The effect of singularity on a type of supplemented modules
نویسندگان
1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
2 Department of Computer Sciences, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
doi
10.22034/as.2023.3044چکیده
Let $R$ be a ring, $M$ a right $R$-module, and $S = End_R(M)$ the ring of all $R$-Endomorphisms of $M.$ We say that $M$ is Endomorphism $\delta$-$H$-supplemented (briefly, $E$-$\delta$-$H$-supplemented) provided that for every $\phi\in S,$ there exists a direct summand $D$ of $M$ such that $M = Im\phi + X$ if and only if $M = D + X$ for every submodule $X$ of $M$ with $M/X$ singular. In this paper, we prove that a non-$\delta$-cosingular module $M$ is $E$-$\delta$-$H$-supplemented if and only if $M$ is dual Rickart. We also show that every direct summand of a weak duo $E$-$\delta$-$H$-supplemented module inherits the property.
