Symbolic powers of prime ideals and their topology

Abstract

For a prime ideal P P of a commutative Noetherian ring R R a necessary and sufficient condition is given to determine when the P P -adic topology is equivalent, resp. linearly equivalent, to the P P -symbolic topology. The last means that the symbolic Rees ring is a finitely generated module over the ordinary Rees ring of P P . Then it is considered when the integral closure of all the powers of P P are primary.