Some special congruences on completely regular semigroups. Issue 7 (3rd July 2019)

• Record Type: Journal Article
• Authors: Wang, Li-Min; Feng, Ying-Ying; Chen, Hong-Hua
• Is Part Of: Communications in algebra. Volume 47:Issue 7(2019)
• Page Start: 2941
• Page End: 2953
• Publication Date: 2019-07-03
• Subjects: Completely regular semigroup -- congruence -- semigroup for which kerσ is a cryptogroup -- semigroup for which kerν is a cryptogroup -- semigroup for which κ is over rectangular bands; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1543427
• Languages: English
• ISSNs: 0092-7872

Abstract

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".