S(N)-almost prime submodules
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초록
In this article, we focus on some notions of prime submod- ules over a commutative ring with identity. Suppose R is a commutative ring with identity and M is an R-module. A proper submodule N of M is called prime if rm is element of N implies r element of (N : M) or m element of N. In this article we give a generalized version of prime submodule in its localization which named as S(N)-almost prime submodule. This generalization was obtained by creating generalized version of almost prime submodule such that the submodule is not al- most prime but its localization is almost prime. Furthermore, some characterizations of S(N)-almost prime submodules and its relation to S(I)-almost prime ideals are given in this article.
Abstract
In this article, we focus on some notions of prime submod- ules over a commutative ring with identity. Suppose R is a commutative ring with identity and M is an R-module. A proper submodule N of M is called prime if rm is element of N implies r element of (N : M) or m element of N. In this article we give a generalized version of prime submodule in its localization which named as S(N)-almost prime submodule. This generalization was obtained by creating generalized version of almost prime submodule such that the submodule is not al- most prime but its localization is almost prime. Furthermore, some characterizations of S(N)-almost prime submodules and its relation to S(I)-almost prime ideals are given in this article.
참고문헌 (12)
- Ali M. M., "Multiplication Modules and Homogeneous Idealization II", Beitrage zur Al-gera und Geometrie, 48(2), pp.321~343 (2007)
- Ameri R, "On The Prime Submodules of Multiplication Modules", IJMMS, 32B(2), pp.1715~1724 (2003)
- Anderson D. D., "Weakly Prime Ideals", Houston Journal of Mathematics, 29(4), pp.831~840 (2003)
- Atani S. E., "Notes on the Primal Submodules", Chiang Mai J. Sci, 35(3), pp.399~410 (2008)
- Atani S. E., "On Weakly Prime Submodules", Tamkang Journal of Math-ematics, 38(3), pp.247~252 (2007)
- Eisenbud D., "Commutative Algebra with a view toward Algebraic Geometry" (2004), Springer-Verlag
- Jabbar A. K., "Generalization of Prime and Weakly Prime Submodules", Pure Math-ematical Sciences, 2(1), pp.1~11 (2013)
- Karsen M. D., "Multiplicative Theory of Ideals" (1971), Academic Press New York
- Khashan H. A., "On Almost Prime Submodules", Acta M. Scientia, 32B(2), pp.645~651 (2012)
- Li H., "An Introduction to Commutative Algebra" (2004), World Scientific Publishing Co. Pte. Ltd
- Bhatwadekar S.M., "Unique Factorization and Birth of Almost Primes", Communications in Algebra., (12), pp.43~49 (2005)
- Steven, Irawati, "On Characterizations of Prime and Almost Prime Submodules", JP Journal of Algebra, Number Theory and Applications, 40(3), pp.341~250 (2018)