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.