IDENTITIES IN MUTATIONS OF BICOMMUTATIVE ALGEBRAS

Abstract

The algebra B=(B,⋅ ) is called bicommutative if for each
element a, b,c қанағаттандыр B satisfies the following equilibrium:
a⋅(b⋅c)=b⋅(a⋅c),
(a⋅b)⋅c=(a⋅c)⋅b.

In this work, we study bicommutative Algebra by the product of mutations and prove that any bicommutative Algebra by the product of mutations satisfies the equilibrium of the third degree.