On Rickart modules

Document Type : Research Paper


1 Eropean University of Lefke, Cyprus

2 Department of Mathematics Ankara University

3 Hacettepe University, Turkey


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 Rickart} if for any $fin S$,
$r_M(f)=Se$ for some $e^2=ein S$. We prove that some results of
principally projective rings and Baer modules can be extended to
Rickart modules for this general settings.