On (finite) distributive lattices with antitone involutions.
Basic algebras are equivalent to bounded lattices with sectional antitone involutions. If this lattice is distributive, the assigned basic algebra is called distributive. It is proved that for every finite distributive basic algebra its underlying lattice is a direct product of chains. Every so-called weakly monotone basic algebra is distributive. Moreover, every finite weakly monotone basic algebra is an MV-algebra. Sharp elements in weakly monotone basic algebras are studied. For every weakly monotone basic algebra \(A\), the set \(S(A)\) of its sharp elements is a subalgbera of \(A\) which is in fact a Boolean algebra. Direct decompositions of weakly monotone basic algebras are characterized.
scientific article; zbMATH DE number 6515462