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arXiv · 1908.05876

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

Harry Gulliver
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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.

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Harry Gulliver. 2019-08-16. The Injective Spectrum of a Right Noetherian Ring I: Injective Spectra and Krull Dimension. https://arxiv.org/abs/1908.05876

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