Free generators in free inverse semigroups
- 1 December 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 7 (3) , 407-424
- https://doi.org/10.1017/s0004972700045251
Abstract
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.Keywords
This publication has 2 references indexed in Scilit:
- A Homomorphism Theorem for SemigroupsJournal of the London Mathematical Society, 1968
- A certain sublattice of the lattice of congruences on a regular semigroupMathematical Proceedings of the Cambridge Philosophical Society, 1964