On objects with a semilocal endomorphism rings in finitely accessible additive categories
type: Item
instance of: scholarly article
title: On objects with a semilocal endomorphism rings in finitely accessible additive categories
zbMATH Open document ID: 1333.18003
author: Mustafa Kemal Berktaş
published in: Algebras and Representation Theory
publication date: 2015-12-07T00:00:00Z
review text: It is well known that objects with semilocal endomorphism rings have interesting and useful properties (e.g. they have the cancellation property). In the present paper the authors prove that if \(A\) is an object in a finitely accessible additive category \(\mathcal{A}\) such that it has finite pure Goldie dimension and that every pure mono endomorphism of \(A\) is an isomorphism, then the endomorphism ring of A is semilocal (Theorem 5).
Mathematics Subject Classification ID: 18C35
Mathematics Subject Classification ID: 18A25
Mathematics Subject Classification ID: 18E25
Mathematics Subject Classification ID: 16L30
zbMATH DE Number: 6516644
zbMATH Keywords: accessible categories
zbMATH Keywords: Grothendieck categories
zbMATH Keywords: Camps-Dicks theorem
zbMATH Keywords: pure Goldie dimension
reviewed by: Simion Sorin Breaz
MaRDI profile type: Publication
full work available at URL: s10468-015-9545-8
OpenAlex ID: W870064504
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DOI: 10.1007/S10468-015-9545-8
description: scientific article; zbMATH DE number 6516644