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Z-prime gamma submodule of gamma modules | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 8، دوره 13، شماره 1، خرداد 2022، صفحه 97-102 اصل مقاله (392.41 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.5461 | ||
| نویسندگان | ||
| Ali Abd Alhussein Zyarah* 1؛ Ahmad Hadi Hussain2؛ Hayder Kadhim Zghair3 | ||
| 1Iraqi Ministry of Education, General Directorate of Education for the Holy Karbala, Karbala, Iraq. | ||
| 2College of Engineering Al-musayab, Department of Energy Engineering, University of Babylon, Babil, Iraq | ||
| 3Information Technology College, Department of Software, University of Babylon, Iraq. | ||
| تاریخ دریافت: 12 اردیبهشت 1400، تاریخ بازنگری: 22 تیر 1400، تاریخ پذیرش: 16 مرداد 1400 | ||
| چکیده | ||
| Let $R$ be a $\Gamma$-ring and $\partial$ be an $R\Gamma$-module. A proper $R\Gamma$-submodule. $T$ of an $R\Gamma$-module $\partial$ is called Z-prime $R\Gamma$-submodule if for each $t\in \partial, \gamma \in \Gamma$ and $f \in \partial^{\ast}=Hom_{R_{\Gamma}}(\partial,R),f(t)\gamma t \in T$ implies that either $t \in T$ or $f(t)\in [T: _{R_{\Gamma}} \ \partial]$. The purpose of this paper is to introduce interesting theorems and properties of Z- prime $R\Gamma$-submodule of $R\Gamma$-module and the relation of Z-prime $R\Gamma$-submodule, which represents of generalization Z-prime R-submodule of R-module. | ||
| کلیدواژه‌ها | ||
| $Gamma$-ring؛ $RGamma$-module؛ $RGamma$-submodule؛ and prime $RGamma$-submodule | ||
| مراجع | ||
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[1] M.S. Abbas, H.R. Hassan and H.A. Abbas, On ΓR-projective gamma modules, Int. J. Algebra, 12(2) (2018) 53–60. [2] M.S. Abbas, H.R. Hassan and H.A. Abbas, ΓR-multiplication and ΓR-projective gamma Modules, Int. J. Contemporary Math. Sci. 13(2) (2018) 87–94. [3] R. Ameri and R. Sadeghi, Gamma modules, Ratio Math. 20(1) (2010) 127–147. [4] W. Barnes, On the Γ-rings of Nobusawa, Pacific J. Math. 18(3) (1966) 411–422. [5] A. ezaei and B. Davvaz, Tensor product of gamma modules, Afrika Mat. 26(7) (2015) 1601–1608. [6] N. Nobusawa, On a generalization of the ring theory, Osaka J. Math. 1(1) (1964) 81–89. [7] U. Tekır, U. Seng¨ul and G. Ziverbey, On prime ΓM-submodules of ΓM-modules, Int. J. Pure Appl. Math. 19(1) (2005) 123–128. [8] S. Uddin and S. Islam, Semi-prime ideals of gamma rings, Ann. Pure Appl. Math. 1(2) (2012) 186–191. [9] A.A.A. Zyarah and A.K.H. Alghafil, General formula for particular solution to the ordinary differential equation by variation of parameters of k th order, J. Interdis. Math.24(4) (2021) 1–6. [10] A.A.A. Zyarah and N.S. Al-Mothafar, On primary radical RΓ-submodules of RΓ-modules, J. Discrete Math. Sci. Crypt. 23(5) (2020) 1001–1007. [11] A.A.A. Zyarah and N.S. Al-Mothafar, Semiprime RΓ-submodules of multiplication RΓ-modules, Iraqi J. Sci. 61(5) (2020) 1104–1114. [12] A.A.A. Zyarah and N.S. Al-Mothafar, On S-prime and S-semiprime RΓ-submodules of RΓ-module, J. Phys. Conf. Ser. IOP Pub. (2021). | ||
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