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
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.