Analytically irreducible ring

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. gave such an example of a normal Noetherian local ring that is analytically reducible.

Nagata's example
Suppose that K is a field of characteristic not 2, and K [x,y] is the formal power series ring over K in 2 variables. Let R be the subring of K [x,y] generated by x, y, and the elements zn and localized at these elements, where
 * $$w=\sum_{m>0} a_mx^m$$ is transcendental over K(x)
 * $$z_1=(y+w)^2$$
 * $$z_{n+1}=(z_1-(y+\sum_{0<m<n}a_mx^m)^2)/x^n$$.

Then R[X]/(X2–z1) is a normal Noetherian local ring that is analytically reducible.