This book is aimed to provide an introduction to local cohomology which takes cognizance
of the breadth of its interactions with other areas of mathematics. It covers topics such as the …

Among the finitely generated modules over a Noetherian ring $ R $, the semidualizing
modules have been singled out due to their particularly nice duality properties. When $ R …

We show that the set S (R) of shift-isomorphism classes of semidualizing complexes over a
local ring R admits a nontrivial metric. We investigate the interplay between the metric and …

In this article we present a systematic study of the reflexivity properties of homologically finite
complexes with respect to semidualizing complexes in the setting of nonlocal rings. One …

Given a homomorphism of commutative noetherian rings R→ S and an S-module N, it is
proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally …

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 …

For finitely generated module $ M $ over a local ring $ R $, the conventional notions of
complete intersection dimension $\cid_R M $ and Cohen-Macaulay dimension $\cmdim_R …

In this article we present a systematic study of the reflexivity properties of homologically finite
complexes with respect to semidualizing complexes in the setting of nonlocal rings. One …