 145 64 n n PRON iajs-200 145 65 is be AUX iajs-200 145 66 an an DET iajs-200 145 67 essential essential ADJ iajs-200 145 68 ( ( PUNCT iajs-200 145 69 hence hence ADV iajs-200 145 70 semi semi ADJ iajs-200 145 71 - - ADJ iajs-200 145 72 essential essential ADJ iajs-200 145 73 ) ) PUNCT iajs-200 145 74 submodule submodule NOUN iajs-200 145 75 of of ADP iajs-200 145 76 m. m. NOUN iajs-200 145 77 proposition proposition NOUN iajs-200 145 78 ( ( PUNCT iajs-200 145 79 2.14 2.14 NUM iajs-200 145 80 ): ): PUNCT iajs-200 145 81 let let VERB iajs-200 145 82 m m PRON iajs-200 145 83 be be AUX iajs-200 145 84 a a DET iajs-200 145 85 finitely finitely ADV iajs-200 145 86 generated generate VERB iajs-200 145 87 r r NOUN iajs-200 145 88 - - PUNCT iajs-200 145 89 module module NOUN iajs-200 145 90 with with ADP iajs-200 145 91 only only ADV iajs-200 145 92 one one NUM iajs-200 145 93 nonzero nonzero NOUN iajs-200 145 94 maximal maximal ADJ iajs-200 145 95 submodule submodule NOUN iajs-200 145 96 n n CCONJ iajs-200 145 97 , , PUNCT iajs-200 145 98 then then ADV iajs-200 145 99 n n PRON iajs-200 145 100 is be AUX iajs-200 145 101 an an DET iajs-200 145 102 essential essential ADJ iajs-200 145 103 ( ( PUNCT iajs-200 145 104 hence hence ADV iajs-200 145 105 semi semi ADJ iajs-200 145 106 - - ADJ iajs-200 145 107 essential essential ADJ iajs-200 145 108 ) ) PUNCT iajs-200 145 109 submodule submodule NOUN iajs-200 145 110 of of ADP iajs-200 145 111 m. m. NOUN iajs-200 145 112 proof proof NOUN iajs-200 145 113 : : PUNCT iajs-200 145 114 in in ADP iajs-200 145 115 similar similar ADJ iajs-200 145 116 way way NOUN iajs-200 145 117 , , PUNCT iajs-200 145 118 and and CCONJ iajs-200 145 119 by by ADP iajs-200 145 120 using use VERB iajs-200 145 121 [ [ X iajs-200 145 122 13 13 NUM iajs-200 145 123 , , PUNCT iajs-200 145 124 prop prop NOUN iajs-200 145 125 ( ( PUNCT iajs-200 145 126 1.6 1.6 NUM iajs-200 145 127 ) ) PUNCT iajs-200 145 128 , , PUNCT iajs-200 145 129 p. p. NOUN iajs-200 145 130 7 7 NUM iajs-200 145 131 ] ] PUNCT iajs-200 145 132 instead instead ADV iajs-200 145 133 of of ADP iajs-200 145 134 [ [ X iajs-200 145 135 6 6 NUM iajs-200 145 136 , , PUNCT iajs-200 145 137 th th X iajs-200 145 138 ( ( PUNCT iajs-200 145 139 2.5 2.5 NUM iajs-200 145 140 ) ) PUNCT iajs-200 145 141 ] ] PUNCT iajs-200 145 142 . . PUNCT iajs-200 146 1 we we PRON iajs-200 146 2 end end VERB iajs-200 146 3 this this DET iajs-200 146 4 work work NOUN iajs-200 146 5 by by ADP iajs-200 146 6 the the DET iajs-200 146 7 following follow VERB iajs-200 146 8 theorem theorem NOUN iajs-200 146 9 which which PRON iajs-200 146 10 gives give VERB iajs-200 146 11 the the DET iajs-200 146 12 hereditary hereditary NOUN iajs-200 146 13 of of ADP iajs-200 146 14 fully fully ADV iajs-200 146 15 essential essential ADJ iajs-200 146 16 property property NOUN iajs-200 146 17 between between ADP iajs-200 146 18 r r NOUN iajs-200 146 19 - - PUNCT iajs-200 146 20 module module NOUN iajs-200 146 21 , , PUNCT iajs-200 146 22 m m PROPN iajs-200 146 23 and and CCONJ iajs-200 146 24 the the DET iajs-200 146 25 ring ring PROPN iajs-200 146 26 r. r. PROPN iajs-200 146 27 184 184 NUM iajs-200 147 1 | | ADV iajs-200 147 2 mathematics mathematic NOUN iajs-200 147 3 2015 2015 NUM iajs-200 147 4 ) ) PUNCT iajs-200 147 5 عام عام ADP iajs-200 147 6 1(العدد 1(العدد NUM iajs-200 147 7 28المجلد 28المجلد NUM iajs-200 147 8 مجلة مجلة PROPN iajs-200 147 9 إبن إبن VERB iajs-200 147 10 الھيثم الھيثم