A realization theorem for sets of lengths (Q1017382)
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scientific article; zbMATH DE number 5554690
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A realization theorem for sets of lengths |
scientific article; zbMATH DE number 5554690 |
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A realization theorem for sets of lengths (English)
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19 May 2009
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It is known that the set of factorization lengths of an integer in an algebraic number field with class-number \(\neq 1,2\) is an almost arithmetical progression (see Definition 4.2.1 and Theorem 4.6.6 in [\textit{A. Geroldinger} and \textit{F. Halter-Koch}, Non-unique factorizations, Chapman \& Hall (2006; Zbl 1113.11002)]). The authors obtain a kind of converse of this result.
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Krull monoid
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factorization lengths
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non-unique factorization
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algebraic number field
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0.9398657
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0.9224242
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0.9017333
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0.8592805
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