Non-distributive Cancellative Residuated Lattices
Cancellative residuated lattices are a natural generalization of lattice-ordered groups (l-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 l-groups. We will construct two examples that shows that this is not necessarily the case.
KeywordsResiduated Lattice Lattice Order Free Monoid Commutative Monoid Cancellative Monoid
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