NOUN iajs-200 147 11 للعلوم للعلوم NOUN iajs-200 147 12 الصرفة الصرفة NOUN iajs-200 148 1 و و PRON iajs-200 148 2 التطبيقية التطبيقية ADJ iajs-200 148 3 ibn ibn PROPN iajs-200 148 4 al al PROPN iajs-200 148 5 - - PUNCT iajs-200 148 6 haitham haitham PROPN iajs-200 148 7 j. j. PROPN iajs-200 148 8 for for ADP iajs-200 148 9 pure pure PROPN iajs-200 148 10 & & CCONJ iajs-200 148 11 appl appl PROPN iajs-200 148 12 . . PUNCT iajs-200 149 1 sci sci PROPN iajs-200 149 2 . . PUNCT iajs-200 149 3 vol vol NOUN iajs-200 149 4 . . PROPN iajs-200 150 1 28 28 NUM iajs-200 150 2 ( ( PUNCT iajs-200 150 3 1 1 NUM iajs-200 150 4 ) ) PUNCT iajs-200 150 5 2015 2015 NUM iajs-200 150 6 theorem theorem NOUN iajs-200 150 7 ( ( PUNCT iajs-200 150 8 2.15 2.15 NUM iajs-200 150 9 ): ): PUNCT iajs-200 150 10 let let VERB iajs-200 150 11 m m PRON iajs-200 150 12 be be AUX iajs-200 150 13 a a DET iajs-200 150 14 nonzero nonzero ADJ iajs-200 150 15 faithful faithful ADJ iajs-200 150 16 and and CCONJ iajs-200 150 17 multiplication multiplication NOUN iajs-200 150 18 r r NOUN iajs-200 150 19 - - NOUN iajs-200 150 20 module module NOUN iajs-200 150 21 . . PUNCT iajs-200 151 1 then then ADV iajs-200 151 2 m m PROPN iajs-200 151 3 is be AUX iajs-200 151 4 a a DET iajs-200 151 5 fully fully ADV iajs-200 151 6 essential essential ADJ iajs-200 151 7 module module NOUN iajs-200 151 8 if if SCONJ iajs-200 151 9 and and CCONJ iajs-200 151 10 only only ADV iajs-200 151 11 if if SCONJ iajs-200 151 12 r r NOUN iajs-200 151 13 is be AUX iajs-200 151 14 a a DET iajs-200 151 15 fully fully ADV iajs-200 151 16 essential essential ADJ iajs-200 151 17 ring ring NOUN iajs-200 151 18 . . PUNCT iajs-200 152 1 proof proof ADJ iajs-200 152 2 ⇒ ⇒ NOUN iajs-200 152 3 ): ): PUNCT iajs-200 152 4 assume assume VERB iajs-200 152 5 that that SCONJ iajs-200 152 6 m m PROPN iajs-200 152 7 is be AUX iajs-200 152 8 a a DET iajs-200 152 9 fully fully ADV iajs-200 152 10 essential essential ADJ iajs-200 152 11 module module NOUN iajs-200 152 12 , , PUNCT iajs-200 152 13 and and CCONJ iajs-200 152 14 let let VERB iajs-200 152 15 i i PRON iajs-200 152 16 be be AUX iajs-200 152 17 a a DET iajs-200 152 18 nonzero nonzero ADJ iajs-200 152 19 semi semi ADJ iajs-200 152 20 - - ADJ iajs-200 152 21 essential essential ADJ iajs-200 152 22 ideal ideal NOUN iajs-200 152 23 of of ADP iajs-200 152 24 r r NOUN iajs-200 152 25 , , PUNCT iajs-200 152 26 then then ADV iajs-200 152 27 i i PRON iajs-200 152 28 m m VERB iajs-200 152 29 is be AUX iajs-200 152 30 a a DET iajs-200 152 31 submodule submodule NOUN iajs-200 152 32 of of ADP iajs-200 152 33 m m PROPN iajs-200 152 34 say say VERB iajs-200 152 35 n. n. PROPN iajs-200 152 36 this this PRON iajs-200 152 37 implies imply VERB iajs-200 152 38 that that SCONJ iajs-200 152 39 n n X iajs-200 152 40 is be AUX iajs-200 152 41 a a DET iajs-200 152 42 semi semi ADJ iajs-200 152 43 - - ADJ iajs-200 152 44 essential essential ADJ iajs-200 152 45 submodule submodule NOUN iajs-200 152 46 of of ADP iajs-200 152 47 m m PROPN iajs-200 152 48 [ [ X iajs-200 152 49 1 1 NUM iajs-200 152 50 ] ] PUNCT iajs-200 152 51 . . PUNCT iajs-200 153 1 since since SCONJ iajs-200 153 2 i i PRON iajs-200 153 3 ( ( PUNCT iajs-200 153 4 0 0 NUM iajs-200 153 5 ) ) PUNCT iajs-200 153 6 and and CCONJ iajs-200 153 7 m m PROPN iajs-200 153 8 is be AUX iajs-200 153 9 a a DET iajs-200 153 10 faithful faithful ADJ iajs-200 153 11 module module NOUN iajs-200 153 12 , , PUNCT iajs-200 153 