In algebraic geometry, a normally flat ring along a proper ideal I is a local ring A such that I n / I n + 1 {\displaystyle I^{n}/I^{n+1}} is flat over A / I {\displaystyle A/I} for each integer n ≥ 0 {\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 Alexander Grothendieck and others.
In algebraic geometry, a normally flat ring along a proper ideal I is a local ring A such that I n / I n + 1 {\displaystyle I^{n}/I^{n+1}} is flat over A / I {\displaystyle A/I} for each integer n ≥ 0 {\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 Alexander Grothendieck and others.
Source: Wikipedia "Normally flat ring" · CC BY-SA 4.0
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