Functorial maximal spectra (Q5960409)

In many situations a certain space of prime ideals is functorially associated with given algebraic structures. Examples are the Zariski spectrum of a commutative ring with unit, the space of prime ideals of a Boolean algebra, and the space of irreducible \(\ell\)-ideals of a lattice-ordered ring. In all cases the space involved contains the subspace of maximal ideals. However, the maximal spectra do not necessarily give rise to a subfunctor. The author considers the question in the context of compact normal frames and establishes the functoriality of their saturation quotients. The latter implies the functoriality of their maximal spectra.