Wreath products and varieties of inverse semigroups
David Cowan · Summit (Simon Fraser University) · 1989
Given two varieties % and %" of inverse semigroups, define Wr( Z, %") to be the variety of inverse semigroups generated by wreath products of semigroups in % with semigroups in K The principal result of this work is a description of the fully invariant congruence on the free inverse semigroup corresponding to Wr( 8, 7 ) in terms of the fully invariant congruences corresponding to % and %" , where % and T are varieties of inverse semigroups.This description makes use of a graphical representation of inverse semigroups with presentations, due to Stephen, which is the inverse semigroup theoretic analogue to the Cayley graphs of group theory.We further show that Wr, considered as a binary operator on the lattice Y(3) of varieties of inverse semigroups, is associative.Thus, the lattice of varieties of inverse semigroups is a semigroup (Y(3), Wr ) under the ..' inverse subsemigroups of sernigroups of this form and so belong to Wr(.dm,91).For each n E 0, n 2 2, let Cn denote the cyclic group of order n.