Some special congruences on completely regular semigroups

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 is a cryptogroup, semigroups for which is a crypt...

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Bibliographic Details
Published in:Communications in algebra 2019-07, Vol.47 (7), p.2941-2953
Main Authors: Wang, Li-Min, Feng, Ying-Ying, Chen, Hong-Hua
Format: Article
Language:English
Subjects:
Completely regular semigroup
congruence
Congruences
is a cryptogroup
Quotients
semigroup for which
semigroup for which κ is over rectangular bands
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Summary: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 is a cryptogroup, semigroups for which is a cryptogroup and semigroups for which κ is over rectangular bands, are studied. and are found to be the least congruences on S such that the quotient semigroups are semigroups for which is a cryptogroup, 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".
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2018.1543427