On the degree function coefficient of a simple complete ideal in   dimension two
  Let $(R,\mathfrak{M})$ be a two-dimensional regular local ring with algebraically closed residue field. Let $I$ be a simple complete $\mathfrak{M}$-primary ideal of $R$ and let $w$ denote its unique Rees valuation. Then the degree function coefficient $d(I,w)=1$.   In this note a short proof of this result is given. 
Raymond Debremaeker
math.AC