The Maximum Idempotent-Separating Congruence on an Inverse Semigroup
- 1 June 1964
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Edinburgh Mathematical Society
- Vol. 14 (1) , 71-79
- https://doi.org/10.1017/s0013091500011251
Abstract
A congruence ρ on a semigroup will be called idempotent-separating if each ρ-class contains at most one idempotent. It is shown below that there exists a maximum such congruence µ on every inverse semigroup S. Two characterisations of µ are found, and it is shown (a) that S/µ⋍E, the semilattice of idempotents of S, if and only if E is contained in the centre of S; (b) that µ is the identical congruence on S if and only if E is self-centralising, in a sense explained below.Keywords
This publication has 7 references indexed in Scilit:
- A Class of Irreducible matrix representations of an Arbitrary Inverse SemigroupProceedings of the Glasgow Mathematical Association, 1961
- A note on representations of inverse semigroupsProceedings of the American Mathematical Society, 1957
- A Note on Representations of Inverse SemigroupsProceedings of the American Mathematical Society, 1957
- Inverse Semi-GroupsJournal of the London Mathematical Society, 1954
- Representations of Inverse Semi-GroupsJournal of the London Mathematical Society, 1954
- On the Structure of SemigroupsAnnals of Mathematics, 1951
- Semigroups Admitting Relative InversesAnnals of Mathematics, 1941