◀ ▲ ▶Branches / Algebra / Definition: Factorial Ring, Generalization of Factorization
Definition: Factorial Ring, Generalization of Factorization
An integral domain $R$ is called a factorial ring, if every $a\in R\setminus \{0\}$ has the factorization $$a=\prod_{i=1}^r p_i^{e_i}$$ of irreducible elements $p_i$ and positive integer exponents $e_i > 0,$ which is unique except of the order of the elements $p_i$ and the associates of all $p_i.$
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Definitions: 1
Lemmas: 2
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References
Bibliography
- Modler, Florian; Kreh, Martin: "Tutorium Algebra", Springer Spektrum, 2013
- Koch, H.; Pieper, H.: "Zahlentheorie - Ausgewählte Methoden und Ergebnisse", Studienbücherei, 1976
