Some special congruences on completely regular semigroups. Issue 7 (3rd July 2019) - Wang, Li-Min
Abstract: This paper enriches the list of properties of the congruence sequences starting from the universal relation and successively performing the operations of lower t and lower k . Three classes of completely regular semigroups, namely semigroups for which ker σ is a cryptogroup, semigroups for which ker ν is a cryptogroup and semigroups for which κ is over rectangular bands, are studied. ( ( ω t ) k ) t, ( ( D t ) k ) t and ( ( ω k ) t ) k are found to be the least congruences on S such that the quotient semigroups are semigroups for which ker σ is a cryptogroup, ker ν is a cryptogroup and κ is over rectangular bands, respectively. The results obtained present a response to three problems in Petrich and Reilly's textbook "Completely Regular Semigroups".