On some intervals of varieties of completely regular semigroups

Abstract

Completely regular semigroups with the unary operation of inversion within their maximal subgroups form a variety under inclusion denoted by $$\mathcal {C}\mathcal {R}$$. The lattice of its subvarieties is denoted by $$\mathcal {L}(\mathcal {C}\mathcal {R})$$. Kernel, trace, left trace and right trace relations on $$\mathcal {L}(\mathcal {C}\mathcal {R})$$ induce operators which can be used to produce networks. For the pairs (kernel, trace)- and (left trace, right trace)-networks we establish strong properties. We consider examples of local- and core-relations networks in some special cases, as well as $$\mathbf {B}^\wedge \mathbf {B}^\vee $$-networks.