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A note on free inverse semigroups

Published online by Cambridge University Press:  20 January 2009

L. O'Carroll
L. O'Carroll
Affiliation:
Mathematical Institute, Chambers Street, Edinburgh EH1 1HZ
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Recently Scheiblich (7) and Munn (3), amongst others, have given explicit constructions for FIA, the free inverse semigroup on a non-empty set A. Further, Reilly (5) has investigated the free inverse subsemigroups of FIA. In this note we generalise two of Reilly's lesser results, and also characterise the surjective endomorphisms of FIA. The latter enables us to determine the group of automorphisms of FIA, and to show that if A is finite then FIA is Hopfian (a result proved independently by Munn (3)). Finally, we give an alternative proof of Reilly's main theorem, which uses Munn's theory of birooted trees.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 1 , March 1974 , pp. 17 - 23
Copyright
Copyright © Edinburgh Mathematical Society 1974

References

REFERENCES

(1) Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups (Math. Surveys No. 7, Amer. Math. Soc, Providence, Vol. I, 1961 and Vol. II, 1967).Google Scholar
(2) Hall, M., Theory of Groups (Macmillan, 1959).Google Scholar
(3) Munn, W. D., Free inverse semigroups, Semigroup Forum, 5 (1973), 262–269.CrossRefGoogle Scholar
(4) Mcfadden, R. and O'Carroll, L., F-inverse semigroups, Proc. London Math. Soc. (3) 22 (1971), 652–666.CrossRefGoogle Scholar
(5) Reilly, N. R., Free generators in free inverse semigroups, Bull. Austral. Math. Soc. 7 (1972), 407–424.CrossRefGoogle Scholar
(6) Saito, T., Proper ordered inverse semigroups, Pacific J. Math. 15 (1965), 649–666.CrossRefGoogle Scholar
(7) Scheiblich, H. E., Free inverse semigroups, Semigroup Forum, 4 (1972), 351–359.CrossRefGoogle Scholar
(8) Vagner, V. V., Theory of generalised heaps and generalised groups, Mat. Sb. (NS) 32 (1953), 545–632. (Russian.)Google Scholar
(9) Vagner, V. V., Generalised heaps and generalised groups with a transitive compatibility relation, Učen. Zap. Saratov. Gos. Univ., meh.-matem., 70 (1961), 25–39. (Russian.)Google Scholar