On a class of dual Rickart modules

R. Tribak

doi:10.37863/umzh.v72i7.6021

R. Tribak Centre Regional des M ´ etiers de l’Education et de la Formation, Tanger, Morocco

DOI: https://doi.org/10.37863/umzh.v72i7.6021

Abstract

UDC 512.5

Let $R$ be a ring and let $\Omega_R$ 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 $Ass(M) \cap \Omega_R$ is a finite set. In addition, we introduce and study a
generalization of sd-Rickart modules.

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