Research ArticleNo Access

Envelopes, covers and semidualizing modules

Lixin Mao

Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, P. R. China

https://doi.org/10.1142/S0219498819501378Cited by:2 (Source: Crossref)

Abstract

Given an $R$ -module $C$ and a class of $R$ -modules $𝒟$ over a commutative ring $R$ , we investigate the relationship between the existence of $𝒟$ -envelopes (respectively, $𝒟$ -covers) and the existence of $Hom (C, 𝒟)$ -envelopes or $C \otimes 𝒟$ -envelopes (respectively, $Hom (C, 𝒟)$ -covers or $C \otimes 𝒟$ -covers) of modules. As a consequence, we characterize coherent rings, Noetherian rings, perfect rings and Artinian rings in terms of envelopes and covers by $C$ -projective, $C$ -flat, $C$ -injective and $C$ - $F P$ -injective modules, where $C$ is a semidualizing $R$ -module.

Communicated by A. Facchini

Keywords:

AMSC: 16D40, 16D90, 18G25

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