The solution of an open problem on semigroup inclusion classes

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 (A lattice of semigroup inclusion classes consisting of unions of varieties of generalised inflations of rectangular bands, 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.