Finite generation properties for various rings of integer-valued polynomials

Manjul Bhargava, Paul Jean Cahen, Julie Yeramian

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

For any subset E of a Dedekind domain D, we show the ring Int{r} (E, D) of polynomials that are integer-valued on E together with all their divided differences of order up to r not to be a finitely generated D-algebra, contrary to the ring Intx (E, D) of integer-valued polynomials on E having a given non-zero modulus x (which is hence Noetherian, since the domain D is so). Localization properties allow us to focus on valuation domains; furthermore, the consideration of precompact subsets allows us to consider valuation domains V of arbitrary dimension.

Original languageEnglish (US)
Pages (from-to)1129-1150
Number of pages22
JournalJournal of Algebra
Volume322
Issue number4
DOIs
StatePublished - Aug 15 2009

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Finite differences
  • Integer-valued polynomials
  • Noetherian property
  • Precompact subset
  • Valuation domain

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