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.
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Presented by R. Willard.
Dedicated to E. Tamás Schmidt.
This article is part of the topical collection “In memory of E. Tamás Schmidt” edited by Robert W. Quackenbush.
This material is based upon work supported by the National Science Foundation Grant no. DMS 1500254 and the Hungarian National Foundation for Scientific Research (OTKA) Grant nos. K104251 and K115518.
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Kearnes, K.A., Kiss, E.W. & Szendrei, Á. Varieties whose finitely generated members are free. Algebra Univers. 79, 3 (2018). https://doi.org/10.1007/s00012-018-0480-5
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DOI: https://doi.org/10.1007/s00012-018-0480-5