CONGRUENCE NETWORKS FOR COMPLETELY SIMPLE SEMIGROUPS

Authors
PETRICH M
Citation
M. Petrich, CONGRUENCE NETWORKS FOR COMPLETELY SIMPLE SEMIGROUPS, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 56, 1994, pp. 243-266
Citations number
8
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
Journal title
Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics → ACNP
ISSN journal
02636115
Volume
56
Year of publication
1994
Part
2
Pages
243 - 266
Database
ISI
SICI code
0263-6115(1994)56:<243:CNFCSS>2.0.ZU;2-N
Abstract
The operators K, k, T and t are defined on the lattice C(S) of congrue nces on a Rees matrix semigroup S as follows. For rho is-an-element-of C(S), rhoK and rhok (rhoT and rhot) are the greatest and the least co ngruences with the same kernel (trace) as rho, respectively. We determ ine 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 rho is-an-element-of C(S) an d the lattice generated by it. The latter is then represented by gener ators and relations.