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Algebra universalis

, 79:3 | Cite as

Varieties whose finitely generated members are free

  • Keith A. Kearnes
  • Emil W. Kiss
  • Ágnes Szendrei
Article
Part of the following topical collections:
  1. In memory of E. Tamás Schmidt

Abstract

We prove that a variety of algebras whose finitely generated members are free must be definitionally equivalent to the variety of sets, the variety of pointed sets, a variety of vector spaces over a division ring, or a variety of affine vector spaces over a division ring.

Keywords

Free algebra Abelian algebra Affine algebra Minimal variety 

Mathematics Subject Classification

Primary 08B20 Secondary 08A05 03C35 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Keith A. Kearnes
    • 1
  • Emil W. Kiss
    • 2
  • Ágnes Szendrei
    • 1
  1. 1.Department of MathematicsUniversity of ColoradoBoulderUSA
  2. 2.Department of Algebra and Number TheoryLoránd Eötvös UniversityBudapestHungary

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