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About: Analytically irreducible ring     Goto   Sponge   NotDistinct   Permalink

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In algebra, an analytically irreducible ring is a local ring whose completion has no zero divisors. Geometrically this corresponds to a variety with only one analytic branch at a point. proved that if a local ring of an algebraic variety is a normal ring, then it is analytically irreducible. There are many examples of reduced and irreducible local rings that are analytically reducible, such as the local ring of a node of an irreducible curve, but it is hard to find examples that are also normal. Nagata gave such an example of a normal Noetherian local ring that is analytically reducible.