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- W3040803051 abstract "Let T be a weak torsion class of left R-modules and n a positive integer. A left R-module M is called (T, n)-injective if Ext(C, M) = 0 for each (T, n + 1)-presented left R-module C; a right R-module M is called (T, n)-flat if Tor(M, C) = 0 for each (T, n +1)-presented left R-module C; a left R-module M is called (T, n)-projective if Ext(M, N) = 0 for each (T, n)-injective left R-module N; the ring R is called strongly (T, n)-coherent if whenever 0 → K → P → C → 0 is exact, where C is (T, n + 1)-presented and P is finitely generated projective, then K is (T, n)-projective; the ring R is called (T, n)-semihereditary if whenever 0 → K → P → C → 0 is exact, where C is (T, n + 1)-presented and P is finitely generated projective, then pd(K) ⩽ n → 1. Using the concepts of (T, n)-injectivity and (T, n)-flatness of modules, we present some characterizations of strongly (T, n)-coherent rings, (T, n)-semihereditary rings and (T, n)-regular rings." @default.
- W3040803051 created "2020-07-16" @default.
- W3040803051 creator A5026654527 @default.
- W3040803051 date "2020-07-07" @default.
- W3040803051 modified "2023-10-16" @default.
- W3040803051 title "Strongly $(mathcal{T},n)$-coherent rings, $(mathcal{T},n)$-semihereditary rings and $(mathcal{T},n)$-regular rings" @default.
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- W3040803051 doi "https://doi.org/10.21136/cmj.2020.0377-18" @default.
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