Geodesic
A Representation Theorem for Distributive l-Monoids
Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 238-240

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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.
DOI : 10.4153/CMB-1984-034-6
Mots-clés : 06 F 05, 20 M 20 
Anderson, Marlow; Edwards, C. C. A Representation Theorem for Distributive l-Monoids. Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 238-240. doi: 10.4153/CMB-1984-034-6
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     title = {A {Representation} {Theorem} for {Distributive} {l-Monoids}},
     journal = {Canadian mathematical bulletin},
     pages = {238--240},
     year = {1984},
     volume = {27},
     number = {2},
     doi = {10.4153/CMB-1984-034-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-034-6/}
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