Semimodularity of the congruence lattice on regular ?-semigroups

Abstract

In this paper a characterization of the regular to-semigroups whose congruence lattice is semimodular is given. The characterization obtained for such semigroups generalizes the one given by Scheiblich for bisimple ~o-semigroups. Notice that we use the definition of semimodularity which other authors call double covering property.~Xm, n ~ ~/m~m+l 9 9 9 ~n--I and, for all ne N, let ~n,n denote the identity automorphism Of Gn(modd).