id sid eid entity type iajs-3013 1 1 ihjpas PERSON iajs-3013 2 1 36(1)2023 300 CARDINAL iajs-3013 2 2 4.0 CARDINAL iajs-3013 2 3 almost approximately CARDINAL iajs-3013 5 1 four CARDINAL iajs-3013 6 1 two CARDINAL iajs-3013 7 1 submodule ORG iajs-3013 8 1 1 CARDINAL iajs-3013 8 2 1 CARDINAL iajs-3013 8 3 24 CARDINAL iajs-3013 9 1 submodule ORG iajs-3013 9 2 ∈ 𝐹 ORG iajs-3013 9 3 ∈ 𝐹 ORG iajs-3013 11 1 three CARDINAL iajs-3013 13 1 two CARDINAL iajs-3013 15 1 almost approximately CARDINAL iajs-3013 16 1 14 CARDINAL iajs-3013 16 2 6 CARDINAL iajs-3013 16 3 november 2022 DATE iajs-3013 16 4 january 2023 DATE iajs-3013 17 1 ibn al-haitham PERSON iajs-3013 17 2 applied sciences journal ORG iajs-3013 17 3 jih.uobaghdad.edu.iq ali PERSON iajs-3013 17 4 tikrit university ORG iajs-3013 17 5 iraq GPE iajs-3013 18 1 ali.shebl@st.tu.edu.iq haibat PERSON iajs-3013 18 2 k. mohammadali PERSON iajs-3013 18 3 tikrit university ORG iajs-3013 18 4 iraq GPE iajs-3013 19 1 mailto:ali.shebl@st.tu.edu.iq mailto:h.mohammadali@tu.edu.iq FAC iajs-3013 20 1 36(1)2023 301 CARDINAL iajs-3013 20 2 𝑅-module LOC iajs-3013 21 1 2 CARDINAL iajs-3013 22 1 2.1 CARDINAL iajs-3013 23 1 5 CARDINAL iajs-3013 24 1 2.2 CARDINAL iajs-3013 24 2 6 CARDINAL iajs-3013 24 3 2.3 CARDINAL iajs-3013 25 1 2.4 CARDINAL iajs-3013 25 2 8 CARDINAL iajs-3013 25 3 2.5 CARDINAL iajs-3013 25 4 1 CARDINAL iajs-3013 25 5 alappnqprime DATE iajs-3013 25 6 𝑄′ ORG iajs-3013 25 7 2.6 CARDINAL iajs-3013 25 8 1 CARDINAL iajs-3013 25 9 alappnqprime DATE iajs-3013 26 1 βŠ† CARDINAL iajs-3013 26 2 𝑄′. ORG iajs-3013 26 3 2.7 CARDINAL iajs-3013 26 4 9 CARDINAL iajs-3013 26 5 1 ∈ 𝑆 QUANTITY iajs-3013 26 6 𝑠)~(π‘žβ€² PERSON iajs-3013 26 7 βˆ’ π‘ β€²π‘ž EVENT iajs-3013 27 1 0 CARDINAL iajs-3013 31 1 2.8 CARDINAL iajs-3013 31 2 10 CARDINAL iajs-3013 31 3 𝑍-regular ORG iajs-3013 31 4 ∈ ORG iajs-3013 31 5 2.9 CARDINAL iajs-3013 32 1 5 CARDINAL iajs-3013 33 1 1 CARDINAL iajs-3013 34 1 2 CARDINAL iajs-3013 34 2 2.10 CARDINAL iajs-3013 34 3 5 CARDINAL iajs-3013 34 4 𝑍-regular 𝑅-module ORG iajs-3013 35 1 2.9 CARDINAL iajs-3013 35 2 2.10 CARDINAL iajs-3013 36 1 ihjpas PERSON iajs-3013 37 1 36(1)2023 302 CARDINAL iajs-3013 37 2 2.11 CARDINAL iajs-3013 37 3 𝑍-regular 𝑅-module ORG iajs-3013 37 4 2.12 CARDINAL iajs-3013 37 5 1 CARDINAL iajs-3013 37 6 2.13 CARDINAL iajs-3013 37 7 11 CARDINAL iajs-3013 37 8 0 CARDINAL iajs-3013 38 1 2.14 CARDINAL iajs-3013 39 1 13 CARDINAL iajs-3013 39 2 2.15 CARDINAL iajs-3013 39 3 9 CARDINAL