FREE OBJECTS IN A VARIETY OF COMMUTATIVE VECTOR VALUED SEMIGROUPS

Abstract

In [5] constructions of free objects in some classes of \((n,m)\)-semigroups are given. In this paper we give a description of a free object with a given nonempty basis in a class of commutative \((n,m)\)-semigroups defined by a system of identities of the form

\[
[x_1^p]=[y_1^q],
\]

where \(p,q>m\) and \((x_1,\ldots,x_p)=(y_1,\ldots,y_q)\).