Skip to main content
Article thumbnail
Location of Repository

The ring of bounded polynomials on a semi-algebraic set

By Daniel Plaumann and Claus Scheiderer


Abstract. Let V be a normal affine R-variety, and let S be a semi-algebraic subset of V (R) which is Zariski dense in V. We study the subring BV (S) of R[V] consisting of the polynomials that are bounded on S. We introduce the notion of S-compatible completions of V, and we prove the existence of such completions when dim(V) ≤ 2orS = V (R). An S-compatible completion X of V yields a ring isomorphism OU (U) ∼ → BV (S) for some (concretely specified) open subvariety U ⊃ V of X. We prove that BV (S) is a finitely generated R-algebra if dim(V) ≤ 2andS is open, and we show that this result becomes false in general when dim(V) ≥ 3

Year: 2013
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.