About: Analytically normal ring

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In algebra, an analytically normal ring is a local ring whose completion is a normal ring, in other words a domain that is integrally closed in its quotient field. proved that if a local ring of an algebraic variety is normal, then it is analytically normal, which is in some sense a variation of Zariski's main theorem. Nagata gave an example of a normal Noetherian local ring that is analytically reducible and therefore not analytically normal.

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  • In algebra, an analytically normal ring is a local ring whose completion is a normal ring, in other words a domain that is integrally closed in its quotient field. proved that if a local ring of an algebraic variety is normal, then it is analytically normal, which is in some sense a variation of Zariski's main theorem. Nagata gave an example of a normal Noetherian local ring that is analytically reducible and therefore not analytically normal. (en)
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  • Nagata (en)
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  • Appendix A1, example 7 (en)
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  • 1958 (xsd:integer)
  • 1962 (xsd:integer)
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  • In algebra, an analytically normal ring is a local ring whose completion is a normal ring, in other words a domain that is integrally closed in its quotient field. proved that if a local ring of an algebraic variety is normal, then it is analytically normal, which is in some sense a variation of Zariski's main theorem. Nagata gave an example of a normal Noetherian local ring that is analytically reducible and therefore not analytically normal. (en)
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  • Analytically normal ring (en)
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