Rings whose pure-injective right modules are direct sums of lifting modules

GUIL ASENSIO P. A., Tutuncu D. K.

JOURNAL OF ALGEBRA, vol.383, pp.78-84, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 383
  • Publication Date: 2013
  • Doi Number: 10.1016/j.jalgebra.2012.12.014
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.78-84
  • Hacettepe University Affiliated: Yes

Abstract

It is shown that every pure-injective right module over a ring R is a direct sum of lifting modules if and only if R is a ring of finite representation type and right local type. In particular, we deduce that every left and every right pure-injective R-module is a direct sum of lifting modules if and only if R is (both sided) serial artinian. Several examples are given to show that this condition is not left right symmetric. (C) 2013 Elsevier Inc. All rights reserved.