A closer look at non-unique factorization via atomic decay and strong atoms (Q2895448)
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scientific article; zbMATH DE number 6052225
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A closer look at non-unique factorization via atomic decay and strong atoms |
scientific article; zbMATH DE number 6052225 |
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2 July 2012
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non-unique factorization
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algebraic number fields
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half-factorial domains
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A closer look at non-unique factorization via atomic decay and strong atoms (English)
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Let \(D\) be a domain. An irreducible element \(x \in D\) is called an atom; an atom is a strong atom if for every \(k \geq 1\), every irreducible divisor of \(x^k\) is an associate of \(x\). The article investigates the notion of strong atoms in rings of integers of algebraic number fields and discusses the examples \({\mathbb Z}[\sqrt{-5}\,]\) and \({\mathbb Z}[5i]\).NEWLINENEWLINEFor the entire collection see [Zbl 1237.13006].
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