Hello is there anyone that would know where I can find an example of a noetherian N-1 ring that is not a Nagata ring. (See the Wikipedia article "[Nagata ring](http://en.wikipedia.org/wiki/Nagata_ring)" for the definitions of N-1 ring and Nagata ring.) 



An example of a noetherian N-1 ring that is not N-2 and/or a Nagata ring
There is a discrete valuation ring $R$ (hence trivially N-1) of characteristic $p>0$ whose completion $\widehat{R}$ contains an element $x\not\in R$ such that $x^p\in R$. Such a ring cannot be N-2.