13 then then ADV iajs-200 153 14 n n CCONJ iajs-200 153 15 ( ( PUNCT iajs-200 153 16 0 0 NUM iajs-200 153 17 ) ) PUNCT iajs-200 153 18 . . PUNCT iajs-200 154 1 but but CCONJ iajs-200 154 2 m m PROPN iajs-200 154 3 is be AUX iajs-200 154 4 a a DET iajs-200 154 5 fully fully ADV iajs-200 154 6 essential essential ADJ iajs-200 154 7 module module NOUN iajs-200 154 8 , , PUNCT iajs-200 154 9 thus thus ADV iajs-200 154 10 n n PRON iajs-200 154 11 is be AUX iajs-200 154 12 an an DET iajs-200 154 13 essential essential ADJ iajs-200 154 14 submodule submodule NOUN iajs-200 154 15 of of ADP iajs-200 154 16 m. m. NOUN iajs-200 154 17 since since SCONJ iajs-200 154 18 m m PROPN iajs-200 154 19 is be AUX iajs-200 154 20 a a DET iajs-200 154 21 faithful faithful ADJ iajs-200 154 22 and and CCONJ iajs-200 154 23 multiplication multiplication NOUN iajs-200 154 24 module module NOUN iajs-200 154 25 , , PUNCT iajs-200 154 26 therefore therefore ADV iajs-200 154 27 i i PRON iajs-200 154 28 is be AUX iajs-200 154 29 an an DET iajs-200 154 30 essential essential ADJ iajs-200 154 31 ideal ideal NOUN iajs-200 154 32 of of ADP iajs-200 154 33 r r NOUN iajs-200 154 34 [ [ X iajs-200 154 35 6 6 NUM iajs-200 154 36 , , PUNCT iajs-200 154 37 th th X iajs-200 154 38 ( ( PUNCT iajs-200 154 39 2.13 2.13 NUM iajs-200 154 40 ) ) PUNCT iajs-200 154 41 ] ] PUNCT iajs-200 154 42 , , PUNCT iajs-200 154 43 that that PRON iajs-200 154 44 is is ADV iajs-200 154 45 r r NOUN iajs-200 154 46 is be AUX iajs-200 154 47 a a DET iajs-200 154 48 fully fully ADV iajs-200 154 49 essential essential ADJ iajs-200 154 50 ring ring NOUN iajs-200 154 51 . . PUNCT iajs-200 155 1 ⇐ ⇐ ADJ iajs-200 155 2 ): ): PUNCT iajs-200 155 3 suppose suppose VERB iajs-200 155 4 that that SCONJ iajs-200 155 5 r r NOUN iajs-200 155 6 is be AUX iajs-200 155 7 a a DET iajs-200 155 8 fully fully ADV iajs-200 155 9 essential essential ADJ iajs-200 155 10 ring ring NOUN iajs-200 155 11 and and CCONJ iajs-200 155 12 let let VERB iajs-200 155 13 ( ( PUNCT iajs-200 155 14 0 0 NUM iajs-200 155 15 ) ) PUNCT iajs-200 155 16 ≠ ≠ PROPN iajs-200 155 17 n n NUM iajs-200 155 18 ≤sem ≤sem PROPN iajs-200 155 19 m. m. NOUN iajs-200 155 20 since since SCONJ iajs-200 155 21 m m PROPN iajs-200 155 22 is be AUX iajs-200 155 23 a a DET iajs-200 155 24 multiplication multiplication NOUN iajs-200 155 25 module module NOUN iajs-200 155 26 , , PUNCT iajs-200 155 27 then then ADV iajs-200 155 28 n n PROPN iajs-200 155 29 = = SYM iajs-200 155 30 i i PRON iajs-200 155 31 m m VERB iajs-200 155 32 for for ADP iajs-200 155 33 some some DET iajs-200 155 34 semi semi ADJ iajs-200 155 35 - - ADJ iajs-200 155 36 essential essential ADJ iajs-200 155 37 ideal ideal NOUN iajs-200 155 38 i i PRON iajs-200 155 39 of of ADP iajs-200 155 40 r. r. PROPN iajs-200 155 41 by by ADP iajs-200 155 42 assumption assumption NOUN iajs-200 155 43 i i PRON iajs-200 155 44 is be AUX iajs-200 155 45 an an DET iajs-200 155 46 essential essential ADJ iajs-200 155 47 ideal ideal NOUN iajs-200 155 48 of of ADP iajs-200 155 49 r. r. PROPN iajs-200 155 50 but but CCONJ iajs-200 155 51 m m PROPN iajs-200 155 52 is be AUX iajs-200 155 53 a a DET iajs-200 155 54 faithful faithful ADJ iajs-200 155 55 and and CCONJ iajs-200 155 56 multiplication multiplication NOUN iajs-200 155 57 module module NOUN iajs-200 155 58 then then ADV iajs-200 155 59 n n PRON iajs-200 155 60 is be AUX iajs-200 155 61 an an DET iajs-200 155 62 essential essential ADJ iajs-200 