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The Maximum Idempotent-Separating Congruence on an Inverse Semigroup

Published online by Cambridge University Press:  20 January 2009

J. M. Howie
J. M. Howie
Affiliation:
Department of Mathematics, The University, Glasgow, W.2
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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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 1 , June 1964 , pp. 71 - 79
Copyright
Copyright © Edinburgh Mathematical Society 1964

References

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