The japanese closure of local noetherian rings

Given a local noetherian ring $R$ whose formal completion is integral, we introduce and study the japanese closure $R^\text{jpn}$. Roughly speaking, this is the largest purely inseparable $R$-subalgebra inside the formal completion $\hat{R}$. It turns out that the finitely generated intermediate rings $R\subset A\subset R^\text{jpn}$ have rather peculiar properties. They can be used in a systematic way to provide examples of integral local rings whose normalization is non-finite, that do not admit a resolution of singularities, and whose formal completion is non-reduced. For discrete valuations rings, the japanese closure is an excellent discrete valuation ring, and $R\subset R^\text{jpn}$ is the smallest extension with this property.