Skip to main content Accessibility help
×
×
Home

On congruence compact monoids

  • S. Bulman-Fleming (a1), E. Hotzel (a2) and P. Normak (a3)
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.

Copyright
References
Hide All
1.Bulman-Fleming, S.. On equationally compact semilattices. Algebra Universalis, 2 (1972), 146151.
2.Bulman-Fleming, S. and Normak, P.. Flatness properties of monocyclic acts. Mh. Math., 122 (1996), 307323.
3.Crawley, P. and Dilworth, R. P.. The Algebraic Theory of Lattices. Prentice-Hall, Englewood Cliffs, N.J., 1973.
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.
5.Fuchs, L.. Infinite Abelian Groups. Academic Press, New York, 1970.
6.Grätzer, G.. General Lattice Theory. Academic Press, New York, 1978.
7.Grätzer, G.. Universal Algebra, 2nd Edition. Springer, New York, 1979.
8.Grätzer, G. and Lakser, H.. Equationally compact semilattices. Colloq. Math., 20 (1969), 2730.
9.Grillet, P. A.. Semigroups: An Introduction to the Structure Theory. Marcel Dekker Inc., New York, 1995.
10.Howie, J. M.. Fundamentals of Semigroup Theory. Oxford University Press, Oxford, 1995.
11.Hotzel, E.. Halbgruppen mit ausschliesslich reesschen Linkskongruenzen. Math. Z., 112 (1969), 300320.
12.Hulanicki, A.. Algebraic characterization of abelian divisible groups which admit compact topologies. Fund. Math., 44 (1957), 192197.
13.Huber, M. and Meier, W.. Linearly compact groups. J. Pure Appl. Algebra, 16 (1980), 167182.
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, 133143.
15.Kelley, J. L.. General Topology. Van Nostrand, Princeton, 1955.
16.Leptin, H.. Über eine Klasse linear kompakter abelscher Gruppen I. Abh. Math. Sern. Hamb., 19 (1954), 2340.
17.Normak, P.. Congruence compact acts. Semigroup Forum, 55 (1997), 299308.
18.Tang, X.. Semigroups with the congruence extension property. Semigroup Forum, 56 (1998), 226264.
19.Zelinsky, D.. Linearly compact modules and rings. Amer. J. Math., 75 (1953), 7990.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed