Abstract
Let R be a ring and n be a positive integer. R is called left n-coherent, if every n-presented left R-module is \((n+1)\)-presented. A left R-module M is called (n, 0)-injective if Ext\(^1_R(V, M)=0\) for every n-presented module V, a right R-module F is called (n, 0)-flat if Tor\(^R_1(F, V)=0\) for every n-presented module V, a left R-module M is called (n, 0)-projective if \(\mathrm{Ext}^1_R(M, N)=0\) for any (n, 0)-injective module N, and a right R-module M is called (n, 0)-cotorsion if \(\mathrm{Ext}^1_R(F, M)=0\) for any (n, 0)-flat module F. We give some characterizations and properties of (n, 0)-projective modules and (n, 0)-cotorsion modules. n-coherent rings, n-hereditary rings and n-regular rings are characterized by (n, 0)-projective modules, (n, 0)-cotorsion modules, (n, 0)-injective modules and (n, 0)-flat modules.
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Zhu, Z. Some results on n-coherent rings, n-hereditary rings and n-regular rings. Bol. Soc. Mat. Mex. 24, 81–94 (2018). https://doi.org/10.1007/s40590-017-0160-z
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DOI: https://doi.org/10.1007/s40590-017-0160-z
Keywords
- (n, 0)-Projective modules
- (n, 0)-Cotorsion modules
- n-Coherent rings
- n-Hereditary rings
- n-Regular rings