The Schröder–Bernstein problem for dual F-Baer modules

Abstract

In this paper we introduce dual [Formula: see text]-Baer modules and give a characterization of them. Let [Formula: see text] be a module and [Formula: see text] a fully invariant submodule of [Formula: see text]. [Formula: see text] is called dual [Formula: see text]-Baer if for every family of endomorphisms [Formula: see text] of [Formula: see text], [Formula: see text] is a direct summand of [Formula: see text]. We prove that [Formula: see text] is dual [Formula: see text]-Baer if and only if [Formula: see text] for some submodule [Formula: see text] of [Formula: see text] with [Formula: see text] dual Baer. We obtain a positive solution for the Schröder–Bernstein problem for certain dual [Formula: see text]-Baer modules.