Abstract residuation over lattices

Abstract

The idea of residuation goes back to Dedekind [3], † who introduced it in the theory of modules. It has since had extensive applications in the theory of algebraic modular systems [6], in the theory of ideals [8], and in certain topics of arithmetic [9]. On account of its fundamental role in several fields of modern algebra, it is desirable to consider residuation abstractly. A postulational treatment also is a necessary preliminary to the investigation of the structure properties of the residual. We give such an abstract formulation.