Normally flat ring

{{Short description|Local ring in algebraic geometry}}

{{more footnotes|date=June 2019}}

In algebraic geometry, a normally flat ring along a proper ideal I is a local ring A such that $I^n/I^\{n+1\}$ is flat over $A/I$ for each integer $n\; \backslash ge\; 0$.

The notion was introduced by Hironaka in his proof of the resolution of singularities as a refinement of equimultiplicity and was later generalized by Alexander Grothendieck and others.