155 63 submodule submodule NOUN iajs-200 155 64 of of ADP iajs-200 155 65 m m PROPN iajs-200 156 1 [ [ X iajs-200 156 2 6 6 NUM iajs-200 156 3 , , PUNCT iajs-200 156 4 th th X iajs-200 156 5 ( ( PUNCT iajs-200 156 6 2.13 2.13 NUM iajs-200 156 7 ) ) PUNCT iajs-200 156 8 ] ] PUNCT iajs-200 156 9 . . PUNCT iajs-200 157 1 that that PRON iajs-200 157 2 is be AUX iajs-200 157 3 m m VERB iajs-200 157 4 is be AUX iajs-200 157 5 a a DET iajs-200 157 6 fully fully ADV iajs-200 157 7 essential essential ADJ iajs-200 157 8 module module NOUN iajs-200 157 9 . . PUNCT iajs-200 158 1 references reference NOUN iajs-200 158 2 [ [ X iajs-200 158 3 1 1 NUM iajs-200 158 4 ] ] X iajs-200 158 5 ali ali PROPN iajs-200 158 6 . . PUNCT iajs-200 159 1 s. s. PROPN iajs-200 159 2 mijbass mijbass PROPN iajs-200 159 3 and and CCONJ iajs-200 159 4 nada nada PROPN iajs-200 159 5 . . PUNCT iajs-200 160 1 k. k. PROPN iajs-200 160 2 abdullah abdullah PROPN iajs-200 160 3 , , PUNCT iajs-200 160 4 ( ( PUNCT iajs-200 160 5 2009 2009 NUM iajs-200 160 6 ) ) PUNCT iajs-200 160 7 , , PUNCT iajs-200 160 8 semi semi ADJ iajs-200 160 9 - - ADJ iajs-200 160 10 essential essential ADJ iajs-200 160 11 submodule submodule NOUN iajs-200 160 12 and and CCONJ iajs-200 160 13 semiuniform semiuniform NOUN iajs-200 160 14 modules module NOUN iajs-200 160 15 . . PUNCT iajs-200 161 1 j. j. PROPN iajs-200 161 2 of of ADP iajs-200 161 3 kirkuk kirkuk PROPN iajs-200 161 4 university university PROPN iajs-200 161 5 - - PUNCT iajs-200 161 6 scientific scientific ADJ iajs-200 161 7 studies study NOUN iajs-200 161 8 ; ; PUNCT iajs-200 161 9 4 4 NUM iajs-200 161 10 ( ( PUNCT iajs-200 161 11 1 1 NUM iajs-200 161 12 ) ) PUNCT iajs-200 161 13 , , PUNCT iajs-200 161 14 48 48 NUM iajs-200 161 15 - - SYM iajs-200 161 16 58 58 NUM iajs-200 161 17 . . PUNCT iajs-200 162 1 [ [ X iajs-200 162 2 2 2 NUM iajs-200 162 3 ] ] PUNCT iajs-200 162 4 anderson anderson PROPN iajs-200 162 5 , , PUNCT iajs-200 162 6 f.w f.w PROPN iajs-200 162 7 . . PROPN iajs-200 162 8 and and CCONJ iajs-200 162 9 fuller full ADJ iajs-200 162 10 , , PUNCT iajs-200 162 11 k.r k.r PROPN iajs-200 162 12 , , PUNCT iajs-200 162 13 ( ( PUNCT iajs-200 162 14 1992 1992 NUM iajs-200 162 15 ) ) PUNCT iajs-200 162 16 , , PUNCT iajs-200 162 17 rings ring NOUN iajs-200 162 18 and and CCONJ iajs-200 162 19 categories category NOUN iajs-200 162 20 of of ADP iajs-200 162 21 modules module NOUN iajs-200 162 22 , , PUNCT iajs-200 162 23 springerverlag springerverlag NOUN iajs-200 162 24 , , PUNCT iajs-200 162 25 new new PROPN iajs-200 162 26 york york PROPN iajs-200 162 27 . . PROPN iajs-200 162 28 , , PUNCT iajs-200 162 29 academic academic PROPN iajs-200 162 30 press press PROPN iajs-200 162 31 inc inc PROPN iajs-200 162 32 . . PROPN iajs-200 162 33 london london PROPN iajs-200 162 34 . . PUNCT iajs-200 163 1 [ [ X iajs-200 163 2 3 3 NUM iajs-200 163 3 ] ] SYM iajs-200 163 4 athab athab NOUN iajs-200 163 5 , , PUNCT iajs-200 163 6 e. e. PROPN iajs-200 163 7 a. a. PROPN iajs-200 163 8 , , PUNCT iajs-200 163 9 ( ( PUNCT iajs-200 163 10 1996 1996 NUM iajs-200 163 11 ) ) PUNCT iajs-200 163 12 , , PUNCT iajs-200 163 13 prime prime ADJ iajs-200 163 14 and and CCONJ iajs-200 163 15 semi semi ADJ iajs-200 163 16 prime prime ADJ iajs-200 163 17 submodules submodules PROPN iajs-200 163 18 m. m. PROPN iajs-200 163 19 sc sc PROPN iajs-200 163 20 . . PUNCT iajs-200 164 1 thesis thesis PROPN iajs-200 164 2 , , PUNCT iajs-200 164 3 university