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Factorization in integral domains. (English) Zbl 0727.13007

Les AA. appellent “atomique” un anneau intègre R dans lequel tout élément est produit fini des éléments irréducibles. Sont étudiés les anneaux atomiques et les anneaux intègres avec la condition maximale pour les idéaux principaux, les anneaux atomique dans lesquels pour tout élément x non nul et non inversible il existe N(x) tel que pour toute décomposition \(x=x_ 1...x_ n\), où \(x_ i\) sont irréducibles, on a \(n\leq N(x)\), les anneaux intégres dans lesquels tout élément non nul a un nombre fini des diviseurs nonassociés, etc.

MSC:

13F15 Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
13G05 Integral domains
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