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 for some irreducible elements , (ii) k ∈ L.
@article{bwmeta1.element.bwnjournal-article-cmv80i1p23bwm,
author = {Florian Kainrath},
title = {Factorization in Krull monoids with infinite class group},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {23-30},
zbl = {0936.20050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv80i1p23bwm}
}
Kainrath, Florian. Factorization in Krull monoids with infinite class group. Colloquium Mathematicae, Tome 79 (1999) pp. 23-30. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv80i1p23bwm/
[000] [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. | Zbl 0897.13001
[001] [2] F. Kainrath, A divisor theoretic approach towards the arithmetic of noetherian domains, Arch. Math., to appear. | Zbl 0964.13005
[002] [3] F. Kainrath, The distribution of prime divisors in finitely generated domains, preprint. | Zbl 0942.13016
[003] [4] I. Kaplansky, Infinite Abelian Groups, third printing, The University of Michigan Press, 1960.