university NOUN iajs-200 164 4 of of ADP iajs-200 164 5 baghdad baghdad PROPN iajs-200 165 1 [ [ X iajs-200 165 2 4 4 NUM iajs-200 165 3 ] ] X iajs-200 165 4 barnard barnard PROPN iajs-200 165 5 , , PUNCT iajs-200 165 6 a. a. NOUN iajs-200 165 7 , , PUNCT iajs-200 165 8 ( ( PUNCT iajs-200 165 9 1981 1981 NUM iajs-200 165 10 ) ) PUNCT iajs-200 165 11 , , PUNCT iajs-200 165 12 multiplication multiplication NOUN iajs-200 165 13 modules module NOUN iajs-200 165 14 . . PUNCT iajs-200 166 1 j. j. PROPN iajs-200 166 2 algebra algebra PROPN iajs-200 166 3 , , PUNCT iajs-200 166 4 71 71 NUM iajs-200 166 5 : : SYM iajs-200 166 6 174 174 NUM iajs-200 166 7 - - SYM iajs-200 166 8 178 178 NUM iajs-200 166 9 . . PUNCT iajs-200 167 1 [ [ X iajs-200 167 2 5 5 NUM iajs-200 167 3 ] ] X iajs-200 167 4 behboodi behboodi NOUN iajs-200 167 5 , , PUNCT iajs-200 167 6 m. m. NOUN iajs-200 167 7 , , PUNCT iajs-200 167 8 karamzadeh karamzadeh PROPN iajs-200 167 9 , , PUNCT iajs-200 167 10 o. o. PROPN iajs-200 167 11 a. a. PROPN iajs-200 167 12 s. s. PROPN iajs-200 167 13 and and CCONJ iajs-200 167 14 koohy koohy PROPN iajs-200 167 15 , , PUNCT iajs-200 167 16 h. h. PROPN iajs-200 167 17 , , PUNCT iajs-200 167 18 ( ( PUNCT iajs-200 167 19 2004 2004 NUM iajs-200 167 20 ) ) PUNCT iajs-200 167 21 , , PUNCT iajs-200 167 22 modules module NOUN iajs-200 167 23 whose whose DET iajs-200 167 24 certain certain ADJ iajs-200 167 25 submodule submodule NOUN iajs-200 167 26 are be AUX iajs-200 167 27 prime prime ADJ iajs-200 167 28 , , PUNCT iajs-200 167 29 vietnam vietnam PROPN iajs-200 167 30 j. j. PROPN iajs-200 167 31 of of ADP iajs-200 167 32 mathematics mathematics PROPN iajs-200 167 33 , , PUNCT iajs-200 167 34 32 32 NUM iajs-200 167 35 ( ( PUNCT iajs-200 167 36 3 3 NUM iajs-200 167 37 ): ): PUNCT iajs-200 167 38 303 303 NUM iajs-200 167 39 - - SYM iajs-200 167 40 317 317 NUM iajs-200 167 41 . . PUNCT iajs-200 168 1 [ [ X iajs-200 168 2 6 6 NUM iajs-200 168 3 ] ] X iajs-200 168 4 el el PROPN iajs-200 168 5 - - PUNCT iajs-200 168 6 bast bast NOUN iajs-200 168 7 , , PUNCT iajs-200 168 8 z. z. PROPN iajs-200 168 9 a. a. PROPN iajs-200 168 10 and and CCONJ iajs-200 168 11 smith smith PROPN iajs-200 168 12 , , PUNCT iajs-200 168 13 p. p. PROPN iajs-200 168 14 f. f. PROPN iajs-200 168 15 , , PUNCT iajs-200 168 16 ( ( PUNCT iajs-200 168 17 1988 1988 NUM iajs-200 168 18 ) ) PUNCT iajs-200 168 19 , , PUNCT iajs-200 168 20 multiplication multiplication NOUN iajs-200 168 21 modules module NOUN iajs-200 168 22 , , PUNCT iajs-200 168 23 comm comm NOUN iajs-200 168 24 . . PUNCT iajs-200 169 1 in in ADP iajs-200 169 2 algebra algebra NOUN iajs-200 169 3 , , PUNCT iajs-200 169 4 16 16 NUM iajs-200 169 5 : : PUNCT iajs-200 169 6 755 755 NUM iajs-200 169 7 - - SYM iajs-200 169 8 779 779 NUM iajs-200 169 9 . . PUNCT iajs-200 170 1 [ [ X iajs-200 170 2 7 7 X iajs-200 170 3 ] ] X iajs-200 170 4 goodearl goodearl PROPN iajs-200 170 5 , , PUNCT iajs-200 170 6 k. k. PROPN iajs-200 170 7 r. r. PROPN iajs-200 170 8 , , PUNCT iajs-200 170 9 ( ( PUNCT iajs-200 170 10 1972 1972 NUM iajs-200 170 11 ) ) PUNCT iajs-200 170 12 , , PUNCT iajs-200 170 13 ring ring NOUN iajs-200 170 14 theory theory NOUN iajs-200 170 15 , , PUNCT iajs-200 170 16 marcel marcel PROPN iajs-200 170 17 dekker dekker PROPN iajs-200 170 18 , , PUNCT iajs-200 170 19 new new PROPN iajs-200 170 20 york york PROPN iajs-200 170 21 . . PUNCT iajs-200 171 1 [ [ X iajs-200 171 2 8 8 NUM iajs-200 171 3 ] ] X