Reductions of ideals in local rings with finite residue fields
Reductions of ideals in local rings with finite residue fields
Let $I$ be a proper nonnilpotent ideal in a local (Noetherian) ring $(R,M)$ and let $J$ be a reduction of $I$; that is, $J$ $\subseteq$ $I$ and $JI^n$ $=$ $I^{n+1}$ for some nonnegative integer $n$. We prove that there exists a finite free local unramified extension ring $S$ of $R$ …