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- Title
Envelopes, covers and semidualizing modules.
- Authors
Mao, Lixin
- 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 ⊗ 𝒟 -envelopes (respectively, Hom (C , 𝒟) -covers or C ⊗ 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.
- Subjects
NOETHERIAN rings; COMMUTATIVE rings; ARTIN rings; GORENSTEIN rings
- Publication
Journal of Algebra & Its Applications, 2019, Vol 18, Issue 7, pN.PAG
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498819501378