iajs-200 171 4 ibrahiem ibrahiem PROPN iajs-200 171 5 , , PUNCT iajs-200 171 6 t. t. PROPN iajs-200 171 7 a. a. PROPN iajs-200 171 8 , , PUNCT iajs-200 171 9 ( ( PUNCT iajs-200 171 10 2011 2011 NUM iajs-200 171 11 ) ) PUNCT iajs-200 171 12 , , PUNCT iajs-200 171 13 prime prime ADJ iajs-200 171 14 extending extending NOUN iajs-200 171 15 module module NOUN iajs-200 171 16 and and CCONJ iajs-200 171 17 s s NOUN iajs-200 171 18 - - PUNCT iajs-200 171 19 prime prime NOUN iajs-200 171 20 module module NOUN iajs-200 171 21 , , PUNCT iajs-200 171 22 j. j. PROPN iajs-200 171 23 of of ADP iajs-200 171 24 al al PROPN iajs-200 171 25 - - PUNCT iajs-200 171 26 nahrain nahrain PROPN iajs-200 171 27 univ univ PROPN iajs-200 171 28 . . PROPN iajs-200 171 29 , , PUNCT iajs-200 171 30 14(4),166 14(4),166 NUM iajs-200 171 31 - - SYM iajs-200 171 32 170 170 NUM iajs-200 171 33 . . PUNCT iajs-200 172 1 [ [ X iajs-200 172 2 9 9 NUM iajs-200 172 3 ] ] SYM iajs-200 172 4 kasch kasch PROPN iajs-200 172 5 , , PUNCT iajs-200 172 6 f. f. PROPN iajs-200 172 7 , , PUNCT iajs-200 172 8 ( ( PUNCT iajs-200 172 9 1982 1982 NUM iajs-200 172 10 ) ) PUNCT iajs-200 172 11 , , PUNCT iajs-200 172 12 modules module NOUN iajs-200 172 13 and and CCONJ iajs-200 172 14 rings ring NOUN iajs-200 172 15 . . PUNCT iajs-200 173 1 london london PROPN iajs-200 173 2 : : PUNCT iajs-200 173 3 academic academic ADJ iajs-200 173 4 press press NOUN iajs-200 173 5 . . PUNCT iajs-200 174 1 [ [ X iajs-200 174 2 10 10 NUM iajs-200 174 3 ] ] X iajs-200 174 4 larsen larsen PROPN iajs-200 174 5 , , PUNCT iajs-200 174 6 m. m. PROPN iajs-200 174 7 d. d. PROPN iajs-200 174 8 and and CCONJ iajs-200 174 9 mccarthy mccarthy PROPN iajs-200 174 10 , , PUNCT iajs-200 174 11 p. p. NOUN iajs-200 174 12 j. j. PROPN iajs-200 174 13 ,(1971 ,(1971 PROPN iajs-200 174 14 ) ) PUNCT iajs-200 174 15 , , PUNCT iajs-200 174 16 multiplicative multiplicative ADJ iajs-200 174 17 theory theory NOUN iajs-200 174 18 of of ADP iajs-200 174 19 ideals ideal NOUN iajs-200 174 20 , , PUNCT iajs-200 174 21 acad acad PROPN iajs-200 174 22 . . PUNCT iajs-200 175 1 press press PROPN iajs-200 175 2 , , PUNCT iajs-200 175 3 new new PROPN iajs-200 175 4 york york PROPN iajs-200 175 5 and and CCONJ iajs-200 175 6 london london PROPN iajs-200 175 7 . . PUNCT iajs-200 176 1 [ [ X iajs-200 176 2 11 11 NUM iajs-200 176 3 ] ] PUNCT iajs-200 176 4 ahmed ahmed PROPN iajs-200 176 5 , , PUNCT iajs-200 176 6 m. m. NOUN iajs-200 176 7 a. a. NOUN iajs-200 176 8 and and CCONJ iajs-200 176 9 dakheel dakheel NOUN iajs-200 176 10 , , PUNCT iajs-200 176 11 sh sh PROPN iajs-200 176 12 . . PROPN iajs-200 176 13 o. o. PROPN iajs-200 176 14 , , PUNCT iajs-200 176 15 s s NOUN iajs-200 176 16 - - ADJ iajs-200 176 17 maximal maximal ADJ iajs-200 176 18 submodules submodule NOUN iajs-200 176 19 , , PUNCT iajs-200 176 20 j. j. PROPN iajs-200 176 21 of of ADP iajs-200 176 22 baghdad baghdad PROPN iajs-200 176 23 for for ADP iajs-200 176 24 science science NOUN iajs-200 176 25 , , PUNCT iajs-200 176 26 preprint preprint NOUN iajs-200 176 27 . . PUNCT iajs-200 177 1 [ [ X iajs-200 177 2 12 12 NUM iajs-200 177 3 ] ] PUNCT iajs-200 177 4 saymeh saymeh NOUN iajs-200 177 5 , , PUNCT iajs-200 177 6 s. s. PROPN iajs-200 177 7 a. a. PROPN iajs-200 177 8 , , PUNCT iajs-200 177 9 ( ( PUNCT iajs-200 177 10 1979 1979 NUM iajs-200 177 11 ) ) PUNCT iajs-200 177 12 , , PUNCT iajs-200 177 13 on on ADP iajs-200 177 14 prime prime ADJ iajs-200 177 15 r r NOUN