H$^*$-condition on the set of submodules of a module

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar

10.29252/as.2019.1427

Abstract

In this work, we introduce $H^*$-condition on the set of submodules of a module. Let $M$ be a module. We say $M$ satisfies $H^*$ provided that for every submodule $N$ of $M$, there is a direct summand
$D$ of $M$ such that $(N+D)/N$ and $(N+D)/D$ are cosingular. We show that over a right perfect right $GV$-ring,
a homomorphic image of a $H^*$ duo module satisfies $H^*$.

Keywords


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