This book is a comprehensive treatment of the representation theory of maximal Cohen-
Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative …

We study Artin algebras Λ and commutative Noetherian complete local rings R in connection
with the following decomposition property of Gorenstein-projective modules: We show that …

A ring is left Gorenstein regular if the classes of left modules with finite projective dimension
and finite injective dimension coincide and the injective and projective finitistic left …

The monomorphism category S n (X) is introduced, where X is a full subcategory of the
module category A-mod of an Artin algebra A. The key result is a reciprocity of the …

Let be an Artin algebra. Under suitable conditions, we describe all the modules in⊥ Λ, and
obtain criteria for the Gorensteinness of Λ. As applications, we determine explicitly all the …

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 …

For a finite acyclic quiver Q, an ideal I of a path algebra kQ generated by monomial relations,
and a finite-dimensional k-algebra A, we introduce the separated monic representations of a …

An artin algebra is called CM-free provided that all its finitely generated Gorenstein
projective modules are projective. We show that a connected artin algebra with radical …

We determine all the Gorenstein-projective modules over the T2-extension of a Gorenstein
algebra, and over (AM0B), where A and B are self-injective algebras, and M is an AB …

An Artin algebra A is said to be CM-finite if there are only finitely many isomorphism classes
of indecomposable finitely generated Gorenstein-projective A-modules. Inspired by …