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
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