On products of k atoms

. Let H be an atomic monoid. For let denote the set of all with the following property: There exist atoms (irreducible elements) u 1 , …, u k , v 1 , …, v m ∈ H with u 1 · … · u k = v 1 · … · v m . We show that for a large class of noetherian domains satisfying some natural finiteness conditions, th...

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Bibliographic Details
Published inMonatshefte für Mathematik Vol. 156; no. 2; pp. 141 - 157
Main Authors Gao, Weidong, Geroldinger, Alfred
Format Journal Article
LanguageEnglish
Published Vienna Springer-Verlag 01.02.2009
Subjects
Mathematics
Mathematics and Statistics
Key words: Non-unique factorizations, sets of lengths, Krull monoids
2000 Mathematics Subject Classification: 11R27, 13F05, 13A05, 20M14
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ISSN0026-9255
1436-5081
DOI10.1007/s00605-008-0547-z

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Summary:. Let H be an atomic monoid. For let denote the set of all with the following property: There exist atoms (irreducible elements) u 1 , …, u k , v 1 , …, v m ∈ H with u 1 · … · u k = v 1 · … · v m . We show that for a large class of noetherian domains satisfying some natural finiteness conditions, the sets are almost arithmetical progressions. Suppose that H is a Krull monoid with finite cyclic class group G such that every class contains a prime (this includes the multiplicative monoids of rings of integers of algebraic number fields). We show that, for every , max which settles Problem 38 in [4].
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-008-0547-z