Normally flat ring

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 $$n \ge 0$$.

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.