Abstract Let R⊆ Q be rings such that the inclusion φ: R→ Q is an epimorphism in the
category of rings and Q is flat both as a right and as a left R-module. Assume that F. dim …

In a celebrated theorem, AW Goldie determined necessary and sufficient conditions that a
ring have a left quotient ring which is semisimple with minimum condition [4]. Our first main …

Abstract Let p: M→ N be a right minimal epimorphism. We prove that there exists a ring
isomorphism between two rings END RM (N)/J (END RM (N)) and END RN (M)/J (END RN …

If R is a hereditary left artinian ring, then R is left pure semisimple if and only if the family R-
ind of all finitely generated indecomposable left R-modules has a (unique) Ext-injective …

Let R be a commutative ring and let M be an R-module with the property that its zero
submodule has a primary decomposition. Let E be an injective R-module with W. Ass R (E) …

Endomorphism rings and the category of finitely generated projective modules Page 1
COMMLTNICATIONS IN ALGEBRA, 28(8), 3837-3 852 (2000) Endomorphism rings and the …

Let R be a commutative Noetherian ring and M a finitely generated R-module. Under various
hypotheses, it is proved that the center of End R (M) coincides with the endomorphism ring …

A ring extension is a ring homomorphism preserving identities. In this paper, we give the
definition of relatively free modules on ring extensions and develop some basic properties of …

If R is a right coherent ring, then left R-modules have covers by submodules of flat R-
modules if and only if all injective left R-modules have flat covers. This is the case if R is …

Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism
Y→ M is neat in Y, ie, the induced map Hom (S, Y)→ Hom (S, M) is surjective for any simple …