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Lattice isomorphisms of inverse semigroups

Published online by Cambridge University Press:  20 January 2009

P. R. Jones
P. R. Jones
Affiliation:
University of Glasgow
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A largely untouched problem in the theory of inverse semigroups has been that of finding to what extent an inverse semigroup is determined by its lattice of inverse subsemigroups. In this paper we discover various properties preserved by lattice isomorphisms, and use these results to show that a free inverse semigroup ℱℐx is determined by its lattice of inverse subsemigroups, in the strong sense that every lattice isomorphism of ℱℐx upon an inverse semigroup T is induced by a unique isomorphism of ℱℐx upon T. (A similar result for free groups was proved by Sadovski (12) in 1941. An account of this may be found in Suzuki's monograph on the subject of subgroup lattices (14)).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 21 , Issue 2 , September 1978 , pp. 149 - 157
Copyright
Copyright © Edinburgh Mathematical Society 1978

References

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