Structure of commutative cancellative integral residuated lattices on \((0, 1]\) (Q2474105)

The algebras of many substructural logics provide interesting examples of lattice-ordered mono\-ids with a residuum. These algebras were first introduced by Ward and Dilworth as a generalization of ideal lattices in rings. Special cases include Hájek's \(\Pi\)MTL-algebras, the algebraic counterpart of the cancellative extension of monoidal t-norm-based logic. The author gives an algebraic characterization of \(\Pi\)MTL chains. His results shed new light on the fine structure of cancellative integral commutative residuated chains.