“…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.…”
Section: The Sandwich Set Of An Elementmentioning
confidence: 87%
“…We start with a more general situation which will provide some additional information, see [2] for related results.…”
“…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.…”
Section: The Sandwich Set Of An Elementmentioning
confidence: 87%
“…We start with a more general situation which will provide some additional information, see [2] for related results.…”
“…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.…”
Section: Put S= \Jaexi% An D Define a Product On S Bymentioning
confidence: 99%
“…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.…”
Section: • 6 An Examplementioning
confidence: 99%
“…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.…”
Section: Put S= \Jaexi% An D Define a Product On S Bymentioning
The congruence lattice of a combinatorial strict inverse semigroup is shown to be isomorphic to a complete subdirect product of congruence lattices of semilattices preserving pseudocomplements.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.