The injective spectrum of aright noetherian ring

[摘要] The injective spectrum is a topological space associated to a ring R, which agrees with the Zariski spectrum when Ris 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. Crown Copyright (C) 2020 Published by Elsevier Inc.

[发布日期] 2020-12-15

[关键词] Injective spectrum;Heisenberg algebra;Grothendieck category;Module category;Injective modules;Noncommutative geometry;Krull dimension