A Research on the Generalizations of Modules Whose Submodules are Isomorphic to a Direct Summand

Fatih Karabacak; Özgür Taşdemir

Makale detayları

A Research on the Generalizations of Modules Whose Submodules are Isomorphic to a Direct Summand

Yazarlar:

Fatih Karabacak | Özgür Taşdemir

Yayıncı:

Erzincan Binali Yildirim University

Ana Başlıklar:

Makine Mühendisliğinde Sayısal Yöntemler

Dergi:

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.17 Issue 1, pp.268-278

Belge Tipi:

Makale

Yayın Tarihi:

3/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001314222

pISSN:

2149-4584

Anahtar kelimeler:

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.

 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.

 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.

 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.

Makale detayları

A Research on the Generalizations of Modules Whose Submodules are Isomorphic to a Direct Summand

Yazarlar: Fatih Karabacak | Özgür Taşdemir

Yayıncı: Erzincan Binali Yildirim University

Ana Başlıklar: Makine Mühendisliğinde Sayısal Yöntemler

Dergi: Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.17 Issue 1, pp.268-278

Belge Tipi: Makale

Yayın Tarihi: 3/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001314222

pISSN: 2149-4584

virtually extending module

epi-retractable module

CH module

virtually semisimple module

Sayı

Yazarlar:

Fatih Karabacak | Özgür Taşdemir

Yayıncı:

Erzincan Binali Yildirim University

Ana Başlıklar:

Makine Mühendisliğinde Sayısal Yöntemler

Dergi:

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.17 Issue 1, pp.268-278

Belge Tipi:

Makale

Yayın Tarihi:

3/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001314222

pISSN:

2149-4584