A RECENT GENERALIZATION OF COFINITELY INJECTIVE MODULES
[ X ]
Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Honam Mathematical Soc
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Let R be an associative ring with identity and M be a left R-module. In this paper, we define modules that have the property (8 CE) ((8-CEE)), these are modules that have a 8-supplement (ample 8 supplements) in every cofinite extension which are generalized version of modules that have the properties (CE) and (CEE) introduced in [6] and so a generalization of Zoschinger's modules with the properties (E) and (EE) given in [23]. We investigate various properties of these modules along with examples. In particular we prove these: (1) a module M has the property (8-CEE) if and only if every submodule of M has the property (8 -CE); (2) direct summands of a module that has the property (8 -CE) also have the property (8 -CE); (3) each factor module of a module that has the property (8 -CE) also has the property (8 -CE) under a special condition; (4) every module with composition series has the property (8 CE); (5) over a 8 -V-ring a module M has the property (8 -CE) if and only if M is cofinitely injective; (6) a ring R is 8-semiperfect if and only if every left R-module has the property (8 -CE).
Açıklama
Anahtar Kelimeler
8-supplement, 8-semiperfect ring, cofinite extension
Kaynak
Honam Mathematical Journal
WoS Q Değeri
N/A
Scopus Q Değeri
N/A
Cilt
45
Sayı
3
