Modules which are reduced over their endomorphism rings

N. Agayev, Sait Halicioglu, A. Harmanci, B. Ungor

Abstract

Let $R$ be an arbitrary ring with identity and
$M$ a right $R$-module with $S=$ End$_R(M)$.  The module $M$ is
called {\it reduced} if for any $m\in M$ and $f\in S$, $fm=0$
implies $f M\cap Sm=0$. In this paper, we investigate properties
of reduced modules and rigid modules.