Cancellative residuated lattices

Abbreviation: CanRL

Definition

A\ cancellative residuated lattice is a residuated lattice L = (L,∨,∧,·,e,\,/) such that

· is right-cancellative:   xz = yz  ⇒  x = y, and
· is left-cancellative:   zx = zy  ⇒  x = y.

Remark:

Morphisms

Let L and M be cancellative residuated lattices. A morphism from L to M is a function h : L→M that is a homomorphism: h(x∨y) = h(x)∨h(y)  and  h(x∧y) = h(x)∧h(y)  and   h(x·y) = h(x)·h(y)  and  h(x\y) = h(x)\h(y)  and  h(x/y) = h(x)/h(y)   and  h(e) = e.

Some results

Examples

Properties

Finite members

Subclasses

Superclasses