Weakly Poor Modules
[ X ]
Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Prof. Dr. Mehmet Zeki SARIKAYA
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this paper, weakly poor modules are introduced as modules whose injectivity domains are contained in the class of all copure-split modules. This notion gives a generalization of both poor modules and copure-injectively poor modules. Properties involving weakly poor modules as well as examples that show the relations between weakly poor modules, poor modules, impecunious modules and copure-injectively poor modules are given. Rings over which every module is weakly poor are right CDS. A ring over which there is a cyclic projective weakly poor module is proved to be weakly poor. Moreover, the characterizations of weakly poor abelian groups is given. It states that an abelian group A is weakly poor if and only if A is impecunious if and only if for every prime integer p, A has a direct summand isomorphic to Zpn for some positive integer n. Consequently, an example of a weakly poor abelian group which is neither poor nor copure-injectively poor is given so that the generalization defined is proper. © 2022, Prof. Dr. Mehmet Zeki SARIKAYA. All rights reserved.
Açıklama
Anahtar Kelimeler
(weakly) poor modules, CDS rings, Copure-injective modules, Copure-split modules
Kaynak
Konuralp Journal of Mathematics
WoS Q Değeri
Scopus Q Değeri
N/A
Cilt
10
Sayı
2
