In this paper, we mainly investigate the $\mathfrak {X} $-Gorenstein projective dimension of
modules and the (left) $\mathfrak {X} $-Gorenstein global dimension of rings. Some …

In this paper, we prove that the Gorenstein analogue of the well-known Auslander's theorem
on the global dimension holds true. Namely, we prove that the Gorenstein global dimension …

Abstract Let T=(A 0 UB) be a formal triangular matrix ring, where A and B are rings and U is
a (B, A)-bimodule. We prove that, if T is a right coherent ring, UB has finite flat dimension, UA …

A ring R is called left “GF-closed”, if the class of all Gorenstein flat left R-modules is closed
under extensions. The class of left GF-closed rings includes strictly the one of right coherent …

In this article, we investigate the change of rings theorems for the Gorenstein dimensions
over arbitrary rings. Namely, by the use of the notion of strongly Gorenstein modules, we …

In this article, we introduce and study the Gorenstein cotorsion dimension of modules and
rings. It is shown that this dimension has nice properties when the ring in question is left GF …

Let $(R,\frak m, k) $ be a noetherian local ring. It is well-known that $ R $ is regular if and
only if the injective dimension of $ k $ is finite. In this paper it is shown that $ R $ is …

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 …

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 …

We define a notion of Gorenstein flat dimension for unbounded complexes over left GF-
closed rings. Over Gorenstein rings we introduce a notion of Gorenstein cohomology for …