The aim of this paper is to give necessary and sufficient conditions for rings for which every
right self-small module is finitely generated. It is proved that: semi-simple rings, commutative …

The natural categorial notion of a compact object, for which the covariant functor Hom
commutes with direct sums, was first time studied in the context of module theory in 60's …

We will study commuting properties of the defect functor Def ß= Coker Hom C (ß,-)
Def_β=CokerHom_C(β,-) associate to a homomorphism ß in a finitely presented category …

Let R be an abelian regular and semiartinian ring with socle chain (Sα∣ α≤ σ). If λα
denotes the rank of the semisimple module Sα+ 1/Sα, for every α< σ, then the dimension …

The paper summarizes and partially deepens known results about von Neumann regular
rings over which there exist infinitely generated small modules ie such modules M that the …

We study the structure of infinitely generated small modules over abelian regular rings, ie,
modules over which the covariant functor Hom commutes with direct sums. It is shown that …