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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: [email protected].
E. Hotzel
Affiliation:
GMD, Schloss BirlinghovenD-53754 St. Augustin, Germany, E-mail: [email protected].
P. Normak
Affiliation:
Tallinna Pedagoogikaülikool, Narva mnt. 25, 10120 Tallinn, Estonia, e-mail: [email protected].
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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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References

1.Bulman-Fleming, S.. On equationally compact semilattices. Algebra Universalis, 2 (1972), 146–151.CrossRefGoogle Scholar
2.Bulman-Fleming, S. and Normak, P.. Flatness properties of monocyclic acts. Mh. Math., 122 (1996), 307–323.CrossRefGoogle Scholar
3.Crawley, P. and Dilworth, R. P.. The Algebraic Theory of Lattices. Prentice-Hall, Englewood Cliffs, N.J., 1973.Google Scholar
4.Clifford, A. H. and Preston, G. B.. The Algebraic Theory of Semigroups, Volume 1. Mathematical Surveys of the American Mathematical Society, Number 7. Providence, R.I., 1961.CrossRefGoogle Scholar
5.Fuchs, L.. Infinite Abelian Groups. Academic Press, New York, 1970.Google Scholar
6.Grätzer, G.. General Lattice Theory. Academic Press, New York, 1978.CrossRefGoogle Scholar
7.Grätzer, G.. Universal Algebra, 2nd Edition. Springer, New York, 1979.CrossRefGoogle Scholar
8.Grätzer, G. and Lakser, H.. Equationally compact semilattices. Colloq. Math., 20 (1969), 27–30.CrossRefGoogle Scholar
9.Grillet, P. A.. Semigroups: An Introduction to the Structure Theory. Marcel Dekker Inc., New York, 1995.Google Scholar
10.Howie, J. M.. Fundamentals of Semigroup Theory. Oxford University Press, Oxford, 1995.CrossRefGoogle Scholar
11.Hotzel, E.. Halbgruppen mit ausschliesslich reesschen Linkskongruenzen. Math. Z., 112 (1969), 300–320.CrossRefGoogle Scholar
12.Hulanicki, A.. Algebraic characterization of abelian divisible groups which admit compact topologies. Fund. Math., 44 (1957), 192–197.CrossRefGoogle Scholar
13.Huber, M. and Meier, W.. Linearly compact groups. J. Pure Appl. Algebra, 16 (1980), 167–182.CrossRefGoogle Scholar
14.Jones, P. R.. On the congruence extension property for semigroups. In Semigroups, Algebraic Theory and Applications to Formal Languages and Codes, Proceedings, Luino, 1992. World Scientific, Singapore, 1993, 133–143.Google Scholar
15.Kelley, J. L.. General Topology. Van Nostrand, Princeton, 1955.Google Scholar
16.Leptin, H.. Über eine Klasse linear kompakter abelscher Gruppen I. Abh. Math. Sern. Hamb., 19 (1954), 23–40.CrossRefGoogle Scholar
17.Normak, P.. Congruence compact acts. Semigroup Forum, 55 (1997), 299–308.CrossRefGoogle Scholar
18.Tang, X.. Semigroups with the congruence extension property. Semigroup Forum, 56 (1998), 226–264.CrossRefGoogle Scholar
19.Zelinsky, D.. Linearly compact modules and rings. Amer. J. Math., 75 (1953), 79–90.CrossRefGoogle Scholar