The Schr\"{o}der-Bernstein problem for Modules
Rings and Algebras
2017-03-16 v1
Abstract
In this paper we study the Schr\"{o}der-Bernstein problem for modules. We obtain a positive solution for the Schr\"{o}der-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 Schr\"{o}der-Bernstein problem has a positive solution even for modules that are invariant only under automorphisms of their injective envelopes or pure-injective envelopes.
Keywords
Cite
@article{arxiv.1703.04787,
title = {The Schr\"{o}der-Bernstein problem for Modules},
author = {Pedro A. Guil Asensio and Berke Kalebogaz and Ashish K. Srivastava},
journal= {arXiv preprint arXiv:1703.04787},
year = {2017}
}