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Congruences on simple regular ω-semigroups

Published online by Cambridge University Press:  09 April 2009

G. R. Baird
G. R. Baird
Affiliation:
University of Western OntarioLondon 72, Canada.
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The set E of idempotents of a semigroup S can be partially ordered by defining e ≦ f if and only if . If E = {ei: i = 0,1, …} and under this ordering e0 > e1 > e2, …, then we call S an ω-semigroup. Munn [7] has given a complete classification of simple regular ω-semigroups in terms of groups and group homomorphisms.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 2 , September 1972 , pp. 155 - 167
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Baird, G. R., ‘On a sublattice of the lattice of congruences on a simple regular ω-semigroup’, J. Aust. Math. Soc. 13 (1972), 461–471.CrossRefGoogle Scholar
[2]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Volume I (Math. Surveys, Number 7, Amer. Math. Soc. 1961).Google Scholar
[3]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Volume II (Math. Surveys, Number 7, Amer. Math. Soc. 1967).Google Scholar
[4]Lallement, G., ‘Congruences et équivalences de Greensur un demi-group régulier’. C. R. Acad. Sc. Paris Serie A262 (1966), 613–616.Google Scholar
[5]Munn, W. D., ‘A class of irreducible matrix representations of an arbitrary inverse semigroup’, Proc. Glasgow Math. Assoc. 5 (1961), 41–48.CrossRefGoogle Scholar
[6]Munn, W. D., ‘The lattice of congruences on a bisimple ω-semigroup’, Proc. Roy. Soc. Edinburgh 67 (1966), 175–184.Google Scholar
[7]Munn, W. D., ‘Regular ω-semigroups,’ Glasgow Math. J. 9 (1968), 46–66.CrossRefGoogle Scholar
[8]Munn, W. D. and Reilly, N. R., ‘Congruences on bisimple ω-semigroups,’ Proc. Glasgow Math. Assoc. 9 (1966), 184–922.CrossRefGoogle Scholar
[9]Reilly, N. R. and Scheiblich, H. E., ‘Congruences on regular semigroups,’ Pacific. J. Math. 23 (1967), 349–360.CrossRefGoogle Scholar
[10]Reilly, N. R., ‘Bisimple ω-semigroups’, Proc. Glasgow Math. Assoc. 7 (1966), 160–167.CrossRefGoogle Scholar