Commutative algebra

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. 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. (Wikipedia).

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From playlist Abstract Algebra

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From playlist Abstract Algebra

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From playlist Abstract Algebra

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From playlist Commutative algebra

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Related pages

Integral domain | Local ring | Noetherian ring | Algebra | Algebraic variety | Zariski's main theorem