A semi-dualizing module over a commutative noetherian ring A is a finitely generated
module C with RHomA (C, C)≃ A in the derived category D (A). We show how each such …

In this paper, we prove that the global Gorenstein projective dimension of a ring $ R $ is
equal to the global Gorenstein injective dimension of $ R $ and that the global Gorenstein …

We study the Gorenstein weak global dimension of associative rings and its relation to the
Gorenstein global dimension. In particular, we prove the conjecture that the Gorenstein …

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

We prove that any faithful Frobenius functor between abelian categories preserves the
Gorenstein projective dimension of objects. Consequently, it preserves and reflects …

For a finitely generated module M over a commutative Noetherian ring R, we settle the
Auslander–Reiten conjecture when at least one of Hom R (M, R) and Hom R (M, M) has …

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 …

In this paper, we investigate the weak Gorenstein global dimension. We are mainly
interested in studying the problem when the left and right weak Gorenstein global …

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

In this paper, we consider the openness of the P-locus of a finitely generated module over a
commutative noetherian ring in the case where P is each of the properties FID, Gor, Can …