2010/12/31 by Nikolaus Vonessen
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Identity (music) #Mathematical analysis #Mathematics #Polynomial #Polynomial ring #Pure mathematics #Rings, Modules, and Algebras #math.RA #msc:14A10 #msc:14L30 #msc:16R20 #msc:16R30
paper · pdf · doi:10.1016/j.jalgebra.2012.08.014
published in Journal of Algebra 371, 462-479 (Elsevier BV) · 24 pages, LaTeX. Many changes. Theorem II.1.3 has been strengthened, Sections II.6-II.8 have been rewritten, and Section II.9 is new
arxiv created 2011/11/12 · openalex publication_date 2012/09/12 · arxiv updated 2012/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In characteristic zero, Zinovy Reichstein and the author generalized the usual relationship between irreducible Zariski closed subsets of the affine space, their defining ideals, coordinate rings, and function fields, to a non-commutative setting, where "varieties" carry a PGLn-action, regular and rational "functions" on them are matrix-valued, "coordinate rings" are prime polynomial identity algebras, and "function fields" are central simple algebras of degree n. In the present paper, much of this is extended to prime characteristic. In addition, a mistake in the earlier paper is corrected. One of the results is that the finitely generated prime PI-algebras of degree n are precisely the rings that arise as "coordinate rings" of "n-varieties" in this setting. For n = 1 the definitions and results reduce to those of classical affine algebraic geometry.