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 all $n\geq 0$.

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.

References

• Herrmann, M.; Ikeda, S.; Orbanz, U. (1988). Equimultiplicity and Blowing Up: An Algebraic Study (2011 softcover ed.). Berlin, Heidelberg: Springer. ISBN 978-3-642-64803-8.