A Representation Theorem for Distributive l-Monoids
Marlow Anderson, Constance C. Edwards · Canadian Mathematical Bulletin · 1984
Abstract 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.