iajs-3013 40 1 3 CARDINAL iajs-3013 41 1 3.1 CARDINAL iajs-3013 42 1 𝑖=1 GPE iajs-3013 42 2 3.2 CARDINAL iajs-3013 43 1 3.3 1 DATE iajs-3013 44 1 𝑍-module NORP iajs-3013 44 2 𝑍-module ORG iajs-3013 44 3 2 CARDINAL iajs-3013 46 1 3 CARDINAL iajs-3013 47 1 3.4 CARDINAL iajs-3013 48 1 ⋃ PRODUCT iajs-3013 48 2 βŠ† CARDINAL iajs-3013 48 3 ⋃ 𝐿𝛼𝑖 𝑛 𝑖=1 PRODUCT iajs-3013 48 4 𝐿1 CARDINAL iajs-3013 48 5 1 CARDINAL iajs-3013 48 6 2 DATE iajs-3013 48 7 ⋃ 𝐿𝛼𝑖 𝑛 𝑖=1 FAC iajs-3013 49 1 ⋃ 𝐿𝛼𝑖 𝑛 𝑖=1 PRODUCT iajs-3013 49 2 𝐿1 CARDINAL iajs-3013 49 3 1 CARDINAL iajs-3013 49 4 2 DATE iajs-3013 49 5 ⋃ 𝐿𝛼𝑖 𝑛 𝑖=1 FAC iajs-3013 49 6 βŠ† CARDINAL iajs-3013 49 7 𝐿2 ORG iajs-3013 51 1 ihjpas PERSON iajs-3013 52 1 36(1)2023 303 CARDINAL iajs-3013 53 1 3.5 CARDINAL iajs-3013 55 1 3.6 CARDINAL iajs-3013 56 1 3.7 CARDINAL iajs-3013 57 1 βŠ† CARDINAL iajs-3013 58 1 βŠ† CARDINAL iajs-3013 58 2 𝑄′ ORG iajs-3013 58 3 𝑄′ ORG iajs-3013 58 4 ∈ ORG iajs-3013 59 1 βŠ† CARDINAL iajs-3013 59 2 βŠ† CARDINAL iajs-3013 60 1 2.5 CARDINAL iajs-3013 60 2 ∈ ORG iajs-3013 61 1 βŠ† CARDINAL iajs-3013 61 2 𝑖=1 GPE iajs-3013 61 3 βŠ† CARDINAL iajs-3013 61 4 𝑃′𝛼𝑖 𝑛 𝑖=1 PRODUCT iajs-3013 62 1 βŠ† CARDINAL iajs-3013 62 2 𝑃′𝛼𝑖 𝑛 𝑖=1 ORG iajs-3013 63 1 𝑄′ ORG iajs-3013 64 1 𝑄′ ORG iajs-3013 64 2 𝑅-module LOC iajs-3013 64 3 βŠ† CARDINAL iajs-3013 64 4 𝐹 βŠ† ORG iajs-3013 64 5 ⋃ PRODUCT iajs-3013 64 6 𝑃𝛼 PERSON iajs-3013 64 7 ∈ ORG iajs-3013 66 1 βŠ† CARDINAL iajs-3013 66 2 βŠ† CARDINAL iajs-3013 66 3 ⋃ PRODUCT iajs-3013 67 1 βŠ† 𝑃𝛼 QUANTITY iajs-3013 67 2 2.6 𝑓(𝑃𝛼 PERSON iajs-3013 67 3 alappnqprime DATE iajs-3013 67 4 𝑄′ ORG iajs-3013 67 5 ∈ ORG iajs-3013 68 1 𝑄′ ORG iajs-3013 69 1 βŠ† CARDINAL iajs-3013 69 2 𝑓(𝑃𝛼𝑖 ORG iajs-3013 69 3 𝑖=1 GPE iajs-3013 70 1 βŠ† CARDINAL iajs-3013 70 2 𝑓(𝑃𝛼𝑖 ORG iajs-3013 70 3 𝑖=1 GPE iajs-3013 70 4 1 CARDINAL iajs-3013 70 5 2 DATE iajs-3013 71 1 𝑓(π‘₯ βˆ’ 𝑏 PERSON iajs-3013 74 1 𝑃𝛼𝑖 𝑛 𝑖=1 ORG iajs-3013 74 2 𝐹 GPE iajs-3013 76 1 3.9 CARDINAL iajs-3013 77 1 𝐹 βŠ† ORG iajs-3013 77 2 ⋃ PRODUCT iajs-3013 77 3 𝑃𝛼 PERSON iajs-3013 77 4 ∈ ORG iajs-3013 77 5 1 CARDINAL iajs-3013 78 1 βŠ† CARDINAL iajs-3013 78 2 βŠ† CARDINAL iajs-3013 78 3 ⋃ PRODUCT iajs-3013 79 1 𝑃𝛼 PERSON iajs-3013 79 2 ∈ ORG iajs-3013 79 3 2.5 CARDINAL iajs-3013 79 4 ∈ ORG iajs-3013 80 1 βŠ† CARDINAL iajs-3013 81 1 𝑖=1 GPE iajs-3013 82 1 ihjpas PERSON iajs-3013 83 1 36(1)2023 304 CARDINAL iajs-3013 83 2 βŠ† CARDINAL iajs-3013 83 3 𝑖=1 GPE iajs-3013 83 4 ⋃ PERSON iajs-3013 83 5 π‘“βˆ’1(𝑃𝛼𝑖))𝑆 𝑛 𝑖=1 