Modules Whose Nonzero Endomorphisms Have E-small Kernels

Abdoul Djibril Diallo, Papa Cheikhou Diop and Mamadou Barry

Journal of Mathematics Research, 2018, vol. 10, issue 3, 111-117

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.

Keywords: Essential submodules; e-small submodules; e-small quasi-Dedekind modules (search for similar items in EconPapers)
Date: 2018
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