Affiliation:
1. Department of Mathematics, Ankara University, Ankara, Turkey
2. Department of Mathematics, Hacettepe University, Ankara, Turkey
Abstract
Let R be a ring with identity, M be a right R-module and F be a fully
invariant submodule of M. The concept of an F-inverse split module M has
been investigated recently. In this paper, we approach to this concept with
a different perspective, that is, we deal with a notion of an F-image split
module M, and study various properties and obtain some characterizations of
this kind of modules. By means of F-image split modules M, we focus on
modules M in which fully invariant submodules F are dual Rickart direct
summands. In this way, we contribute to the notion of a T-dual Rickart
module M by considering Z?2 (M) as the fully invariant submodule F of M. We
also deal with a notion of relatively image splitness to investigate direct
sums of image split modules. Some applications of image split modules to
rings are given.
Publisher
National Library of Serbia