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Free generators in free inverse semigroups

Published online by Cambridge University Press:  17 April 2009

N.R. Reilly
N.R. Reilly
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada.
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Abstract

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Using the characterization of the free inverse semigroup F on a set X, given by Scheiblich, a necessary and sufficient condition is found for a subset K of an inverse semigroup S to be a set of free generators for the inverse sub semigroup of S generated by K. It is then shown that any non-idempotent element of F generates the free inverse semigroup on one generator and that if |X| > 2 then F contains the free inverse semigroup on a countable number of generators. In addition, it is shown that if |X| = 1 then F does not contain the free inverse semigroup on two generators.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 3 , December 1972 , pp. 407 - 424
Copyright
Copyright © Australian Mathematical Society 1972

References

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