For $p,q>1$, relatively prime, $x^p - y^q$ is irreducible in $K[x,y]$. Is it also irreducible in $K[[x,y]]$ and how would you show it? I'm quite stuck at the moment.
Also $K[x,y]/(x^p - y^q)$ is not integrally closed in its quotient field. Does the same hold for $K[[x,y]]/(x^p - y^q)$? (This wouldn't make sense if $(x^p -y^q)$ were not irreducible, hence the first question)