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The injective spectrum is a topological space associated to a ring $R$, whichagrees with the Zariski spectrum when $R$ is commutative noetherian. Weconsider injective spectra of right noetherian rings (and locally noetherianGrothendieck categories) and establish some basic topological results and afunctoriality result, as well as links between the topology and the Krulldimension of the ring (in the sense of Gabriel and Rentschler). Finally, we usethese results to compute a number of examples.

The Injective Spectrum of a Right Noetherian Ring I: Injective Spectra and Krull Dimension