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A congruence-free semigroup associated with an infinite cardinal number

Published online by Cambridge University Press:  14 November 2011

M. Paula O. Marques
M. Paula O. Marques
Affiliation:
Mathematical Institute, University of St Andrews
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Synopsis

Let X be a set with infinite cardinality m and let Qm be the semigroupof balanced elements in ℐ(X), as described by Howie. If I is the ideal{αεQm:|Xα|<m} then the Rees factor Pm = Qm/I is O-bisimple and idempotent-generated. Its minimum non-trivial homomorphic image has both these properties and is congruence-free. Moreover, has depth 4, in the sense that [E()]4 = , [E()]3≠

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 3-4 , 1983 , pp. 245 - 257
Copyright
Copyright © Royal Society of Edinburgh 1983

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