Equationally extremal semilattices

Abstract

In the current paper we study extremal semilattices with respect to their equational properties. In the class ${\mathbf{S}}_n$ of all semilattices of order $n$ we find semilattices which have maximal (minimal) number of consistent equations. Moreover, we find a semilattice in ${\mathbf{S}}_n$ with maximal sum of numbers of solutions of equations.