The solution of an open problem on semigroup inclusion classes

Abstract

The semigroup inclusion class $\mathbf{I} = [xyxy = xy; xyz \in \{xywz, xuyz\}]$ is the union of two maximal subvarieties of $\mathbf{GRB} = [xyzxy=xy]$. Monzo ( arXiv:1411.4860 ) described the lattice of semigroup inclusion classes below $\mathbf{I}$ and asked if $\mathbf{I}$ is covered by $\mathbf{GRB}$. Our main result is a characterization of $\mathbf{I}$ which makes it easy to answer Monzo's question in the negative.