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Non-distributive cancellative residuated lattices. (English) Zbl 1073.06006
Martínez, Jorge (ed.), Ordered algebraic structures. Proceedings of the conference on lattice-ordered groups and $$f$$-rings held at the University of Florida, Gainesville, FL, USA, February 28–March 3, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0752-3). Developments in Mathematics 7, 205-212 (2002).
Summary: Cancellative residuated lattices are a natural generalization of lattice-ordered groups ($$\ell$$-groups). In studying this variety, several questions have occurred about residuated lattice orders on free monoids and commutative free monoids. One of these questions is whether every residuated lattice order on a (commutative) free monoid is distributive, a fact known about $$\ell$$-groups. We construct two examples that show that this is not necessarily the case.
For the entire collection see [Zbl 1068.06001].

##### MSC:
 06F05 Ordered semigroups and monoids
##### Keywords:
residuated lattice orders; free monoids