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

Gorenstein homological dimensions are refinements of the classical homological
dimensions, and finiteness singles out modules with amenable properties reflecting those of …

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 …

A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative
noetherian ring R is introduced and studied. One of the main results characterizes C-rigid …

The classical homological dimensions—the projective, flat, and injective ones—are usually
defined in terms of resolutions and then proved to be computable in terms of vanishing of …

Homological algebra originated in late 19th century topology. Homological studies of
algebraic objects, such as rings and modules, only got under way in the middle of the 20th …

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 show that the small and large restricted injective dimensions coincide for Cohen-
Macaulay rings of finite Krull dimension. Based on this, and inspired by the recent work of …

WIDTH OF COMPLEXES OF MODULES Introduction The extension of homological algebra
from modules to complexes of modules was started Page 1 ACTA MATHEMATICA …

RIGIDITY OF EXT AND TOR WITH COEFFICIENTS IN RESIDUE FIELDS OF A COMMUTATIVE
NOETHERIAN RING Page 1 Proceedings of the Edinburgh Mathematical Society (2019) 62 …