Stone and Flat Topologies on the Minimal Prime Spectrum of a Commutator Lattice

We investigate from an algebraic and topological point of view the minimal prime spectrum of a commutator lattice, considering the prime elements with respect to the commutator operation. We obtain characterizations for minimal prime elements, then study the Stone and flat topologies on the minimal prime spectra of commutator lattices. We thus obtain abstractions for our results from [1] on congruence lattices and generalizations for results on frames and quantales, but also further cases in which these results hold.