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RAD-SUPPLEMENTING MODULES
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 Title & Authors
RAD-SUPPLEMENTING MODULES
Ozdemir, Salahattin;
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 Abstract
Let R be a ring, and let M be a left R-module. If M is Rad-supplementing, then every direct summand of M is Rad-supplementing, but not each factor module of M. Any finite direct sum of Rad-supplementing modules is Rad-supplementing. 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, reduced and the free left R-module is Rad-supplementing if and only if R is reduced and the free left R-module 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 left perfect, where P(R) is the sum of all left ideals I of R such that Rad I = I.
 Keywords
supplement;Rad-supplement;supplementing module;Rad-supplementing module;perfect ring;
 Language
English
 Cited by
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