A note on existence of envelopes and covers

Author:

Chen Jianlong,Ding Nanqing

Abstract

We prove the following results for a ring R. (a) If C is a class of right R-modules closed under direct summands and isomorphisms, then every right R-module has an epic C-envelope if and only if C is closed under direct products and submodules. (b) If R is left T-coherent and pure injective as a right R-module, then every T-finitely presented right R-module has a T-flat envelope, (c) Let R be a left T-coherent ring and injective right R-modules be T-flat. If every finitely presented left R-module has a flat envelope, then every T-finitely presented right R-module has a projective cover.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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1. Strongly J-n-Coherent rings;International Electronic Journal of Algebra;2023-10-28

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3. On rings with envelopes and covers regarding to C3, D3 and flat modules;Journal of Algebra and Its Applications;2020-09-19

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