iajs-200 177 16 - - PUNCT iajs-200 177 17 submodules submodules NOUN iajs-200 177 18 , , PUNCT iajs-200 177 19 univ univ PROPN iajs-200 177 20 . . PUNCT iajs-200 177 21 ndc ndc PROPN iajs-200 177 22 . . PUNCT iajs-200 178 1 tucuma'n tucuma'n PROPN iajs-200 178 2 rev rev PROPN iajs-200 178 3 . . PROPN iajs-200 178 4 ser ser PROPN iajs-200 178 5 . . PROPN iajs-200 178 6 a29 a29 PROPN iajs-200 178 7 , , PUNCT iajs-200 178 8 129 129 NUM iajs-200 178 9 - - SYM iajs-200 178 10 136 136 NUM iajs-200 178 11 . . PUNCT iajs-200 179 1 [ [ X iajs-200 179 2 13 13 NUM iajs-200 179 3 ] ] SYM iajs-200 179 4 sharp sharp ADJ iajs-200 179 5 , , PUNCT iajs-200 179 6 d.w d.w PROPN iajs-200 179 7 . . PROPN iajs-200 179 8 and and CCONJ iajs-200 179 9 vamos vamos PROPN iajs-200 179 10 , , PUNCT iajs-200 179 11 p. p. NOUN iajs-200 179 12 , , PUNCT iajs-200 179 13 ( ( PUNCT iajs-200 179 14 1972 1972 NUM iajs-200 179 15 ) ) PUNCT iajs-200 179 16 , , PUNCT iajs-200 179 17 injective injective ADJ iajs-200 179 18 modules module NOUN iajs-200 179 19 , , PUNCT iajs-200 179 20 cambridge cambridge PROPN iajs-200 179 21 univ univ PROPN iajs-200 179 22 . . PUNCT iajs-200 179 23 press press PROPN iajs-200 179 24 . . PUNCT iajs-200 179 25     SPACE iajs-200 180 1 185 185 NUM iajs-200 180 2 | | NOUN iajs-200 180 3 mathematics mathematic NOUN iajs-200 180 4 2015 2015 NUM iajs-200 180 5 ) ) PUNCT iajs-200 180 6 عام عام ADP iajs-200 180 7 1(العدد 1(العدد NUM iajs-200 180 8 28المجلد 28المجلد NUM iajs-200 180 9 مجلة مجلة PROPN iajs-200 180 10 إبن إبن VERB iajs-200 180 11 الھيثم الھيثم NOUN iajs-200 180 12 للعلوم للعلوم NOUN iajs-200 180 13 الصرفة الصرفة NOUN iajs-200 181 1 و و PRON iajs-200 181 2 التطبيقية التطبيقية ADJ iajs-200 181 3 ibn ibn PROPN iajs-200 181 4 al al PROPN iajs-200 181 5 - - PUNCT iajs-200 181 6 haitham haitham PROPN iajs-200 181 7 j. j. PROPN iajs-200 181 8 for for ADP iajs-200 181 9 pure pure PROPN iajs-200 181 10 & & CCONJ iajs-200 181 11 appl appl PROPN iajs-200 181 12 . . PUNCT iajs-200 182 1 sci sci PROPN iajs-200 182 2 . . PUNCT iajs-200 182 3 vol vol NOUN iajs-200 182 4 . . PROPN iajs-200 183 1 28 28 NUM iajs-200 183 2 ( ( PUNCT iajs-200 183 3 1 1 NUM iajs-200 183 4 ) ) PUNCT iajs-200 183 5 2015 2015 NUM iajs-200 183 6 حول حول NOUN iajs-200 183 7 المقاسات المقاسات PROPN iajs-200 183 8 الجزئية الجزئية PROPN iajs-200 183 9 شبه شبه VERB iajs-200 183 10 الجوھرية الجوھرية NOUN iajs-200 183 11 منى منى NOUN iajs-200 183 12 عباس عباس VERB iajs-200 183 13 أحمد أحمد NOUN iajs-200 183 14 ميساء ميساء PROPN iajs-200 183 15 رياض رياض PROPN iajs-200 183 16 عباس عباس VERB iajs-200 183 17 جامعة جامعة NOUN iajs-200 183 18 بغداد بغداد NOUN iajs-200 183 19 – – PUNCT iajs-200 183 20 كلية كلية NOUN iajs-200 183 21 العلوم العلوم NOUN iajs-200 183 22 للبنات للبنات ADJ iajs-200 183 23 – – PUNCT iajs-200 183 24 قسم قسم PRON iajs-200 183 25 الرياضيات الرياضيات NOUN iajs-200 183 26 2015كانون 2015كانون NUM iajs-200 183 27 الثاني الثاني PROPN iajs-200 183 28 5قبل 5قبل PROPN iajs-200 183 29 البحث البحث VERB iajs-200 183 30 في في X iajs-200 183 31 : : PUNCT iajs-200 183 32 2014تشرين 2014تشرين NUM iajs-200 183 33 االول االول NOUN iajs-200 183 34 20أستلم 20أستلم NUM iajs-200 183 35 البحث البحث NOUN iajs-200 183 36 في في DET iajs-200 183 37 : : PUNCT iajs-200 183 38 الخالصة الخالصة PROPN iajs-200 183 39 ً ً PROPN iajs-200 183 40 أحادياً أحادياً PROPN iajs-200 183 41 أيسر أيسر NOUN iajs-200 183 42 على على NOUN iajs-200 183 43 mحلقة mحلقة NOUN iajs-200 183 44 