The solution of an open problem on semigroup inclusion classes
2021
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.
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