On Objects with a Semilocal Endomorphism Rings in Finitely Accessible Additive Categories
Algebras and Representation Theory, vol.18, no.5, pp.1389-1393, 2015 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 18 Issue: 5
- Publication Date: 2015
- Doi Number: 10.1007/s10468-015-9545-8
- Journal Name: Algebras and Representation Theory
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.1389-1393
- Keywords: Accessible categories, Grothendieck categories, Camps-Dicks theorem, Pure Goldie dimension
- Usak University Affiliated: Yes
Abstract
It is proved that if A is an object in a finitely accessible additive category A such that A has finite pure Goldie dimension and that every pure monomorphism A→A is an isomorphism, then its endomorphism ring EndA(A) is semilocal.