Let SCR be a semidualizing bimodule with S left coherent and R right coherent. For a non-
negative integer n, it is shown that l. FP-id S (C)= r. FP-id R (C)≤ n if and only if every finitely …

设PC (R) 和BC (R) 是与半对偶模C 相关的C-投射模类和Bass 类, PC (R)⊆ W⊆ BC (R).
本文主要研究与半对偶模相关的Gorenstein 范畴ÇC (W) 的性质, 证明了ÇC (W) 投射分解类 …

From the notion of (co) generator in relative homological algebra, we present the concept of
finite balanced system $[(\mathcal {X},\omega);(\nu,\mathcal {Y})] $ as a tool to induce …

We first introduce in the paper the W_F-Gorenstein modules to establish the following Foxby
equivalence: \xymatrix@C=80ptG(F)∩A_C\ar@\lt0.5ex>r^C⊗_R-\amp\,\,\,\,G(W_F)\ar@\lt0 …

Let S and {iaR} be two associative rings, let SCR be a semidualizing (S, R)-bimodule. We
introduce and investigate properties of the totally reflexive module with respect to SCR and …

Let S and R be rings and SCR a semidualizing bimodule. We define and study GC-FP-
injective R-modules, and these modules are exactly C-Gorenstein injective R-modules …

We contribute to the theory of G-dimension relative to a semidualizing module C, in
connection to the properties of a module being totally C-reflexive, Ck-torsionless, and Ck …

We use the theory of Auslander–Buchweitz approximations to classify certain resolving
subcategories containing a semidualizing or a dualizing module. In particular, we show that …

It is now well known that the conditions used by Auslander to define the Gorenstein
projective modules on Noetherian rings are independent. Recently, Ringel and Zhang …

Let 𝒜 be an abelian category with enough projectives. In the category of 𝒜-complexes, we
introduce generalized Tate cohomology with respect to subcategories, and show that there …