Abstract
Suppose that F is a field of prime characteristic p and V p is the variety of associative algebras over F defined by the identities [[x, y], z] = 0 and x p = 0 if p > 2 and by the identities [[x, y], z] = 0 and x 4 = 0 if p = 2 (here [x, y] = xy − yx). As is known, the free algebras of countable rank of the varieties V p contain non-finitely generated T-spaces. We prove that the varieties V p are minimal with respect to this property.
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