nLab maximal spectrum



Given a ring, or a kk-algebra (unital or not) AA, its maximal spectrum Spec mASpec_m A is the set of its maximal ideals.


If kk is a field, and RR is a finitely generated noetherian commutative unital kk-algebra without nilpotent elements, then Spec mASpec_m A equipped with the Zariski topology is a noetherian topological space; the varieties in the classical sense (cf. chapter 1 of Hartshorne) are exactly the spectra of such kk-algebras. A more appropriate spectrum for general commutative unital rings is the prime spectrum.

Last revised on April 11, 2016 at 06:20:04. See the history of this page for a list of all contributions to it.