On rings admitting nonzero homomorphisms between non-projective modules
[ X ]
Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Taylor & Francis Inc
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In a recent paper, Turkoglu have studied the rings admitting nonzero homomorphisms between any two non-projective modules (property (T)). His work raises the following question: What are the rings with nonzero maps between non-projective right modules and singular simple modules? As a generalization of the property (T), we consider two families of rings: those rings with nonzero maps from any non-projective module to any singular simple module (property (T1)) and those rings with nonzero maps from any singular simple module to any non-projective module (property (T2)). Complete characterizations of both classes of rings are obtained and it is shown, in particular, that the rings satisfying property (T) are precisely those rings satisfying both properties (T1) and (T2). We show that R satisfies (T) if and only if R has a unique singular simple right R-module, and R is either two-sided Artinian hereditary serial or right completely coretractable. Furthermore, we prove that a commutative ring R has the property (T) if and only if there is a ring decomposition R approximately equal to AxB , where A is semisimple Artinian and B satisfies one of the following conditions: (1) B is a semi-Artinian max ring with unique singular simple right R-module. (2) B is an Artinian hereditary serial ring with unique singular simple right R-module.
Açıklama
Anahtar Kelimeler
Projective modules, (semi-)Artininan rings, singular simple modules
Kaynak
Communications in Algebra
WoS Q Değeri
Q3
Scopus Q Değeri
Q2
Cilt
51
Sayı
4
