Symbolic power of a prime ideal

In algebra, given a ring R and a prime ideal P in it, the n-th symbolic power of P is the ideal

It is the smallest P-primary ideal containing the n-th power Pⁿ. Very roughly, it consists of functions with zeros of order n along the variety defined by P. If R is Noetherian, then it is the P-primary component in the primary decomposition of Pⁿ. We have: P ( 1 ) = P and if P is a maximal ideal, then P ( n ) = P n .