Modules having Baer summands

Calci T., HALICIOĞLU S., Harmanci A.

Communications in Algebra, vol.45, no.11, pp.4610-4621, 2017 (SCI-Expanded) 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 (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4610-4621
  • Keywords: Baer module, F-Baer module, t-Baer module, RICKART MODULES, DIRECT SUMS
  • Ankara University Affiliated: Yes


© 2017 Taylor & Francis.Let R be an arbitrary ring with identity and M a right R-module with S = EndR(M). Let F be a fully invariant submodule of M and I−1(F) denotes the set {m∈M:Im⊆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⊕N where N is a Baer module. By using F-Baer modules, we obtain some new results for Baer rings.