On $\tau_M$-Semilocal Modules and Rings

Authors

  • Y. Talebi Department of Mathematics, Faculty of Science, University of Mazandaran, Babolsar
  • T. Amoozegar Department of Mathematics, Faculty of Science, University of Mazandaran, Babolsar
  • Zh. Mansoury Department of Mathematics, Faculty of Science, University of Mazandaran, Babolsar

DOI:

https://doi.org/10.26713/cma.v1i3.122

Keywords:

$\tau_M$-Supplement submodules, Weakly $\tau_M$-supplemented modules, $\tau_M$-Semilocal rings

Abstract

Let $\tau_M$ be any preradical for $\sigma[M]$ and $N$ any module in $\sigma[M]$. In [2], Al-Takhman, Lomp and Wisbauer defined and studied the concept of $\tau_M$-supplemented module. In this paper we define the concept of weakly $\tau_M$-supplemented module and investigate some properties of such modules. We show that weakly $\tau_M$-supplemented module $N$ is $\tau_M$-semilocal (i.e., $N/\tau_M(N)$ is semisimple) and that $R$ is a $\tau$-semilocal ring if and only if $_{R}R$ (or $R_R$) is weakly $\tau_M$-supplemented.

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CITATION

How to Cite

Talebi, Y., Amoozegar, T., & Mansoury, Z. (2010). On $\tau_M$-Semilocal Modules and Rings. Communications in Mathematics and Applications, 1(3), 145–151. https://doi.org/10.26713/cma.v1i3.122

Issue

Vol. 1 No. 3 (2010)

Section

Research Article

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