Normally flat ring

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

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.

References

• Herrmann, M., S. Ikeda, and U. Orbanz: Equimultiplicity and Blowing Up. An Algebraic Study with an Appendix by B. Moonen. Springer Verlag, Berlin Heidelberg New-York, 1988.