Rings whose nonsingular right modules are R-projective
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Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Charles Univ, Fac Mathematics & Physics
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
A right R-module M is called R-projective provided that it is projective relative to the right R-module R-R. This paper deals with the rings whose all nonsingular right modules are R-projective. For a right nonsingular ring R, we prove that R-R is of finite Goldie rank and all nonsingular right R-modules are R-projective if and only if R is right finitely Sigma-CS and fiat right R-modules are R-projective. Then, R-projectivity of the class of nonsingular injective right modules is also considered. Over right nonsingular rings of finite right Goldie rank, it is shown that R-projectivity of nonsingular injective right modules is equivalent to R-projectivity of the injective hull E(R-R). In this case, the injective hull E(R-R) has the decomposition E(R-R) = U-R circle plus V-R, where U is projective and Hom(V, R/I) = 0 for each right ideal I of R. Finally, we focus on the right orthogonal class N-perpendicular to of the class IV of nonsingular right modules.
Açıklama
Anahtar Kelimeler
nonsingular module, R-projective module, flat module, perfect ring
Kaynak
Commentationes Mathematicae Universitatis Carolinae
WoS Q Değeri
N/A
Scopus Q Değeri
Q4
Cilt
62
Sayı
4