MONEY iajs-3013 84 1 𝑖=1 GPE iajs-3013 85 1 1 CARDINAL iajs-3013 85 2 2 DATE iajs-3013 85 3 𝑃𝛼𝑗 GPE iajs-3013 85 4 π‘“βˆ’1(𝑃𝛼𝑖))𝑆 𝑛 𝑖=1 MONEY iajs-3013 86 1 ⋃ PRODUCT iajs-3013 86 2 π‘“βˆ’1(𝑃𝛼𝑖))𝑆 𝑛 𝑖=1 MONEY iajs-3013 87 1 π‘“βˆ’1(𝑃𝛼𝑖))𝑆 𝑛 𝑖=1 MONEY iajs-3013 87 2 1 CARDINAL iajs-3013 87 3 2 DATE iajs-3013 87 4 𝑃𝛼𝑗 GPE iajs-3013 88 1 𝑖=1 GPE iajs-3013 89 1 ⋃ PERSON iajs-3013 89 2 π‘“βˆ’1(𝑃𝛼𝑖))𝑆 𝑛 𝑖=1 βŠ† MONEY iajs-3013 89 3 𝑖=1 GPE iajs-3013 90 1 𝑄𝑆. DATE iajs-3013 90 2 1 CARDINAL iajs-3013 91 1 1 CARDINAL iajs-3013 91 2 1 CARDINAL iajs-3013 91 3 βŠ† CARDINAL iajs-3013 91 4 1 CARDINAL iajs-3013 91 5 1 CARDINAL iajs-3013 91 6 𝑓(π‘₯ PERSON iajs-3013 91 7 𝐹 βŠ† ORG iajs-3013 91 8 𝑄𝑆. DATE iajs-3013 91 9 𝑖=1 GPE iajs-3013 91 10 𝑃𝛼𝑖 𝑛 𝑖=1 ORG iajs-3013 92 1 𝐹 PERSON iajs-3013 92 2 𝑄𝑆. DATE iajs-3013 93 1 4 CARDINAL iajs-3013 94 1 first ORDINAL iajs-3013 95 1 4.1 CARDINAL iajs-3013 95 2 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 96 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 97 1 4.2 CARDINAL iajs-3013 97 2 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 98 1 4.3 CARDINAL iajs-3013 98 2 𝐹 GPE iajs-3013 98 3 1 CARDINAL iajs-3013 98 4 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 99 1 2 CARDINAL iajs-3013 100 1 βŠ† CARDINAL iajs-3013 101 1 3. TIME iajs-3013 102 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 103 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 104 1 1 CARDINAL iajs-3013 104 2 2 CARDINAL iajs-3013 105 1 3 CARDINAL iajs-3013 105 2 1 CARDINAL iajs-3013 105 3 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 106 1 βŠ† CARDINAL iajs-3013 106 2 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 107 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 109 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 110 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„ PERSON iajs-3013 110 2 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 110 3 βŠ† CARDINAL iajs-3013 110 4 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 111 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„ PERSON iajs-3013 111 2 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 112 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 113 1 ihjpas PERSON iajs-3013 114 1 36(1)2023 305 CARDINAL iajs-3013 114 2 4.4 CARDINAL iajs-3013 115 1 𝑍-regular ORG iajs-3013 115 2 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 116 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 117 1 𝑍-regular ORG