ابدالية ابدالية NOUN iajs-200 183 45 ذات ذات VERB iajs-200 183 46 عنصر عنصر NOUN iajs-200 183 47 محايد محايد NOUN iajs-200 183 48 , , PUNCT iajs-200 183 49 وليكن وليكن VERB iajs-200 183 50 rلتكن rلتكن NOUN iajs-200 183 51 . . PUNCT iajs-200 184 1 ھدفنا ھدفنا NOUN iajs-200 184 2 في في ADP iajs-200 185 1 ھذا ھذا NOUN iajs-200 185 2 البحث البحث PROPN iajs-200 185 3 rمقاسا rمقاسا NOUN iajs-200 185 4 وھرية وھرية PROPN iajs-200 185 5 التي التي PROPN iajs-200 185 6 قدمھا قدمھا PROPN iajs-200 185 7 ھو ھو ADP iajs-200 185 8 التقصي التقصي PROPN iajs-200 185 9 عن عن PROPN iajs-200 185 10 بعض بعض NOUN iajs-200 185 11 النتائج النتائج NOUN iajs-200 185 12 الجديدة الجديدة PROPN iajs-200 185 13 ( ( PUNCT iajs-200 185 14 على على NOUN iajs-200 185 15 حد حد ADP iajs-200 185 16 علمنا علمنا NOUN iajs-200 185 17 ) ) PUNCT iajs-200 185 18 حول حول PROPN iajs-200 185 19 المقاسات المقاسات PROPN iajs-200 185 20 الجزئية الجزئية PROPN iajs-200 185 21 شبه شبه VERB iajs-200 185 22 الج الج VERB iajs-200 185 23 n n PART iajs-200 185 24 ∩ ∩ PROPN iajs-200 185 25 p p X iajs-200 185 26 ≠ ≠ PROPN iajs-200 185 27 0بأنه 0بأنه NUM iajs-200 185 28 شبه شبه NOUN iajs-200 185 29 جوھري جوھري PROPN iajs-200 185 30 ، ، PROPN iajs-200 185 31 إذا إذا PROPN iajs-200 185 32 كان كان PROPN iajs-200 185 33 mمن mمن PROPN iajs-200 185 34 nالباحثان nالباحثان ADJ iajs-200 185 35 علي علي NOUN iajs-200 185 36 سبع سبع X iajs-200 185 37 وندى وندى ADP iajs-200 185 38 الدبان الدبان PROPN iajs-200 185 39 ، ، PROPN iajs-200 185 40 إذ إذ PROPN iajs-200 185 41 يقال يقال PROPN iajs-200 185 42 للمقاس للمقاس PROPN iajs-200 185 43 الجزئي الجزئي NOUN iajs-200 185 44 لقد لقد PROPN iajs-200 185 45 قمنا قمنا ADV iajs-200 185 46 بإجراء بإجراء PROPN iajs-200 185 47 تعديل تعديل PROPN iajs-200 185 48 يسير يسير PROPN iajs-200 185 49 لھذا لھذا PROPN iajs-200 185 50 التعريف التعريف PROPN iajs-200 185 51 ليشمل ليشمل VERB iajs-200 185 52 المقاس المقاس NOUN iajs-200 185 53 m.من m.من PROPN iajs-200 185 54 nلكل nلكل NOUN iajs-200 185 55 مقاس مقاس VERB iajs-200 185 56 جزئي جزئي NOUN iajs-200 185 57 أولي أولي PROPN iajs-200 185 58 غير غير AUX iajs-200 185 59 صفري صفري ADJ iajs-200 185 60 الصفري الصفري NOUN iajs-200 185 61 ، ، NOUN iajs-200 185 62 كما كما PROPN iajs-200 185 63 قدمنا قدمنا PROPN iajs-200 186 1 العديد العديد PROPN iajs-200 187 1 من من INTJ iajs-200 188 1 القضايا القضايا PROPN iajs-200 188 2 والخواص والخواص PROPN iajs-200 188 3 الجديدة الجديدة VERB iajs-200 188 4 لھذا لھذا PROPN iajs-200 188 5 النوع النوع PROPN iajs-200 188 6 من من PRON iajs-200 188 7 المقاسات المقاسات PROPN iajs-200 188 8 الجزئية الجزئية PROPN iajs-200 188 9 . . PUNCT iajs-200 189 1 نتظمة نتظمة PROPN iajs-200 189 2 ، ، PROPN iajs-200 189 3 المقاسات المقاسات PROPN iajs-200 189 4 الم الم VERB iajs-200 189 5 المقاسات المقاسات PROPN iajs-200 189 6 الجزئية الجزئية PROPN iajs-200 189 7 شبه شبه VERB iajs-200 189 8 الجوھرية الجوھرية PROPN iajs-200 189 9 ، ، PROPN iajs-200 189 10 المقاسات المقاسات PROPN iajs-200 189 11 الجزئية الجزئية VERB iajs-200 189 12 الجوھرية،الكلمات الجوھرية،الكلمات VERB iajs-200 189 13 المفتاحية المفتاحية PROPN iajs-200 189 14 : : PUNCT iajs-200 189 15 المنتظمة المنتظمة PROPN iajs-200 189 16 ، ، PROPN iajs-200 189 17 المقاسات المقاسات PROPN iajs-200 189 18 األولية األولية PROPN iajs-200 189 19 المتكاملة المتكاملة PROPN iajs-200 189 20 , , PUNCT iajs-200 189 21 المقاسات المقاسات NOUN iajs-200 189 22 الجوھرية الجوھرية VERB iajs-200 189 23 المتكاملة.المقاسات المتكاملة.المقاسات NOUN iajs-200 189 24 شبه شبه VERB