On K-extending modules

Tayyebeh Amouzegar

Abstract


Let $M$ be a right $R$-module and $S=End_R(M)$. We call $M$ a $\mathcal{K}$-extending module if for every element $\phi\in S$, Ker$\phi$ is essential in a direct summand of $M$. In this paper we investigate these modules. We give a characterization of $\mathcal{K}$-extending modules. We prove that if $M$ is a projective self-generator module, then $M$ is a $\mathcal{K}$-extending module and every finitely generated projective right ideal of $S$ is a summand if and only if $S$ is semiregular and $\Delta(M)=Jac(S)$, where $\Delta(M)=\{f\in S \mid Ker f\leq^e M \}$ if and only if $M$ is $Z(M)$-$\mathcal{I}$-lifting.

Keywords


continuous module; extending module; lifting module; semiregular ring.

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References


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DOI: http://dx.doi.org/10.5556/j.tkjm.48.2017.1838

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