Let 𝒜 be an abelian category having enough projective and injective objects, and let 𝒯 be
an additive subcategory of 𝒜 closed under direct summands. A known assertion is that in a …

Let A be an abelian category. A subcategory X of A is called a resolving subcategory if X is
closed under extensions and kernels of epimorphisms and contains all projective objects of …

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …

Let C be a semidualizing module over a commutative noetherian ring R. We exhibit an
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …

As a dual of the Auslander transpose of modules, we introduce and study the cotranspose of
modules with respect to a semidualizing module C. Then using it we introduce nC …

The definition of a pseudo-dualizing complex is obtained from that of a dualizing complex by
dropping the injective dimension condition, while retaining the finite generatedness and …

Let R be an associative ring with identity. We establish that the generalized Auslander-
Reiten conjecture implies the Wakamatsu tilting conjecture. Furthermore, we prove that any …

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

Let R and S be rings and RωS a semidualizing bimodule. We introduce and study the
adjoint cotransposes of modules and adjoint n-ω-cotorsionfree modules. We show that the …

Let R and S be rings, and let R ω S be a semidualizing bimodule. We prove that there exists
a Morita equivalence between the class of∞-ω-cotorsion-free modules and a subclass of the …