Necessary and sufficient conditions for equality over the pseudovariety CR of all finite completely regular semigroups are obtained. They are inspired by the solution of the word problem for free completely regular semigroups and clarify the role played by groups in the structure of such semigroups. A strengthened version of Ash's inevitability theorem (κ-reducibility of the pseudovariety G of all finite groups) is proposed as an open problem and it is shown that, if this stronger version holds, then CR is also κ-reducible and, therefore, hyperdecidable. © Clearance Centre, Inc.

Item Type:	Refereed Article
Research Division:	Mathematical Sciences
Research Group:	Pure mathematics
Research Field:	Group theory and generalisations
Objective Division:	Expanding Knowledge
Objective Group:	Expanding knowledge
Objective Field:	Expanding knowledge in the mathematical sciences
UTAS Author:	Almeida, J (Professor Jane Almeida)
UTAS Author:	Trotter, PG (Dr Peter Trotter)
ID Code:	21221
Year Published:	2001
Web of Science® Times Cited:	12
Deposited By:	Mathematics
Deposited On:	2001-08-01
Last Modified:	2002-05-09
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