Factorization in Krull monoids with infinite class group

Florian Kainrath

Colloquium Mathematicae (1999)

  • Volume: 80, Issue: 1, page 23-30
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Kainrath, Florian. "Factorization in Krull monoids with infinite class group." Colloquium Mathematicae 80.1 (1999): 23-30. <http://eudml.org/doc/210702>.

@article{Kainrath1999,
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 $h=u_1·...· u_k$ for some irreducible elements $u_i$, (ii) k ∈ L.},
author = {Kainrath, Florian},
journal = {Colloquium Mathematicae},
keywords = {factorization lengths; Krull monoids; class groups; factorizations into irreducibles; Noetherian domains},
language = {eng},
number = {1},
pages = {23-30},
title = {Factorization in Krull monoids with infinite class group},
url = {http://eudml.org/doc/210702},
volume = {80},
year = {1999},
}

TY - JOUR
AU - Kainrath, Florian
TI - Factorization in Krull monoids with infinite class group
JO - Colloquium Mathematicae
PY - 1999
VL - 80
IS - 1
SP - 23
EP - 30
AB - 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.
LA - eng
KW - factorization lengths; Krull monoids; class groups; factorizations into irreducibles; Noetherian domains
UR - http://eudml.org/doc/210702
ER -

References

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  1. [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. Zbl0897.13001
  2. [2] F. Kainrath, A divisor theoretic approach towards the arithmetic of noetherian domains, Arch. Math., to appear. Zbl0964.13005
  3. [3] F. Kainrath, The distribution of prime divisors in finitely generated domains, preprint. Zbl0942.13016
  4. [4] I. Kaplansky, Infinite Abelian Groups, third printing, The University of Michigan Press, 1960. 

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