Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-17T23:19:56.317Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Clifford, A. H. and Preston, G. B.. The algebraic theory of semigroups, vols 1 and 2 (Providence, R. I.: Amer. Math. Soc. 1961 and 1967).Google Scholar
2Howie, J. M.. The subsemigroup generated by the idempotents of a full transformation semigroup. J. London Math. Soc. 41 (1966), 707–716.CrossRefGoogle Scholar
3Howie, J. M.. An introduction to semigroup theory (London: Academic Press, 1976).Google Scholar
4Howie, J. M.. Some subsemigroups of infinite full transformation semigroups. Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), 159–167.CrossRefGoogle Scholar
5Howie, J. M.. A class of bisimple, idempotent-generated congruence-free semigroups. Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), 169–184.CrossRefGoogle Scholar
6Lindsey, D. and Madison, B.. The lattice of congruences on a Baer-Levi semigroup. Semigroup Forum 12 (1976), 63–70.CrossRefGoogle Scholar
7Mal'cev, A. I.. Symmetric groupoids. Mat. Sbomik (N.S.) 31 (1952), 136–151 (Russian).Google Scholar
8Schein, B. M.. Homomorphisms and subdirect decompositions of semigroups. Pacific J. Math. 17 (1966), 529–547.CrossRefGoogle Scholar
9Trotter, P. G.. Congruence-free regular semigroups with zero. Semigroup Forum 12 (1976), 1–5.CrossRefGoogle Scholar