Some special congruences on completely regular semigroups
Limin Wang, Ying-Ying Feng, Honghua Chen · Communications in Algebra · 2019
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 kerσ is a cryptogroup, semigroups for which kerν is a cryptogroup and semigroups for which κ is over rectangular bands, are studied. ((ωt)k)t,((Dt)k)t and ((ωk)t)k are found to be the least congruences on S such that the quotient semigroups are semigroups for which kerσ is a cryptogroup, kerν 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”.