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Ideals of free inverse semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

W. D. Munn
W. D. Munn
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
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Abstract

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It is shown that no proper ideal of a free inverse semigroup is free and that every isomorphism between ideals is induced by a unique automorphism of the whole semigroup. In addition, necessary and sufficient conditions are given for two principal ideals to be isomorhic.

MSC classification

Secondary: 20M99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 2 , December 1980 , pp. 157 - 167
Copyright
Copyright © Australian Mathematical Society 1980

References

Howie, J. M. (1976), An introduction to semigroup theory (Academic Press, London).Google Scholar
Munn, W. D. (1961), ‘A class of irreducible matrix representations of an arbitrary inverse semigroup’, Proc. Glasgow Math. Assoc. 5, 41–48.Google Scholar
Munn, W. D. (1974), ‘Free inverse semigroups’, Proc. London Math. Soc. (3) 29, 385–404.CrossRefGoogle Scholar
Munn, W. D. (to appear) ‘An embedding theorem for free inverse semigroups’, Glasgow Math. J.Google Scholar
O'Carroll, L. (1974), ‘A note on free inverse semigroups’, Proc. Edinburgh Math. Soc. (2) 19, 17–23.CrossRefGoogle Scholar
Reilly, N. R. (1972), ‘Free generators in free inverse semigroups’, Bull. Austral. Math. Soc. 7, 407–424.Google Scholar
Reilly, N. R. (1973), ‘Free generators in free inverse semigroups’, Bull. Austral. Math. Soc. 9, 479.CrossRefGoogle Scholar
Reilly, N. R. (1976), ‘Free inverse semigroups’, Algebraic theory of semigroups, pp. 479–508 (Colloquia Mathematica Societatis János Bolyai 20).Google Scholar
Scheiblich, H. E. (1972), ‘Free inverse semigroups’, Semigroup Forum 4, 351–359.CrossRefGoogle Scholar
Scheiblich, H. E. (1973), ‘Free inverse semigroups’, Proc. Amer. Math. Soc. 38, 1–7.CrossRefGoogle Scholar