  We study some natural generalizations of the spectral spaces in the contexts
of commutative rings and distributive lattices. We obtain a topological
characterization for the spectra of commutative (not necessarily unitary) rings
and we find spectral versions for the up-spectral and down-spectral spaces. We
show that the duality between distributive lattices and Balbes-Dwinger spaces
is the co-equivalence associated to a pair of contravariant right adjoint
functors between suitable categories.
