Certain homomorphisms of the lattice of varieties of completely simple semigroups
Mario Petrich, Norman R. Reilly · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1984
Abstract Completely simple semigroups form a variety, , of algebras with the operations of multiplication and inversion. It is known that the mapping , where is the variety of all groups, is an isomorphism of the lattice of all subvarieties of onto a subdirect product of the lattice of subvarieties of and the interval . We consider embeddings of into certain direct products on the above pattern with rectangular bands, rectangular groups and central completely simple semigroups in place of groups.