Residuated Lattices
Morgan Ward, R. P. Dilworth · Birkhäuser Boston eBooks · 1938
We propose to develop here a systematic theory of lattices† over which an auxiliary operation of multiplication or residuation is defined. We begin by showing that the two operations correspond to one another; under quite general conditions in every lattice over which a multiplication is defined a residuation may be defined and conversely. The residuation and multiplication we introduce have the properties of the like-named operations in the particular instance of polynomial ideal theory. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.