Baer-Kaplansky classes of vector spaces and modules determined by numerical invariants

D'Este G., KESKİN TÜTÜNCÜ D., Tribak R.

COMMUNICATIONS IN ALGEBRA, vol.51, no.3, pp.1089-1104, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.1080/00927872.2022.2125981
  • 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.1089-1104
  • Keywords: Abelian groups, Baer-Kaplansky classes, Baer-Kaplansky theorem, quivers and their representations
  • Hacettepe University Affiliated: Yes

Abstract

We show that reasonably large classes C of vector spaces, modules over non-commutative algebras and abelian groups are Baer-Kaplansky classes with additional properties. Indeed, modules in C such that their endomorphism rings are isomorphic vector spaces, or modules such that their endomorphism rings are isomorphic vector spaces with the same number of primitive idempotents may be actually isomorphic.