An additive category with direct limits is said to be locally finitely presented provided that the
full subcategory of finitely presented objects is skeletally small and every object is a direct …

In this paper we show that how the representation theory of subcategories (of the category of
modules over an Artin algebra) can be connected to the representation theory of all modules …

Throughout this note, all rings will be self-basic connected artin algebras over a fixed
commutative local artin ring k and all modules will be finitely generated. Homomorphisms …

This paper aims to initiate a study of the representation theory of representation-finite artin
algebras in terms of the nilpotency of the radical of their module category. Firstly, we shall …

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 …

We characterize the finiteness of the representation type of an artin algebra in terms of the
behavior of the projective covers and the injective envelopes of the simple modules with …

Throughout this discussion R denotes a commutative artin ring with radical r. An R-algebra A
is said to be an artin R-algebra if it is finitely generated as an R-module. Suppose A is an …

Auslander-Reiten duality for module categories is generalized to some sufficiently nice
subcategories. In particular, our consideration works for $\mathcal {P}^{<\infty}(\Lambda) …

We study irreducible morphisms in the bounded derived category of finitely generated
modules over an Artin algebra Λ, denoted Db (Λmod), by means of the underlying category …

Let D be a full subcategory of an abelian category A. We study the relation between the
following properties of the subcategory D.(1) The subcategory D is contravariantly finite in …