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Uniform labelled semilattices

Part of: Ordered sets Semigroups Algebraic structures

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

Ash, C. J. (1979a), ‘The -classes of an inverse semigroup’, J. Austral. Math. Soc., (Ser. A) 28, 427–432.CrossRefGoogle Scholar
Ash, C. J. (1979b), ‘The lattice of ideals of a semigroup’, Algebra Universalis (to appear).CrossRefGoogle Scholar
Ash, C. J. (1979c), ‘Generalized cardinal systems’ (to appear).Google Scholar
Ash, C. J. and Hall, T. E. (1975), ‘Inverse semigroups on graphs’, Semigroup Forum 11, 140–145.CrossRefGoogle Scholar
Cohen, P. M. (1966), Set theory and the continuum hypothesis (Benjamin, New York).Google Scholar
Hall, T. E. (1973), ‘The partially ordered set of all -classes of an inverse semigroup’, Semigroup Forum 6, 263–264.CrossRefGoogle Scholar
Jónsson, B. (1960), ‘Homogeneous universal relational systems’, Math. Scand. 8, 137–142.CrossRefGoogle Scholar
Morley, M. and Vaught, R. L. (1962), ‘Homogeneous universal models’, Math. Scand. 11, 37–57CrossRefGoogle Scholar
Rhodes, J. (1972), ‘Research problem 24’, Semigroup Forum 5, 92.Google Scholar