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## 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 $p_i.$

| | | | | created: 2019-06-29 09:44:07 | modified: 2019-06-29 09:45:46 | by: bookofproofs | references: [677], [8250]

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