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On congruence compact monoids

Part of: Semigroups

Published online by Cambridge University Press:  26 February 2010

S. Bulman-Fleming ,
E. Hotzel  and
P. Normak
S. Bulman-Fleming
Affiliation:
Department of Mathematics, Wilfrid Laurier UniversityWaterloo, ON N2L 3C5, Canada E-mail: sbulman@wlu.ca.
E. Hotzel
Affiliation:
GMD, Schloss BirlinghovenD-53754 St. Augustin, Germany, E-mail: ehotzel@gmd.de.
P. Normak
Affiliation:
Tallinna Pedagoogikaülikool, Narva mnt. 25, 10120 Tallinn, Estonia, e-mail: pnormak@tpu.ee.
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Abstract

A universal algebra is called congruence compact if every family of congruence classes with the finite intersection property has a non-empty intersection. This paper determines the structure of all right congruence compact monoids S for which Green's relations ℐ and ℋ coincide. The results are thus sufficiently general to describe, in particular, all congruence compact commutative monoids and all right congruence compact Clifford inverse monoids.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999 , pp. 205 - 224
Copyright
Copyright © University College London 1999

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