Saturation of Ideals

Given an ideal I and an element or ideal J in a ring R, the saturation I : J^∞ = { f ∈ R | ∃ n with J^n f ⊆ I } (commonly I : f^∞ when J = (f)) removes components of V(I) contained in V(J) and produces an ideal whose vanishing set is V(I) minus the part supported inside V(J).