The congruence lattice of a strict regular semigroup

On sandwich sets and congruences on regular semigroups

“…The first two formulae in (3) follow directly from (2); the third by the definition of f , and p 2 = p by (2). By (2), we have ep = ef whence a ap = a af so that ap = af = a 2 a which implies the fourth formula in (3) since p, q ∈ S(e, f )f which by Theorem 3.3 is a left zero semigroup.…”

“…We start with a more general situation which will provide some additional information, see [2] for related results.…”

The congruence lattice of a combinatorial strict inverse semigroup

“…The following definitions and results are from [1] where congruences on strict regular semigroups (that is, regular subdirect products of completely simple and/or completely 0-simple semigroups) are studied. For aeX let (a] = {yeX|y^a} denote the principal order ideal in X generated by a.…”

“…In [1], it is shown that there is a (finite) combinatorial strict inverse semigroup S whose structure set X consists of five elements and is depicted by Fig. 1.…”

“…For aeX let (a] = {yeX|y^a} denote the principal order ideal in X generated by a. By Proposition 2.3 in [1] we have the following.…”