M. Tamer KOŞAN

72102

Quasi-Dual Modules

Let R be a ring, M be a right R-module and S = EndR(M). M is called a quasi-dual module if, for every R-submodule N of M, N is a direct summand of rM(X) where X \subseteq S. In this article, we study and provide several characterizations of this module classes. We show that if M is quasi-dual module, then, for all m \in M, rM \ellS(m) = mR \oplus K for some submodule K of M. We also show that every quasi-dual module is a Kasch module and Z(SM) \subseteq Rad (MR).

Anahtar Kelimeler:

Quasi-dual module, Kasch module, Ikeda-Nakayama module

Quasi-Dual Modules

Let R be a ring, M be a right R-module and S = EndR(M). M is called a quasi-dual module if, for every R-submodule N of M, N is a direct summand of rM(X) where X \subseteq S. In this article, we study and provide several characterizations of this module classes. We show that if M is quasi-dual module, then, for all m \in M, rM \ellS(m) = mR \oplus K for some submodule K of M. We also show that every quasi-dual module is a Kasch module and Z(SM) \subseteq Rad (MR).

Keywords:

Quasi-dual module, Kasch module, Ikeda-Nakayama module,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

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