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. Nagata's example. Suppose that "K" is a field of characteristic not 2, and "K"  is the formal power series ring over "K" in 2 variables. Let "R" be the subring of "K"  generated by "x", "y", and the elements "z" and localized at these elements, where Then "R"["X"]/("X"–"z") is a normal Noetherian local ring that is analytically reducible.