A new approach to $H$-supplemented modules via homomorphisms

Authors : Ali Reza Moniri HAMZEKOLAEE, Abdullah HARMANCI, Yahya TALEBI, Burcu ÜNGÖR

Pages : 1941-1955

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :The class of $H$-supplemented modules, which is a nice generalization of that of lifting modules, has been studied extensively in the last decade. As the concept of homomorphisms plays an important role in module theory, we are interested in $H$-supplemented modules relative to homomorphisms. Let $R$ be a ring, $M$ a right $R$-module, and $S=$ End$_{R}insert ignore into journalissuearticles values(M);$. We say that $M$ is endomorphism $H$-supplemented insert ignore into journalissuearticles values(briefly, $E$-$H$-supplemented); provided that for every $f\in S$ there exists a direct summand $D$ of $M$ such that $Imf+X=M$ if and only if $D+X=M$ for every submodule $X$ of $M$. In this paper, we deal with the $E$-$H$-supplemented property of modules and also a similar property for a module $M$ by considering Hom$_Rinsert ignore into journalissuearticles values(N,M);$ instead of $S$ where $N$ is any module.
Keywords : H Supplemented module, E H supplemented module, dual Rickart module, small submodule