On Singly Flat and Singly Injective Modules
[ X ]
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Singapore Pte Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Recall that a left module A (resp. right module B) is said to be singly injective (resp. singly flat) if Ext(R)(1) (F/K, A) = 0 (resp. Tor(1)(R)(B, F/K) = 0) for any cyclic submodule K of any finitely generated free left R-module F. In this paper, we continue to study and investigate the homological objects related to singly flat and singly injective modules and module homomorphisms. Along the way, the right orthogonal class of singly flat right modules and the left orthogonal class of singly injective left modules are introduced and studied. These concepts are used to extend the some known results and to characterize pseudo-coherent rings and left singly injective rings. In terms of some derived functors, some homological dimensions are investigated. As applications, some new characterizations of von Neumann regular rings and left PP rings are given. Finally, we study the singly flatness and singly injectivity of homomorphism modules over a commutative ring.
Açıklama
Anahtar Kelimeler
Singly flat module, Singly injective module, l-Projective module, l-Cotorsion module, PP ring, von Neumann regular ring
Kaynak
Bulletin of The Iranian Mathematical Society
WoS Q Değeri
Q4
Scopus Q Değeri
Q2
Cilt
47
Sayı
4
