Varieties of bicommutative algebras with identity of degree three
Abstract
The variety of bicommutative algebras is the class of all nonassociative algebras satisfying the polynomial identities (x1x2)x3=(x1x3)x2 and x1(x2x3)=x2(x1x3). In this paper we provide a complete description of varieties of bicommutative algebras over a field of characteristic zero that satisfy a polynomial identity of degree three. Furthermore, we establish a sufficient and necessary condition for a variety of bicommutative algebras to have a distributive lattice of subvarieties.
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