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A Representation Theorem for Distributive l-Monoids

Published online by Cambridge University Press:  20 November 2018

Marlow Anderson  and
C. C. Edwards
Marlow Anderson
Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University at Fort WayneFort Wayne, Indiana46805
C. C. Edwards
Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University at Fort WayneFort Wayne, Indiana46805
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Abstract

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In this note the Holland representation theorem for l-groups is extended to l-monoids by the following theorem: an l-monoid is distributive if and only if it may be embedded into the l-monoid of order-preserving functions on some totally ordered set. A corollary of this representation theorem is that a monoid is right orderable if and only if it is a subsemigroup of a distributive l-monoid; this result is analogous to the group theory case.

Keywords

06 F 0520 M 20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 2 , 01 June 1984 , pp. 238 - 240
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Bigard, A., Keimel, K. and Wolfenstein, S., Groupes et Anneaux Réticulés, Springer-Verlag, Berlin, 1977.Google Scholar
2. Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups, Volume II, AMS, Providence, 1967.Google Scholar
3. Conrad, P., Right-ordered groups, Michigan Math. J. 6 (1959), 267–275.Google Scholar
4. Edwards, C. C. and Anderson, M., Lattice properties of the symmetric weakly inverse semigroup on a totally ordered set, J. Austral. Math. Soc. 31 (1981), 395–404.Google Scholar
5. Fuchs, L., Teilweise Geordnete Algebraische Strukturen, Vanderhoeck and Ruprecht, Göttingen, 1966.Google Scholar
6. Holland, W. C., The lattice-ordered group of automorphisms of an ordered set, Michigan Math J. 10 (1963), 399–408.Google Scholar
7. Iséki, K., A characterization of distributive lattices, Nederl. Akad. Wetensch. Proc. Ser A 54 (1951), 388–389.Google Scholar
8. Merlier, T., Sur les demi-groupes reticules et les o-demi -groupes, Semigroup Forum 2 (1971), 64–70.Google Scholar