iajs-3013 117 2 2.11 CARDINAL iajs-3013 118 1 𝑃𝛼 PERSON iajs-3013 118 2 ∈ ORG iajs-3013 119 1 βŠ† CARDINAL iajs-3013 119 2 𝑃𝛼 PERSON iajs-3013 119 3 𝐹 βŠ† 𝑃𝛼. ORG iajs-3013 119 4 2.12 CARDINAL iajs-3013 119 5 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 120 1 βŠ† CARDINAL iajs-3013 120 2 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 121 1 4.5 CARDINAL iajs-3013 124 1 𝐹1 CARDINAL iajs-3013 124 2 𝐹1 βŠ‚ PERCENT iajs-3013 124 3 ∈ ORG iajs-3013 125 1 𝐹1 CARDINAL iajs-3013 126 1 𝐹2 CARDINAL iajs-3013 128 1 𝐹1 CARDINAL iajs-3013 128 2 𝐹2 CARDINAL iajs-3013 129 1 βŠ‚ GPE iajs-3013 129 2 ∈ ORG iajs-3013 131 1 𝐹3 CARDINAL iajs-3013 132 1 𝐹1 βŠ† CARDINAL iajs-3013 132 2 𝐹2 ORG iajs-3013 132 3 βŠ† PRODUCT iajs-3013 134 1 4.6 CARDINAL iajs-3013 134 2 ∈ ORG iajs-3013 134 3 4.7 CARDINAL iajs-3013 135 1 4.8 CARDINAL iajs-3013 135 2 submodule ORG iajs-3013 135 3 convers ORG iajs-3013 135 4 𝑍2 GPE iajs-3013 136 1 0Μ… CARDINAL iajs-3013 136 2 π‘₯𝑍2 GPE iajs-3013 136 3 2𝑍2 CARDINAL iajs-3013 136 4 π‘₯𝑍2 ORG iajs-3013 136 5 2𝑍2 CARDINAL iajs-3013 136 6 π‘₯𝑍2 GPE iajs-3013 136 7 2𝑍2 CARDINAL iajs-3013 138 1 4.9 CARDINAL iajs-3013 138 2 𝑅-module LOC iajs-3013 141 1 36(1)2023 306 CARDINAL iajs-3013 142 1 ⋃ PERSON iajs-3013 142 2 π‘ž)π‘žβˆˆπΉ ORG iajs-3013 142 3 βŠ† CARDINAL iajs-3013 142 4 ⋃ PRODUCT iajs-3013 143 1 ∈ ORG iajs-3013 143 2 𝐹 βŠ† ORG iajs-3013 144 1 𝐹 PERSON iajs-3013 145 1 𝐹𝛼 PERSON iajs-3013 145 2 ∈ ORG iajs-3013 145 3 ⋃ PRODUCT iajs-3013 146 1 ∈ ORG iajs-3013 146 2 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„((π‘ž GPE iajs-3013 146 3 βŠ† CARDINAL iajs-3013 146 4 βŠ† CARDINAL iajs-3013 148 1 4.10 CARDINAL iajs-3013 148 2 𝑅-module LOC iajs-3013 149 1 1 CARDINAL iajs-3013 151 1 2. CARDINAL iajs-3013 151 2 𝐹 βŠ‚ 𝑄 ORG iajs-3013 151 3 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 NORP iajs-3013 153 1 3 CARDINAL iajs-3013 153 2 𝐹 βŠ‚ 𝑄 ORG iajs-3013 153 3 𝐹𝛼}π›ΌβˆˆΚŒ ORG iajs-3013 153 4 𝐹 ORG iajs-3013 153 5 ∈ ORG iajs-3013 153 6 𝐹 βŠ† PRODUCT iajs-3013 154 1 4. CARDINAL iajs-3013 154 2 𝐹 βŠ‚ 𝑄 ORG iajs-3013 154 3 𝐹𝛼}π›ΌβˆˆΚŒ ORG iajs-3013 154 4 ∈ ORG iajs-3013 154 5 1 CARDINAL iajs-3013 154 6 2 CARDINAL iajs-3013 154 7 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 157 1 βŠ† CARDINAL iajs-3013 157 2 ⋃ PRODUCT iajs-3013 157 3 πΎπ‘ž PERSON iajs-3013 158 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 NORP iajs-3013 160 1 2 CARDINAL iajs-3013 160 2 3 CARDINAL iajs-3013 161 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 