On a class of dual Rickart modules - Tribak, R. (Ukrains’kyi Matematychnyi Zhurnal, 2020)
UDC 512.5Let $R$ be a ring and let $Ω_R$ be the set of maximal right ideals of $R$. An $R$-module $M$ is called an sd-Rickart module if for every nonzero endomorphism $ f$ of $M$, $\Im f$ is a fully invariant direct summand of $M$. We obtain a characterization for an arbitrary direct sum of sd-Rickart modules to be sd-Rickart. We also obtain a decomposition of an sd-Rickart $R$-module $M$, provided $R$ is a commutative noetherian ring and $Ass(M) \cap Ω_R$ is a finite set. In addition, we introduce and study ageneralization of sd-Rickart modules.