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Uniform labelled semilattices

Part of: Algebraic structures Ordered sets Semigroups

Published online by Cambridge University Press:  09 April 2009

C. J. Ash
C. J. Ash
Affiliation:
Department of Mathematics Monash University Clayton, Victoria 3168, Australia
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Abstract

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Let P be a partially-ordered set in which every two elements have a common lower bound. It is proved that there exists a lower semilattice L whose elements are labelled with elements of P in such a way that (i) comparable elements of L are labelled with elements of P in the same strict order relation; (ii) each element of P is used as a label and every two comparable elements of P are labels of comparable elements of L; (iii) for any two elements of L with the same label, there is a label-preserving isomorphism between the corresponding principal ideals. Such a structure is called a full, uniform P-labelled semilattice.

MSC classification

Secondary: 06A12: Semilattices 08A99: None of the above, but in this section 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 4 , December 1979 , pp. 385 - 397
Copyright
Copyright © Australian Mathematical Society 1979

References

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