Abstract
Let R be a ring. A subclass T of left R-modules is called a weak torsion class if it is closed under homomorphic images and extensions. Let T be a weak torsion class of left R-modules and n a positive integer. Then a left R-module M is called T-finitely generated if there exists a finitely generated submodule N such that M/N ∈ T; a left R-module A is called (T,n)-presented if there exists an exact sequence of left R-modules
such that F0,..., Fn−1 are finitely generated free and Kn−1 is T-finitely generated; a left R-module M is called (T,n)-injective, if Extn R (A,M) = 0 for each (T, n+1)-presented left R-module A; a right R-module M is called (T,n)-flat, if TorR n (M,A) = 0 for each (T, n+1)-presented left R-module A. A ring R is called (T,n)-coherent, if every (T, n+1)-presented module is (n + 1)-presented. Some characterizations and properties of these modules and rings are given.
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This research was supported by the Natural Science Foundation of Zhejiang Province, China (LY18A010018).
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Zhu, Z. Coherence relative to a weak torsion class. Czech Math J 68, 455–474 (2018). https://doi.org/10.21136/CMJ.2018.0494-16
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DOI: https://doi.org/10.21136/CMJ.2018.0494-16