Factorization in Krull monoids with infinite class group

Florian Kainrath

ArticleOriginal scientific text

Title

Factorization in Krull monoids with infinite class group

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Affiliations

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

Abstract

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} \cdot ... \cdot u_{k}

for some irreducible elements

u_{i}

, (ii) k ∈ L.

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.
F. Kainrath, A divisor theoretic approach towards the arithmetic of noetherian domains, Arch. Math., to appear.
F. Kainrath, The distribution of prime divisors in finitely generated domains, preprint.
I. Kaplansky, Infinite Abelian Groups, third printing, The University of Michigan Press, 1960.

Title

Factorization in Krull monoids with infinite class group

Affiliations

Abstract

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