A dual approach to the theory of inverse split modules

Abstract

Let R be an arbitrary ring with identity, M a right R-module and F a fully invariant submodule of M. The notion of an F-inverse split module M has been defined and studied by the present authors recently. In this paper, we introduce its dual notion, namely, dual F-inverse split module M. This work is devoted to investigation of various properties and characterizations of a dual F-inverse split module M. We include applications for rings and cosingular submodules. We also deal with the notion of relatively dual inverse splitness to investigate direct sums of dual inverse split modules.