Homological objects of min-pure exact sequences
[ X ]
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Hacettepe Univ, Fac Sci
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In a recent paper, Mao has studied min-pure injective modules to investigate the existence of min-injective covers. A min-pure injective module is one that is injective relative only to min-pure exact sequences. In this paper, we study the notion of min-pure projective modules which is the projective objects of min-pure exact sequences. Various ring characterizations and examples of both classes of modules are obtained. Along this way, we give conditions which guarantee that each min-pure projective module is either injective or projective. Also, the rings whose injective objects are min-pure projective are considered. The commutative rings over which all injective modules are min-pure projective are exactly quasi-Frobenius. Finally, we are interested with the rings all of its modules are min-pure projective. We obtain that a ring R is two-sided K & ouml;the if all right R-modules are min-pure projective. Also, a commutative ring over which all modules are min-pure projective is quasi-Frobenius serial. As consequence, over a commutative indecomposable ring with J(R)(2) = 0, it is proven that all R-modules are min-pure projective if and only if R is either a field or a quasi-Frobenius ring of composition length 2.
Açıklama
Anahtar Kelimeler
(min-)purity, K & ouml;the rings, universally mininjective rings, quasi-Frobenius rings
Kaynak
Hacettepe Journal of Mathematics and Statistics
WoS Q Değeri
N/A
Scopus Q Değeri
Q2
Cilt
53
Sayı
2