NORP iajs-3013 163 1 ⋃ PRODUCT iajs-3013 163 2 ∈ ORG iajs-3013 164 1 βŠ† CARDINAL iajs-3013 164 2 𝐹 βŠ† PRODUCT iajs-3013 164 3 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 165 1 βŠ† CARDINAL iajs-3013 166 1 𝐹 βŠ† π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹𝛼 ORG iajs-3013 167 1 3 CARDINAL iajs-3013 167 2 4 CARDINAL iajs-3013 167 3 𝐹 ORG iajs-3013 167 4 ∈ ORG iajs-3013 167 5 𝐹 βŠ† PRODUCT iajs-3013 167 6 𝐹𝛽is PERSON iajs-3013 167 7 4 CARDINAL iajs-3013 167 8 1 CARDINAL iajs-3013 168 1 𝐹𝛼 PERSON iajs-3013 168 2 ∈ ORG iajs-3013 169 1 𝐹 PERSON iajs-3013 169 2 ⋃ PERSON iajs-3013 170 1 ∈ ORG iajs-3013 170 2 𝐹 βŠ† π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹𝛼 ORG iajs-3013 172 1 4.11 CARDINAL iajs-3013 173 1 𝐹1 CARDINAL iajs-3013 173 2 𝐹2 CARDINAL iajs-3013 173 3 𝐹1 βŠ† CARDINAL iajs-3013 175 1 𝐹𝛼}π›ΌβˆˆΚŒ ORG iajs-3013 176 1 36(1)2023 307 CARDINAL iajs-3013 176 2 𝐹 ORG iajs-3013 177 1 ⋃ PRODUCT iajs-3013 178 1 ⋃ PRODUCT iajs-3013 179 1 12 CARDINAL iajs-3013 179 2 2.14 CARDINAL iajs-3013 179 3 ∈ ORG iajs-3013 182 1 𝑍-regular ORG iajs-3013 183 1 4.12 CARDINAL iajs-3013 183 2 𝑍-regular 𝑅-module ORG iajs-3013 184 1 4.10 CARDINAL iajs-3013 184 2 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 NORP iajs-3013 186 1 𝑍-regular ORG iajs-3013 186 2 4.4 CARDINAL iajs-3013 186 3 𝐹 PERSON iajs-3013 188 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 190 1 4.10 CARDINAL iajs-3013 192 1 4.13 CARDINAL iajs-3013 192 2 at least one CARDINAL iajs-3013 193 1 𝐹1 βŠ† CARDINAL iajs-3013 193 2 𝐹2 ORG iajs-3013 193 3 βŠ† PRODUCT iajs-3013 193 4 ⋃ 𝐹𝑖𝑖 PERSON iajs-3013 193 5 ⋃ 𝐹𝑖𝑖 PERSON iajs-3013 194 1 4.10 CARDINAL iajs-3013 195 1 ⋃ DATE iajs-3013 195 2 βŠ† 𝐹𝑗 PRODUCT iajs-3013 196 1 4.10 CARDINAL iajs-3013 196 2 𝐹1 βŠ† CARDINAL iajs-3013 196 3 𝐹2 ORG iajs-3013 197 1 4.13 CARDINAL iajs-3013 198 1 4.14 CARDINAL iajs-3013 199 1 β‰  𝑄. PERSON iajs-3013 200 1 4.15 CARDINAL iajs-3013 201 1 4.16 CARDINAL iajs-3013 202 1 4.13 CARDINAL iajs-3013 203 1 ihjpas PERSON iajs-3013 204 1 36(1)2023 308 CARDINAL iajs-3013 204 2 4.17 CARDINAL iajs-3013 206 1 4.5 CARDINAL iajs-3013 206 2 𝐹 = π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐿 ORG iajs-3013 206 3 4.3 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PERSON iajs-3013 207 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„ TIME iajs-3013 208 1 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 PRODUCT iajs-3013 210 1 4.10 CARDINAL iajs-3013 211 1 