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Generators and factorisations of transformation semigroups

Published online by Cambridge University Press:  14 November 2011

Peter M. Higgins ,
John M. Howie  and
Nikola Ruškuc
Peter M. Higgins
Affiliation:
Department of Mathematics, University of Essex, Colchester CO4 3SQ, U.K.
John M. Howie
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews, Fife KY16 9SS, U.K.
Nikola Ruškuc
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews, Fife KY16 9SS, U.K.
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Extract

If E is the set of idempotents and G the group of units within a full transformation semigroup ℐx, then EG = GE = ℐx if X is finite. The question of identifying the subsemigroup EG = GE = 〈G∪E〉 in the case where X is infinite leads to an investigation of interrelations among various naturally occurring subsemigroups of ℐX. In the final section it is shown that precisely two additional elements µ, v are needed in order that G∪E∪{µ, v} should generate ℐx.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 6 , 1998 , pp. 1355 - 1369
Copyright
Copyright © Royal Society of Edinburgh 1998

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