The affine scheme associated to a non-Noetherian prime PI algebra
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)].
affine prime polynomial identity algebra
scientific article; zbMATH DE number 3973081