The Schroder-Bernstein problem for modules

Guil Asensio P. A., KALEBOĞAZ B., Srivastava A. K.

JOURNAL OF ALGEBRA, vol.498, pp.153-164, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 498
  • Publication Date: 2018
  • Doi Number: 10.1016/j.jalgebra.2017.11.029
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.153-164
  • Hacettepe University Affiliated: Yes

Abstract

In this paper we study the Schroder-Bernstein problem for modules. We obtain a positive solution for the Schroder Bernstein problem for modules invariant under endomorphisms of their general envelopes under some mild conditions that are always satisfied, for example, in the case of injective, pure-injective or cotorsion envelopes. In the particular cases of injective envelopes and pure-injective envelopes, we are able to extend it further and we show that the Schroder-Bernstein problem has a positive solution even for modules that are invariant only under automorphisms of their injective envelopes or pure-injective envelopes. (C) 2017 Elsevier Inc. All rights reserved.