Factorization in Krull monoids with infinite class group

• Autorzy: Florian Kainrath
• Języki publikacji: EN

Abstrakty

EN

Let H be a Krull monoid with infinite class group and such that each divisor class of H contains a prime divisor. We show that for each finite set L of integers ≥2 there exists some h ∈ H such that the following are equivalent: (i) h has a representation $h=u_1·...· u_k$ for some irreducible elements $u_i$, (ii) k ∈ L.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 80
• Numer: 1
• Strony: 23-30

Daty

wydano

1999

otrzymano

1998-02-26

Twórcy

autor

Florian Kainrath

• Institut für Mathematik, Karl-Franzes-Universität, Heinrichstraße 36, A-8010 Graz, Austria

Bibliografia

• [1] S. Chapman and A. Geroldinger, Krull domains and monoids, their sets of lengths, and associated combinatorial problems, in: Factorization in Integral Domains, D. D. Anderson (ed.), Lecture Notes in Pure and Appl. Math. 189, Marcel Dekker, 1997, 73-112.
• [2] F. Kainrath, A divisor theoretic approach towards the arithmetic of noetherian domains, Arch. Math., to appear.
• [3] F. Kainrath, The distribution of prime divisors in finitely generated domains, preprint.
• [4] I. Kaplansky, Infinite Abelian Groups, third printing, The University of Michigan Press, 1960.