Let R {\displaystyle {}R} be a normal excellent local domain with maximal ideal m {\displaystyle {}{\mathfrak {m}}} over a field of positive characteristic. Let f 1 , … , f n {\displaystyle {}f_{1},\ldots ,f_{n}} generate an m {\displaystyle {}{\mathfrak {m}}} -primary ideal I {\displaystyle {}I} and let f {\displaystyle {}f} be another element in R {\displaystyle {}R} . Then f ∈ I ∗ {\displaystyle {}f\in I^{*}} if and only if
where A = R [ T 1 , … , T n ] / ( f 1 T 1 + ⋯ + f n T n + f ) {\displaystyle {}A=R[T_{1},\ldots ,T_{n}]/{\left(f_{1}T_{1}+\cdots +f_{n}T_{n}+f\right)}} denotes the forcing algebra of these elements.
![{\displaystyle {}A=R[T_{1},\ldots ,T_{n}]/{\left(f_{1}T_{1}+\cdots +f_{n}T_{n}+f\right)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/62f634a8f4c60ccf017398d7c2fc2c4bb484bdaa)