Editing Spectrum of a ring (section)

== Generalizations ==
The spectrum can be generalized from rings to [[C*-algebra]]s in [[operator theory]], yielding the notion of the [[spectrum of a C*-algebra]]. Notably, for a [[Hausdorff space]], the [[algebra of scalars]] (the bounded continuous functions on the space, being analogous to regular functions) is a ''commutative'' C*-algebra, with the space being recovered as a topological space from <math>\operatorname{MaxSpec}</math> of the algebra of scalars, indeed functorially so; this is the content of the [[Banach–Stone theorem]]. Indeed, any commutative C*-algebra can be realized as the algebra of scalars of a Hausdorff space in this way, yielding the same correspondence as between a ring and its spectrum. Generalizing to ''non''-commutative C*-algebras yields [[noncommutative topology]].