4.18 CARDINAL iajs-3013 212 1 βŠ† CARDINAL iajs-3013 213 1 βŠ† CARDINAL iajs-3013 213 2 𝑄′ ORG iajs-3013 213 3 𝑄′ ORG iajs-3013 213 4 ∈ ORG iajs-3013 214 1 βŠ† CARDINAL iajs-3013 215 1 βŠ† CARDINAL iajs-3013 216 1 𝑄′ ORG iajs-3013 216 2 2.5 CARDINAL iajs-3013 216 3 ∈ ORG iajs-3013 218 1 βŠ† CARDINAL iajs-3013 218 2 ∈ ORG iajs-3013 219 1 βŠ† CARDINAL iajs-3013 219 2 ∈ ORG iajs-3013 220 1 𝑄′. ORG iajs-3013 220 2 𝑄′ ORG iajs-3013 221 1 𝑄′ ORG iajs-3013 221 2 𝑅-module LOC iajs-3013 221 3 βŠ† CARDINAL iajs-3013 221 4 𝐹 βŠ† ORG iajs-3013 221 5 ⋃ PRODUCT iajs-3013 221 6 𝑃𝛼 PERSON iajs-3013 221 7 ∈ ORG iajs-3013 223 1 βŠ† CARDINAL iajs-3013 223 2 βŠ† CARDINAL iajs-3013 223 3 ⋃ PRODUCT iajs-3013 224 1 βŠ† 𝑃𝛼 QUANTITY iajs-3013 224 2 2.6 𝑓(𝑃𝛼 PERSON iajs-3013 224 3 alappnqprime DATE iajs-3013 224 4 𝑄′ ORG iajs-3013 224 5 ∈ ORG iajs-3013 225 1 𝑄′ ORG iajs-3013 225 2 βŠ† CARDINAL iajs-3013 225 3 ∈ ORG iajs-3013 226 1 βŠ† CARDINAL iajs-3013 227 1 𝑏 ∈ 𝑃𝛽 PERSON iajs-3013 227 2 𝑓(π‘₯ βˆ’ 𝑏 PERSON iajs-3013 229 1 𝐹 βŠ† 𝑃𝛽 FAC iajs-3013 229 2 ∈ ORG iajs-3013 231 1 4.19 CARDINAL iajs-3013 233 1 ⋃ PRODUCT iajs-3013 233 2 𝑃𝛼 PERSON iajs-3013 233 3 ∈ ORG iajs-3013 234 1 1 CARDINAL iajs-3013 235 1 βŠ† CARDINAL iajs-3013 235 2 βŠ† CARDINAL iajs-3013 235 3 ⋃ PRODUCT iajs-3013 236 1 𝑃𝛼 PERSON iajs-3013 236 2 ∈ ORG iajs-3013 236 3 2.5 CARDINAL iajs-3013 236 4 ∈ ORG iajs-3013 237 1 βŠ† CARDINAL iajs-3013 237 2 ∈ ORG iajs-3013 238 1 βŠ† CARDINAL iajs-3013 239 1 𝑄𝑆. DATE iajs-3013 240 1 36(1)2023 309 CARDINAL iajs-3013 240 2 1 CARDINAL iajs-3013 240 3 1 CARDINAL iajs-3013 240 4 1 CARDINAL iajs-3013 240 5 βŠ† CARDINAL iajs-3013 240 6 1 CARDINAL iajs-3013 240 7 1 CARDINAL iajs-3013 240 8 𝑓(π‘₯ PERSON iajs-3013 240 9 𝐹 βŠ† ORG iajs-3013 240 10 𝑄𝑆. DATE iajs-3013 240 11 βŠ† CARDINAL iajs-3013 240 12 ∈ ORG iajs-3013 240 13 ∈ ORG iajs-3013 241 1 𝐹 PERSON iajs-3013 243 1 5 CARDINAL iajs-3013 243 2 β€’ CARDINAL iajs-3013 244 1 𝑆 of 𝑅. β€’ ORG iajs-3013 246 1 𝑅-module LOC iajs-3013 247 1 1 CARDINAL iajs-3013 249 1 2. CARDINAL iajs-3013 249 2 𝐹 βŠ‚ 𝑄 ORG iajs-3013 249 3 π΄π‘™π‘Žπ‘π‘π‘›π‘žπ‘Ÿπ‘Žπ‘‘π‘„(𝐹 NORP iajs-3013 251 1 3 CARDINAL iajs-3013 251 2 𝐹 βŠ‚ 𝑄 ORG iajs-3013 251 3 𝐹𝛼}π›ΌβˆˆΚŒ ORG iajs-3013 251 4 𝐹 ORG iajs-3013 251 5 ∈ ORG iajs-3013 251 6 𝐹 βŠ† PRODUCT iajs-3013 252 1 4. CARDINAL iajs-3013 252 2 𝐹 βŠ‚ 𝑄 ORG iajs-3013 252 3 𝐹𝛼}π›ΌβˆˆΚŒ ORG iajs-3013 252 4 ∈ ORG iajs-3013 252 5 1 CARDINAL iajs-3013 252 6 ali PERSON iajs-3013 252 7 a. PERSON iajs-3013 252 8 haibat