Talk:Residuated lattice

The definition as presently stated is an incorrect mixture of properties of residuated lattices and Heyting algebras. While it is true that the unit of the monoid in a Heyting algebra does double duty as top, it is not true in general of residuated lattices, for example (Z, min, max, +, -, 0), which has neither a greatest nor least integer, yet is a residuated lattice with monoid (Z, +, 0) and common left and right residuals x-y - y. It is also not true in general that the monoid is commutative, the example par excellence being relation algebras. I have rewritten the definition to agree in content and notation with the lattice theory literature while pointing out alternative more recently used notations. --Vaughan Pratt 10:14, 15 July 2007 (UTC)

Quasigroup?

Are these related (other than by notation) with quasigroups? 86.127.138.67 (talk) 04:26, 19 April 2015 (UTC)