J Austral Math Soc Ser A 56 pp243--266, 1994.

Congruence Networks for Completely Simple Semigroups

Mario Petrich

(Received 8 April 1991; revised 1 July 1991)

Abstract

The operators K, k, T and t are defined on the lattice C(S) of congruences on a Rees matrix semigroup S as follows. For r Î C(S), rK and rk (rT and rt) are the greatest and the least congruences with the same kernel (trace) as r, respectively. We determine the semigroup generated by the operators K, k, T and t as they act on all completely simple semigroups. We also determine the network of congruences associated with a congruence r Î C(S) and the lattice generated by it. The latter is then represented by generators and relations.

1991 AMS Subject Classification: 20M10

Browse the article

Read the article in your browser. (Scale your print to fit your paper).

Authors

Mario Petrich: Department of Mathematics, Simon Fraser University, Burnaby, B.C. V5A156, Canada.

Editor JAMSB(E): editor at anziamj.austms.org.au
WWW Administrator: webmaster at anziamj.austms.org.au

Last Modified: Fri Jan 10 8:53:40 2003