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- In mathematics, the Cohen structure theorem, introduced by Cohen, describes the structure of complete Noetherian local rings. Some consequences of Cohen's structure theorem include three conjectures of Krull:
* Any complete regular equicharacteristic Noetherian local ring is a ring of formal power series over a field. (Equicharacteristic means that the local ring and its residue field have the same characteristic, and is equivalent to the local ring containing a field.)
* Any complete regular Noetherian local ring that is not equicharacteristic but is unramified is uniquely determined by its residue field and its dimension.
* Any complete Noetherian local ring is the image of a complete regular Noetherian local ring. (en)
- В комутативній алгебрі структурна теорема Коена описує будову повних нетерових локальних кілець. Теорему довів у 1946 році американський математик Ірвінг Коен. (uk)
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- В комутативній алгебрі структурна теорема Коена описує будову повних нетерових локальних кілець. Теорему довів у 1946 році американський математик Ірвінг Коен. (uk)
- In mathematics, the Cohen structure theorem, introduced by Cohen, describes the structure of complete Noetherian local rings. Some consequences of Cohen's structure theorem include three conjectures of Krull: (en)
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- Cohen structure theorem (en)
- Структурна теорема Коена (uk)
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