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

Abstract

The injective spectrum is a topological space associated to a ring $R$, which agrees with the Zariski spectrum when $R$ is commutative noetherian. We consider injective spectra of right noetherian rings (and locally noetherian Grothendieck categories) and establish some basic topological results and a functoriality result, as well as links between the topology and the Krull dimension of the ring (in the sense of Gabriel and Rentschler). Finally, we use these results to compute a number of examples.

arXiv comment29 pages, 1 figure

References in corpus (1)

• Classifying Serre subcategories via atom spectrum

Cited by in corpus (1)

• The Injective Spectrum of a Right Noetherian Ring II: Sheaves and Torsion Theories