Modules having Baer summands


Calci T. P. , Halicioglu S., Harmanci A.

COMMUNICATIONS IN ALGEBRA, vol.45, no.11, pp.4610-4621, 2017 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 11
  • Publication Date: 2017
  • Doi Number: 10.1080/00927872.2016.1273360
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.4610-4621

Abstract

Let R be an arbitrary ring with identity and M a right R-module with S= End(R)(M). Let F be a fully invariant submodule of M and I-1(F) denotes the set {m is an element of M : Im subset of F} for any subset I of S. The module M is called F-Baer if I-1(F) is a direct summand of M for every left ideal I of S. This work is devoted to the investigation of properties of F-Baer modules. We use F-Baer modules to decompose a module into two parts consists of a Baer module and a module determined by fully invariant submodule F, namely, for a module M, we show that M is F-Baer if and only if M = F circle plus N where N is a Baer module. By using F-Baer modules, we obtain some new results for Baer rings.