On Weak Dual Rickart Modules and Dual Baer Modules |
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Authors: | Rachid Tribak |
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Affiliation: | 1. Centre Régional des Métiers de l'Education et de la Formation (CRMEF)-Tanger , Tangier , Morocco tribak12@yahoo.com |
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Abstract: | We introduce and study the notion of wd-Rickart modules (i.e. modules M such that for every nonzero endomorphism ? of M, the image of ? contains a nonzero direct summand of M). We show that the class of rings R for which every right R-module is wd-Rickart is exactly that of right semi-artinian right V-rings. We prove that a module M is dual Baer if and only if M is wd-Rickart and M has the strong summand sum property. Several structure results for some classes of wd-Rickart modules and dual Baer modules are provided. Some relevant counterexamples are indicated. |
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Keywords: | Dual Rickart modules Dual Baer modules Endomorphism rings Semipotent rings and modules Weak dual Rickart modules |
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