Normally flat ring

In algebraic geometry, a normally flat ring along a proper ideal ${\displaystyle I}$ is a local ring ${\displaystyle A}$ such that ${\displaystyle I^{n}/I^{n+1}}$ is flat over ${\displaystyle A/I}$ for all ${\displaystyle n\geq 0}$.

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