Talk:Residuated lattice

Latest comment: 9 years ago by 86.127.138.67 in topic Quasigroup?

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)Reply

Quasigroup?

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