The congruence lattice of a strict regular semigroup

AbstractThe structure of a strict regular semigroup S is uniquely determined by the partially ordered set of its principal ideals S/J, the J-classes of S which are the nonzero parts of completely 0-simple semigroups and certain partial homomorphisms between these partial groupoids. The congruences on S are described in terms of these parameters. Formulas for join and meet of a set of congruences are developed. As an application, necessary and sufficient conditions for a strict regular semigroup are obtained in order that its congruence lattice be contained in a variety of modular lattices