Let A be an abelian category and C an additive full subcategory of A. We provide a method
to construct a proper C-resolution (resp. coproper C-coresolution) of one term in a short …

Let S and R be rings and SCR a semidualizing bimodule. We investigate the relation
between the GC-syzygy with the C-syzygy of a module as well as the relation between the …

In this article, the new concept of relative Gorenstein flat modules is introduced. We give a
survey of their behavior in terms of both structural and dimension properties. We relate the …

We introduce and investigate Tate homology \rmtor of modules of finite Gorenstein flat
dimension. In particular, we show that over a right coherent ring R, \rmtor_i^R(M,N)≅ …

The notion of linkage with respect to a semidualizing module is introduced. This notion
enables us to study the theory of linkage for modules in the Bass class with respect to a …

This paper aims at generalizing the notions of “Auslander dual”,“k-torsionless” and “k-th
syzygy” modules to the relative setting with respect to a semidualizing module. It is shown …

In this paper, we contribute to the theory of reduced G-perfection and horizontal linkage of
modules over a commutative, Noetherian (typically, local) ring R, in the general setting …

In this paper we further develop the theory of linkage with respect to a semidualizing module
C introduced in 2018 by Dibaei and Sadeghi. It is shown that under certain conditions a …

Let (L, A) be a fixed complete duality pair. Firstly, the author introduced the Gorenstein (L, A)-
injective dimension of complexes, gave its characterization, and proved that Gorenstein (L …

We introduce and investigate in this paper a kind of Tate homology of modules over a
commutative coherent ring based on Tate ℱC-resolutions, where C is a semidualizing …