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The minimal faithful degree of a fundamental inverse semigroup

Published online by Cambridge University Press:  17 April 2009

D. Easdown
D. Easdown
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, W.A. 6009
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Abstract

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This paper shows that the smallest size of a set for which a finite fundamental inverse semigroup can be faithfully represented by partial transformations of that set is the number of join irreducible elements of its semilattice of idempotents.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 3 , June 1987 , pp. 373 - 378
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Howie, J. M., An introduction to semigroup theory. (London Mathematical Society Monographs 7, Academic Press, London, 1976).Google Scholar
[2]Ljapin, E. S., Semigroups. (Translations of Mathematical Monographs, Volume 3, American Mathematical Society, Providence, R.I., 1974).Google Scholar
[3]Munn, W. D., “Uniform semilattices and bisimple inverse semigroups”, Quart. J. Math. Oxford Ser. (2) 17 (1966), 151–159.CrossRefGoogle Scholar
[4]Munn, W. D., “Fundamental inverse semigroups”, Quart. J. Math. Oxford Ser. (2) 21 (1970), 152–170.CrossRefGoogle Scholar
[5]Petrich, Mario, Inverse semigroups. (Pure and Applied Mathematics, John Wiley & Sons, 1984).Google Scholar
[6]Preston, G. B., “Representations of inverse semigroups by one-to-one partial transformations of a set”, Semigroup Forum 6 (1973), 240–245; addendum : Semigroup Forum 8 (1974), 277.CrossRefGoogle Scholar
[7]Shevrin, L. N., “The Sverdlovsk Tetrad”, Semigroup Forum 4 (1972), 274–280.Google Scholar
[8]Vagner, V. V., “The theory of generalized heaps and generalized groups”, Mat. Sb. 32 (1953), 545–632 (Russian).Google Scholar