For an arbitrary ring R (always associative with 1) we denote by Mod R th category of all left
R-modules and by mod R the full subcategory of Mod R wi objects the finitely presented …

Introduction. The study of homologically finite subcategories has turned out to be important
in several contexts, especially in the representation theory of artin algebras. In this paper we …

We prove the following results for the subcategories of an abelian category: 1) The full
subcategory whose objects are kernels of the maps between two covariantly finite …

1. Preliminaries. For rings with identity, well known proper inclusions exist among the
classes of semisimple, left hereditary, left semihereditary, left noetherian, yon Neumann …

0.1. All rings considered in this paper have a nonzero identity and all modules are unital. For
every ring R, Mod-R (R-Mod) denotes the category of all right (left) R-modules. The symbol …

A Serre class in an abelian category is a nonempty subclass J> of cĄ closed under
subobjects, quotient objects, and extensions. Th importance of such classes stems from the …

This paper continues the investigation begun in [4] concerning conditions on rings which
lead to a unique decomposition of" torsion" modules into a direct sum of" primary" …

We are familiar to study rings S with identity if we are interested in homological method on
the ring theory. On the other hand, it seems for us that the theory of categories is some kind …

Let<'{f be an abelian category and F a (covariant) functor from<'{f to abelian groups. We say
that F is a coherent functor if there exists an exact sequence (X, _)--+(Y, _)--+ F--+ 0 where …

Let A be a ring with an identity and let AJ~ be the category of all left A-modules; throughout
this paper modules are assumed to be unitary. Let V be a finitely cogenerating, injective left …