Analytically normal ring

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.

Zariski (1950) 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 (1958, 1962,Appendix A1, example 7) gave an example of a normal Noetherian local ring that is analytically reducible and therefore not analytically normal.

单词	Analytically normal local ring
释义	Analytically normal local ring 英语百科 Analytically normal ring 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. Zariski (1950) 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 (1958, 1962,Appendix A1, example 7) gave an example of a normal Noetherian local ring that is analytically reducible and therefore not analytically normal.
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Analytically normal local ring

Analytically normal ring