Analytically unramified ring

In algebra, an analytically unramified ring is a local ring whose completion is reduced (has no nonzero nilpotent).
The following rings are analytically unramified:
 showed that every local ring of an algebraic variety is analytically unramified.
 gave an example of an analytically ramified reduced local ring. showed that every 1-dimensional normal Noetherian local ring is analytically unramified; more precisely he showed that a 1-dimensional normal Noetherian local domain is analytically unramified if and only if its integral closure is a finite module. This prompted to ask whether a local Noetherian domain such that its integral closure is a finite module is always analytically unramified. However gave an example of a 2-dimensional normal analytically ramified Noetherian local ring. Nagata also showed that a slightly stronger version of Zariski's question is correct: if the normalization of every finite extension of a given Noetherian local ring "R" is a finite module, then "R" is analytically unramified.
There are two classical theorems of that characterize analytically unramified rings. The first says that a Noetherian local ring ("R", "m") is analytically unramified if and only if there are a "m"-primary ideal "J" and a sequence formula_1 such that formula_2, where the bar means the integral closure of an ideal. The second says that a Noetherian local domain is analytically unramified if and only if, for every finitely-generated "R"-algebra "S" lying between "R" and the field of fractions "K" of "R", the integral closure of "S" in "K" is a finitely generated module over "S". The second follows from the first.
Nagata's example.
Let "K"0 be a perfect field of characteristic 2, such as F2.
Let "K" be "K"0({"u""n", "v""n" : "n" ≥ 0}), where the "u""n" and "v""n" are indeterminates.
Let "T" be the subring of the formal power series ring "K"  generated by "K" and "K""2"  and the element ∑("u""n""x""n"+ "v""n""y""n"). Nagata proves that "T" is a normal local noetherian domain whose completion has nonzero nilpotent elements, so "T" is analytically ramified.