On $\tau_M$-Semilocal Modules and Rings

Y. Talebi, T. Amoozegar, Zh. Mansoury

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.

Keywords


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

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DOI: http://dx.doi.org/10.26713%2Fcma.v1i3.122

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eISSN 0975-8607; pISSN 0976-5905