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arXiv · 1210.2893

Rad-supplementing modules

Salahattin Özdemir
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Abstract

Let R be an associative ring with unity and let M be an R-module. We call M (ample) Rad-supplementing if M has a (ample) Rad-supplement in every extension. If M is Rad-supplementing, then every direct summand of M is Rad-supplementing, but not each factor module of M. Every module with composition series is (Rad-)supplementing. M has a Rad-supplement in its injective envelope if and only if M has a Rad-supplement in every essential extension. R is left perfect if and only if R is semilocal and reduced, and the direct sum of countably many copies of R is Rad-supplementing if and only if R is reduced and the direct sum of countably many copies of R is ample Rad-supplementing. M is ample Rad-supplementing if and only if every submodule of M is Rad-supplementing. Every left R-module is (ample) Rad-supplementing if and only if R/P(R) is a left perfect ring, where P(R) is the sum of all left ideals of R such that Rad I=I.

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BibTeXRIS

Salahattin Özdemir. 2012-10-10. Rad-supplementing modules. https://doi.org/10.4134/jkms.2016.53.2.403

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