2004/03/12 by Edward S. Letzter, Letzter, Edward S.
Mathematics · #16D25 #16S20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA #msc:16D25 #msc:16S20
paper · pdf · doi:10.48550/arxiv.math/0403204
13 pages; AMS-TeX. Minor revisions; reference added. To appear in Proceedings of the Edinburgh Mathematical Society
openalex publication_date 2004/03/12 · arxiv created 2005/05/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study topological properties of the correspondence of prime spectra associated to a noncommutative ring homomorphism R -> S. Our main result provides criteria for the adjointness of certain functors between the categories of Zariski closed subsets of Spec(R) and Spec(S); these functors arise naturally from restriction and extension of scalars. When R and S are left noetherian, adjointness occurs only for centralizing and ``nearly centralizing'' homomorphisms.