Narrow Results

This paper deals with the variety of commutative non associative algebras satisfying the identity , γ ∈ K. In [3] it is proved that if γ = 0, 1 then any finitely generated algebra is nilpotent. Here we generalize this result by proving that if γ ≠ -1, then any such algebra is locally nilpotent. Our results require characteristic ≠ 2, 3.

Using purely syntactical arguments, it is shown that every nontrivial pseudovariety of monoids contained in DO whose corresponding variety of languages is closed under unambiguous product, for instance DA, is local in the sense of Tilson.