F-Baer objects with respect to a fully invariant short exact sequence in abelian categories

Crivei S., KESKİN TÜTÜNCÜ D., Olteanu G.

COMMUNICATIONS IN ALGEBRA, vol.49, no.12, pp.5041-5060, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 12
  • Publication Date: 2021
  • Doi Number: 10.1080/00927872.2021.1935986
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.5041-5060
  • Keywords: Abelian category, (dual) (strongly) Baer object, (dual) (strongly) F-Baer object, fully invariant short exact sequence, STRONGLY RICKART OBJECTS, DIRECT SUMS, T-RICKART, MODULES
  • Hacettepe University Affiliated: Yes

Abstract

We introduce and study (dual) relative F-Baer objects as specializations of (dual) relative split objects with respect to a fully invariant short exact sequence in AB3* (AB3) abelian categories. We analyze their relationship with (dual) relative Baer objects, and we study direct summands and direct sums of (dual) relative F-Baer objects. We give applications to module and comodule categories.