Abstract

Let $R$ be a commutative ring and  $M$ an unital $R$-module.  A submodule $L$ of $M$ is called essential submodule of $M$, if $L\cap K\neq\lbrace 0\rbrace$ for any nonzero submodule $K$ of $M$. A submodule $N$ of $M$ is called e-small submodule of $M$ if, for any  essential submodule   $L$ of $M$, $N+L= M$  implies $L=M$. An $R$-module $M$ is called e-small quasi-Dedekind module if, for each $f\in End_{R}(M),$ $ f\neq 0$ implies $Kerf$ is e-small in $M$. In this paper we introduce the concept of e-small quasi-Dedekind modules as a generalisation of quasi-Dedekind modules, and give some of their  properties and characterizations.

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