Let R {\displaystyle {}R} be a noetherian domain of positive characteristic and let I ⊆ R {\displaystyle {}I\subseteq R} be an ideal. The tight closure of I {\displaystyle {}I} is the ideal
![{\displaystyle {}I^{*}={\left\{f\in R\mid {\text{ there exists }}z\neq 0{\text{ such that }}zf^{q}\in I^{[q]}{\text{ for all }}q=p^{e}\right\}}\,.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73e19d08b5e9712f4297e86be0cf8df5a73c9dd3)