Stefan Schröer. Source: Journal of Commutative Algebra, Volume 12, Number 1, 135--151.Abstract:
Given a local noetherian ring [math] whose formal completion is integral, we introduce and study the [math] -radical closure [math] . Roughly speaking, this is the largest purely inseparable [math] -subalgebra inside the formal completion [math] . It turns out that the finitely generated intermediate rings [math] have rather peculiar properties. They can be used in a systematic way to provide examples of integral local rings whose normalization is nonfinite, that do not admit a resolution of singularities, and whose formal completion is nonreduced.