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 study generalizations of regular modules by Ramamurthy and Mabuchi. These are also
generalizations of fully right idempotent and fully left idempotent rings, respectively. We also …

A regular ring R is separative provided that for all finitely generated projective right R-
modules A and B, A⊕ A≅ A⊕ B≅ A⊕ B implies that A≅ B. We prove, in this article, that a …

ON REGULARITY OF RINGS 1 Page 1 ON REGULARITY OF RINGS 1 Jianlong Chen Department
of Mathematics, Harbin Institute of Technology Harbin 150001, PR China and Department of …

A ring is right weakly regular (rwr) if every right ideal of the ring is idempotent. Such rings are
also called fully right idempotent. This paper gives a survey of the theory of rwr rings and …

A strongly regular ring R is one in which for all x∈ R, there is an a∈ R with x= x2a.
Equivalently, for all x there is an a with x= ax2. Such a ring is regular, duo, biregular, and a …

Building on a categorical approach of G. Janelidze and W. Tholen to descent theory for
modules, we show how this theory can be presented at the level of enriched categories …

In analogy to the elementwise definition of von Neumann regular rings an $ R $-module $ M
$ is called regular if given any element $ m\in M $ there exists $ f\in {\operatorname {Hom} …

On purely extending modules Page 1 Trends in Mathematics, © 1999 BirkhäuserVerlag
BaseJlSwitzeriand On purely extending modules John Clark * Abstract This note considers a …

In this paper, we consider associative rings with unit and unitary modules over these rings.
Let R be a ring and M a right unitary R-module. We denote by J (R) and J (M) the Jacobson …