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december 2015 On weakly classical primary submodules
Hojjat Mostafanasab
Bull. Belg. Math. Soc. Simon Stevin 22(5): 743-760 (december 2015). DOI: 10.36045/bbms/1450389246

Abstract

In this paper all rings are commutative with nonzero identity. Let $M$ be an $R$-module. A proper submodule $N$ of $M$ is called a {\it classical primary submodule}, if for each $m\in M$ and elements $a,b\in R$, $abm\in N$ implies that either $am\in N$ or $b^tm\in N$ for some $t\geq1$. We introduce the notion of ``weakly classical primary submodules''. A proper submodule $N$ of $M$ is a {\it weakly classical primary submodule} if whenever $a,b\in R$ and $m\in M$ with $0\neq abm\in N$, then either $am\in N$ or $b^tm\in N$ for some $t\geq1$.

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Hojjat Mostafanasab. "On weakly classical primary submodules." Bull. Belg. Math. Soc. Simon Stevin 22 (5) 743 - 760, december 2015. https://doi.org/10.36045/bbms/1450389246

Information

Published: december 2015
First available in Project Euclid: 17 December 2015

zbMATH: 1336.13001
MathSciNet: MR3435080
Digital Object Identifier: 10.36045/bbms/1450389246

Subjects:
Primary: 13A15
Secondary: 13C99 , 13F05

Keywords: Classical primary submodule , Weakly classical primary submodule , Weakly primary submodule

Rights: Copyright © 2015 The Belgian Mathematical Society

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Vol.22 • No. 5 • december 2015
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