Weakly Nearly Semiprime Submodules and Some Related Concepts
DOI:
https://doi.org/10.29304/jqcm.2020.12.2.686Keywords:
Weakly semiprime submodules, WN-semiprime submodules, Jacobson radical of submodules, Multiplication R-modulesAbstract
In present paper the concept of WN-semiprime submodule of unitary left R-module over a commutative ring with identity are introduced and studied, as a generalization of weakly semiprime submodules. Numerous basic properties of this concept are investigate. Where a proper submodule A of an R-module is said to be WN-semiprime, if whenever , for , implies that . Furthermore many characterizations of WN-semiprime submodule are introduced. Moreover, some properties of WN-semiprime submodules in some classes of modules are given.
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References
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[2] Haibat K. M. and Khalaf H. A., "Weakly Semi-2-Absorbing Submodules", Journal of Anbar university for Pure Sci. 12(2)(2018), 57-62.
[3] Haibat K. M. and Saif A. H., "WE-prime Subodules and WE-semiprime Submodules", Ibn AL-Haitham J. for Pure and Applied sci. 31(3)(2018), 109-117.
[4] Haibat K. M. and Ali S. S., "Weakly Nearly Prime Submodules", Ibn AL-Haitham J. for Pure and Applied sci. 33(2)(2020), To Appear
[5] Kasch, F., "Modules and Rings", London Math. Soc. Monographs, New York, Academic press, 1982.
[6] Smith P., "Some Remarks on Multiplication Modules",Arch. Math. 50(1988), 223-226.
[7] Goldi A. W., "Torsion free Modules and Rings", Journal of Algbra 1(1964), 266-287.
[8] Nuha H. A., 'The Radicals of Modules", M. Sc. Thesis, university of Baghdad(1996).
[9] Payman M. H., "Hollow Modules and Semi hollw Modules", M. Sc. Thesis, university of Baghdad (2005).
[10] Majid M. A. and Ghafur A., "Generalization Of Generalized Supplemented Modules", International J. of Algebra 6(29)(2012), 1431-1441.
[11] Anderson, F.W. and Fuller, K.R., "Rings and Categories of Modules", Springer-Verlag, New York. 1992.
[12] Ali S. M., "On cancellation Modules", M. Sc. Thesis, university of Baghdad(1992).
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Published
2020-05-05
How to Cite
Mohammadali, H. K., & Sadiq, A. S. (2020). Weakly Nearly Semiprime Submodules and Some Related Concepts. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(2), Math Page 1 – 10. https://doi.org/10.29304/jqcm.2020.12.2.686
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Math Articles
