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- W2073235899 abstract "Let C be a class of some finitely presented left R -modules. A left R -module M is called C -injective, if Ext R 1 ( C , M ) = 0 for each C ∈ C . A right R -module M is called C-flat, if Tor 1 R ( M , C ) = 0 for each C ∈ C . A ring R is called C -coherent, if every C ∈ C is 2-presented. A ring R is called C -semihereditary, if whenever 0 → K → P → C → 0 is exact, where C ∈ C and P is finitely generated projective and K is finitely generated, then K is also projective. A ring R is called C -regular, if whenever P / K ∈ C , where P is finitely generated projective and K is finitely generated, then K is a direct summand of P. Using the concepts of C -injectivity and C -flatness of modules, we present some characterizations of C -coherent rings, C -semihereditary rings, and C -regular rings." @default.
- W2073235899 created "2016-06-24" @default.
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- W2073235899 date "2013-12-01" @default.
- W2073235899 modified "2023-10-16" @default.
- W2073235899 title "C-coherent rings, C-semihereditary rings and C-regular rings" @default.
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- W2073235899 doi "https://doi.org/10.1556/sscmath.50.2013.4.1256" @default.
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