We investigate for an artin algebra Λ when categories of dth syzygy modules are closed
under extensions. In this case they are functorially finite resolving, and have an associated …

For an exact category E, we study the Butler's condition “AR= Ex”: the relation of the
Grothendieck group of E is generated by Auslander-Reiten conflations. Under some …

This paper is devoted to showing how one can use the general theory for relative cotilting
modules developed in [6, 7] to construct artin algebras (i) with dominant dimension at least …

An Artin algebra is by definition virtually Gorenstein if the class of modules which are right
orthogonal (with respect to $\operatorname {Ext}^*(-,-) $) to all Gorenstein projective …

An artin algebra A is said to be CM-finite if there are only finitely many, up to isomorphisms,
indecomposable finitely generated Gorenstein-projective A-modules. We prove that for a …

Auslander conjectured that every Artin algebra satisfies a certain condition on vanishing of
cohomology of finitely generated modules. The failure of this conjecture—by a 2003 …

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 introduce a notion of generalized Serre duality on a Hom-finite Krull–Schmidt
triangulated category T. This duality induces the generalized Serre functor on T, which is a …

Let Λ be an artin algebra over a local commutative artinian ring k. We consider the category
P (Λ) whose objects are morphims f: P→ Q with P and Q projective left Λ-modules. In P (Λ) …

Let A be a self-injective artin algebra and X a finitely generated module. In this paper, we are
mainly concerned with the problem posed by Tachikawa [16]: If Ext"(X, X)= 0 for all n> _ 1, is …