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Symmetric modules over their endomorphism rings

Symmetric modules over their endomorphism rings

Let \(R\) be an arbitrary ring with identity and \(M\) a right\(R\)-module with \(S=End_R(M)\). In this paper, we study right\(R\)-modules \(M\) having the property for \(f,g \in End_R(M)\) andfor \(m\in M\), the condition \(fgm = 0\) implies \(gfm = 0\). We provethat some results of symmetric rings...

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Bibliographic Details
Main Authors: Ungor, Burcu, Kurtulmaz, Yosum, Halicioglu, Sait, Harmanci, Abdullah
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2015
Subjects:
symmetric modules
reduced modules
rigid modules
semicommutative modules
abelian modules
Rickart modules
principally projective modules
13C99
16D80
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/71
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Summary:Let \(R\) be an arbitrary ring with identity and \(M\) a right\(R\)-module with \(S=End_R(M)\). In this paper, we study right\(R\)-modules \(M\) having the property for \(f,g \in End_R(M)\) andfor \(m\in M\), the condition \(fgm = 0\) implies \(gfm = 0\). We provethat some results of symmetric rings can be extended to symmetricmodules for this general setting.

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