On products of <Emphasis Type="Italic">k</Emphasis> atoms |
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Authors: | Weidong Gao Alfred Geroldinger |
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Institution: | 1.Nankai University,Tianjin,P.R. China;2.Karl-Franzens-Universit?t Graz,Graz,Austria |
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Abstract: | 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].
Authors’ addresses: W. Gao, Center for Combinatorics, Nankai University, Tianjin 300071, P.R. China; A. Geroldinger, Institut
für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit?t Graz, Heinrichstra?e 36, 8010 Graz, Austria |
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Keywords: | 2000 Mathematics Subject Classification: 11R27 13F05 13A05 20M14 |
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