  We dualize a construction of Aguzzoli-Flaminio-Ugolini of a large class of
MTL-algebras from ordered quadruples consisting of a Boolean algebra, a
generalized MTL-algebra, and two maps parameterizing the connection between
these pieces. Our dualized construction gives a uniform way of building the
extended Priestley duals of MTL-algebras in this class from the Stone duals of
their Boolean skeletons, the extended Priestley duals of their radicals, and a
family of closure operators associating the two. In order to facilitate this
work, we also offer some new results regarding the extended Priestley duals of
MTL-algebras and GMTL-algebras.

Logic