On Priestley spaces of lattice-ordered algebraic structures (Q1970922)

The Priestley duality for implicative lattices has been studied by the second author [see \textit{H. A. Priestley}, ``Natural dualities'', in: K. A. Baker et al. (eds.), Lattice theory and its applications (Res. Expo. Math. 23, Heldermann Verlag, Lemgo), 185-209 (1995; Zbl 0839.06009)]. In the paper under review a new approach to this duality is presented. Further, in a series of theorems the authors show that their result on implicative lattices can be specialized in order to give the Priestley duality for the following classes of algebras: Ockham algebras; \(\ell\)-groups; Abelian \(\ell\)-groups and representable \(\ell\)-groups; MV-algebras; linear Heyting algebras. From the authors' abstract: ``The approach focuses on distinguished subsets of the prime lattice filters of an implicative lattice, ordered as usual by inclusion. A decomposition theorem is proved, and the extent to which the order on the prime lattice filters determines the implicative structure is thereby revealed''.