On a class of dual Rickart modules

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

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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Published
15.07.2020
How to Cite
Tribak, R. “On a Class of Dual Rickart Modules”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 7, July 2020, pp. 960-7, doi:10.37863/umzh.v72i7.6021.
Section
Research articles