Baer-Kaplansky classes in categories: transfer via functors

Crivei S., Tutuncu D., Tribak R.

COMMUNICATIONS IN ALGEBRA, vol.48, pp.3157-3169, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48
  • Publication Date: 2020
  • Doi Number: 10.1080/00927872.2020.1729785
  • 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.3157-3169
  • Hacettepe University Affiliated: Yes

Abstract

We study the transfer of Baer-Kaplansky classes via additive functors between preadditive categories. We show that the Baer-Kaplansky property is well behaved with respect to fully faithful functors, but not with respect to their usual generalizations such as faithful, full, separable, naturally full, Maschke or dual Maschke functors. We also present the transfer of the Baer-Kaplansky property between subclasses of static and adstatic objects induced by adjoint pairs of functors. We mainly give applications to (graded) module categories and comodule categories.