Varieties whose finitely generated members are free
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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.
KeywordsFree algebra Abelian algebra Affine algebra Minimal variety
Mathematics Subject ClassificationPrimary 08B20 Secondary 08A05 03C35
- 3.Freese, R., McKenzie, R.: Commutator Theory for Congruence Modular Varieties, vol, 125. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (1987)Google Scholar
- 5.Hobby, D., McKenzie, R.: The Structure of Finite Algebras, vol. 76. Contemporary Mathematics. American Mathematical Society, Providence (1988)Google Scholar
- 8.Kearnes, K.A., Kiss, E.W.: The shape of congruence lattices. Mem. Amer. Math. Soc. 222, no. 1046 (2013)Google Scholar