The affine scheme associated to a non-Noetherian prime PI algebra
type: Item
instance of: scholarly article
title: The affine scheme associated to a non-Noetherian prime PI algebra
zbMATH Open document ID: 0603.16014
DOI: 10.1007/BF02772674
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let R be an affine prime polynomial identity algebra, and Spec R the space of prime ideals with the Zariski topology. Let ''R-bimodule'' mean a two-sided R-module M that is generated by the centralizer of R in M, and ''extension'' mean a ring map \(f: R\to S\) such that S is an R-bimodule. Using bimodule localization a structure sheaf for R over Spec R is constructed, which enjoys functorial properties with respect to extensions. The sheaf reduces to the usual one when R is commutative. This generalizes to non-noetherian algebras a construction obtained earlier by \textit{F. Van Oystaeyen} and the author in the case where R is left noetherian [Noncommutative algebraic geometry (Lect. Notes Math. 887; 1981; Zbl 0477.16001)].
Mathematics Subject Classification ID: 16Rxx
Mathematics Subject Classification ID: 16Dxx
Mathematics Subject Classification ID: 16P50
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16S90
Mathematics Subject Classification ID: 14A20
zbMATH DE Number: 3973081
zbMATH Keywords: affine prime polynomial identity algebra
zbMATH Keywords: bimodule localization
zbMATH Keywords: structure sheaf
zbMATH Keywords: extensions
zbMATH Keywords: non-noetherian algebras
author: Alain Verschoren
reviewed by: A. C. Mewborn
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3973081