Relative polynomial closure and monadically Krull monoids of integer-valued polynomials

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandBegutachtung


Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f∈Int(D), we explicitly construct a divisor homomorphism from [[f]], the divisor-closed submonoid of Int(D) generated by f, to a finite sum of copies of (N0,+). This implies that [[f]] is a Krull monoid. For V a discrete valuation domain, we give explicit divisor theories of various submonoids of Int(V). In the process, we modify the concept of polynomial closure in such a way that every subset of D has a finite polynomially dense subset . The results generalize to Int(S,V), the ring of integer-valued polynomials on a subset, provided S does not have isolated points in v-adic topology
TitelMultiplicative Ideal Theory and Factorization Theory
UntertitelCommutative and Non-commutative Perspectives
Redakteure/-innenScott Chapman, Marco Fontana, Alfred Geroldinger, Bruce Olberding
Herausgeber (Verlag)Springer International Publishing AG
ISBN (elektronisch)978-3-319-38855-7
ISBN (Print)978-3-319-38853-3
PublikationsstatusVeröffentlicht - 2016


Name Springer Proceedings in Mathematics & Statistics
Herausgeber (Verlag)Springer
ISSN (Print)2194-1009


  • commutative rings, factorization, monoids, divisor theory, arithmetic

ASJC Scopus subject areas

  • Algebra und Zahlentheorie

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


Untersuchen Sie die Forschungsthemen von „Relative polynomial closure and monadically Krull monoids of integer-valued polynomials“. Zusammen bilden sie einen einzigartigen Fingerprint.

Dieses zitieren