Factorization properties of Krull monoids with infinite class group

• Autorzy: Wolfgang Hassler
• Języki publikacji: EN

Abstrakty

EN

For a non-unit a of an atomic monoid H we call
$L_H(a) = {k ∈ ℕ | a = u₁... u_k with irreducible u_i ∈ H}$
the set of lengths of a. Let H be a Krull monoid with infinite divisor class group such that each divisor class is the sum of a bounded number of prime divisor classes of H. We investigate factorization properties of H and show that H has sets of lengths containing large gaps. Finally we apply this result to finitely generated algebras over perfect fields with infinite divisor class group.

Kategorie tematyczne

• 20M14: Commutative semigroups
• 13A05: Divisibility; factorizations
• 13F05: Dedekind, Pr\"ufer, Krull and Mori rings and their generalizations
• 13C20: Class groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 92
• Numer: 2
• Strony: 229-242

Daty

wydano

2002

Twórcy

autor

Wolfgang Hassler

• Institut für Mathematik, Karl-Franzens-Universität Graz, Heinrichstraße 36/4, A-8010 Graz, Austria

Identyfikatory

DOI

10.4064/cm92-2-7