A Research on the Generalizations of Modules Whose Submodules are Isomorphic to a Direct Summand
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Tarih
2024
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Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
A module M is called virtually semisimple (resp. virtually extending) if every submodule (resp. complement submodule) of M is isomorphic to a direct summand of M. It is known that virtually extending modules is a generalization of virtually semisimple modules. In this paper, the relationships between virtually extending modules and other generalizations of virtually semisimple modules are examined. Moreover, we introduce a new generalization of virtually semisimple modules; namely CH modules: We say a module M is a c-epi-retractable (or briefly CH module) if any complement submodule of M is a homomorphic image of M. CH modules contains the class of virtually extending modules and the class of epi-retractable modules. We also give some basic properties of this new module class.
Açıklama
Anahtar Kelimeler
Kaynak
Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi
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Cilt
17
Sayı
1
