Envelopes, covers and semidualizing modules
L Mao - Journal of Algebra and Its Applications, 2019 - World Scientific
L Mao
Journal of Algebra and Its Applications, 2019•World ScientificGiven 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-FP-injective modules, where C is a semidualizing R-module.
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-FP-injective modules, where C is a semidualizing R-module.
Given an -module and a class of -modules over a commutative ring , we investigate the relationship between the existence of -envelopes (respectively, -covers) and the existence of -envelopes or -envelopes (respectively, -covers or -covers) of modules. As a consequence, we characterize coherent rings, Noetherian rings, perfect rings and Artinian rings in terms of envelopes and covers by -projective, -flat, -injective and --injective modules, where is a semidualizing -module.
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