k. m. PERSON iajs-3013 253 1 14(3 CARDINAL iajs-3013 253 2 2022 CARDINAL iajs-3013 254 1 2 CARDINAL iajs-3013 254 2 abdul-razak h. m. quasi-prime PERSON iajs-3013 255 1 univ NORP iajs-3013 255 2 baghdad GPE iajs-3013 256 1 1999 DATE iajs-3013 257 1 3 CARDINAL iajs-3013 257 2 nuhad GPE iajs-3013 257 3 s. a. PERSON iajs-3013 257 4 j. a. PERSON iajs-3013 257 5 2017 CARDINAL iajs-3013 257 6 5(1 CARDINAL iajs-3013 257 7 170 CARDINAL iajs-3013 258 1 4 CARDINAL iajs-3013 258 2 ali PERSON iajs-3013 258 3 a. PERSON iajs-3013 258 4 omar a. a. PERSON iajs-3013 259 1 haibat k. m. PERSON iajs-3013 259 2 ibn alhaitham ORG iajs-3013 259 3 sci ORG iajs-3013 259 4 2020 DATE iajs-3013 259 5 33(4 CARDINAL iajs-3013 259 6 92-101 CARDINAL iajs-3013 260 1 5 CARDINAL iajs-3013 260 2 athab PERSON iajs-3013 260 3 e. a. prime PERSON iajs-3013 261 1 univ NORP iajs-3013 261 2 baghdad GPE iajs-3013 262 1 1996 DATE iajs-3013 263 1 6 CARDINAL iajs-3013 263 2 el-bast ORG iajs-3013 263 3 z. a. PERSON iajs-3013 263 4 smith, p. f. multiplication modules ORG iajs-3013 264 1 1988 DATE iajs-3013 264 2 16(4 DATE iajs-3013 264 3 755 CARDINAL iajs-3013 264 4 ahmad PERSON iajs-3013 264 5 a. a. PERSON iajs-3013 264 6 univ NORP iajs-3013 264 7 baghdad GPE iajs-3013 264 8 1993 DATE iajs-3013 265 1 8 CARDINAL iajs-3013 265 2 dung, n.v. ORG iajs-3013 265 3 huynh PERSON iajs-3013 265 4 d.v. GPE iajs-3013 265 5 smith GPE iajs-3013 265 6 p.i. GPE iajs-3013 265 7 r. NORP iajs-3013 267 1 longman ORG iajs-3013 267 2 harlow PERSON iajs-3013 267 3 1994 DATE iajs-3013 268 1 9 CARDINAL iajs-3013 268 2 larsen PERSON iajs-3013 268 3 m. d. PERSON iajs-3013 268 4 mccarthy PERSON iajs-3013 268 5 j. multiplicative PERSON iajs-3013 268 6 new york GPE iajs-3013 268 7 london GPE iajs-3013 269 1 1971 DATE iajs-3013 270 1 10 CARDINAL iajs-3013 270 2 zelmanowitz PERSON iajs-3013 270 3 american mathematical society ORG iajs-3013 270 4 1972 DATE iajs-3013 270 5 163 CARDINAL iajs-3013 270 6 341 CARDINAL iajs-3013 271 1 11 CARDINAL iajs-3013 272 1 kasch, f. modules ORG iajs-3013 272 2 london GPE iajs-3013 274 1 new york GPE iajs-3013 275 1 1982 DATE iajs-3013 276 1 12 CARDINAL iajs-3013 277 1 barnard, a. multiplication modules ORG iajs-3013 277 2 1981 DATE iajs-3013 277 3 71(1 CARDINAL iajs-3013 277 4 174 CARDINAL iajs-3013 277 5 ihjpas PERSON iajs-3013 278 1 36(1)2023 310 13 DATE iajs-3013 279 1 ali PERSON iajs-3013 279 2 a. PERSON iajs-3013 279 3 haibat k. m. PERSON iajs-3013 279 4 j. of al-qadisiyah PERSON