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)≅ …

In this article, we establish, as a generalization of a result on the classical homological
dimensions of commutative rings, an upper bound on the Gorenstein global dimension of …

The main result asserts that a local commutative Noetherian ring is Gorenstein, if it
possesses a non-zero cyclic module of finite Gorenstein injective dimension. From this …

The main purpose of this article is to present some applications of the notion of Gorenstein
injective dimension of complexes over an associative ring. Among the applications, we give …

Yoneda raised the question of whether the tensor product of injective modules is injective.
Ishikawa showed that for a commutative noetherian ring R this is the case if the injective …

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 …

Let R be a commutative noetherian henselian non-Gorenstein local ring of depth zero.
Denote by mod R the category of all finitely generated R-modules, and by the full …

The so-called Ding-Chen ring is an n-FC ring which is both left and right coherent, and has
both left and right self FP-injective dimensions at most n for some non-negative integer n. In …

This book is intended as a reference for mathematicians working with homological
dimensions in commutative algebra and as an introduction to Gorenstein dimensions for …

We apply tilting theory to study modules of finite projective dimension. We introduce the
notion of finite and cofinite type for tilting and cotilting classes of modules, respectively …