The Dual notion of fuzzy prime submodules

Authors

  • Habibollah Ansari-Toroghy University of Guilan
  • Farideh Mahboobi-Abkenar University of Guilan

DOI:

https://doi.org/10.30495/jme.v13i0.773

Keywords:

fuzzy submodule, fuzzy second submodule, minimal fuzzy submodule

Abstract

Let $R$ be a commutative ring and let $M$ be an $R$-module. In this paper, we introduce the dual notion of fuzzy prime (that is, fuzzy second) submodules of $M$ and explore some of the basic properties of this class of submodules. We say a non-zero fuzzy submodule $\mu$ of $M$ is fuzzy second if for each $r \in R$, we have $1_r.\mu = \mu$ or $1_r.\mu = 1_\theta$. It is shown that the fuzzy second submodules is a proper subclass of the fuzzy coprimary submodules.

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Published

2019-01-08

Issue

Vol. 13

Section

Vol. 13, No. 2, (2019)

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