# Factorization in Krull monoids with infinite class group

Colloquium Mathematicae (1999)

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

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topKainrath, 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

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

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