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Anti-uniform semilattices

Published online by Cambridge University Press:  17 April 2009

J. M. Howie  and
B. M. Schein
J. M. Howie
Affiliation:
University of Stirling, Stirling, Scotland, and University of Saratov, Saratov, USSR.
B. M. Schein
Affiliation:
University of Stirling, Stirling, Scotland, and University of Saratov, Saratov, USSR.
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Abstract

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An inverse semigroup which is a union of groups is called Cliffordian. A semilattice E is called universally Cliffordian if every inverse semigroup having E as semilattice of idempotents is Cliffordian. It is shown that E is universally Cliffordian if and only if it is anti-uniform, that is, if and only if no two distinct principal ideals of E are isomorphic.

A semilattice E satisfying the minimum condition is anti-uniform if and only if it is a well-ordered chain. Examples are given of anti-uniform semilattices of more complicated types.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 2 , August 1969 , pp. 263 - 268
Copyright
Copyright © Australian Mathematical Society 1969

References

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