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 …

We introduce a notion of total acyclicity associated to a subcategory of an abelian category
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius …

Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

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 …

In the last years (Gorenstein) homological dimensions relative to a semidualizing module C
have been subject of several works as interesting extensions of (Gorenstein) homological …

We introduce relative preresolving subcategories and precoresolving subcategories of an
abelian category and define homological dimensions and codimensions relative to these …

We introduce the right (left) Gorenstein subcategory relative to an additive subcategory CC
of an abelian category AA, and prove that the right Gorenstein subcategory rG (G (C) G (C)) …

In this paper, we give a relationship between projective generators (resp., injective
cogenerators) in the category of R-modules and the counterparts in the category of …

Let R be a commutative (possibly non-Noetherian) ring (in order to make things less
technical) and C a semidualizing R-module. In this article, we introduce and investigate the …