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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

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