Prime filtrations of the powers of an ideal

TL;DR

This paper proves that for any ideal in a ring, it is possible to select prime filtrations for all powers of the ideal simultaneously, with a finite set of primes appearing across all filtrations.

Contribution

It introduces a method to choose prime filtrations of all powers of an ideal simultaneously with a finite prime set, advancing understanding of ideal filtrations.

Findings

Prime filtrations can be chosen for all powers of an ideal simultaneously.

The set of primes in these filtrations is finite.

This result holds for all powers of the ideal.

Abstract

We prove that for all $n$, simultaneously, we can choose prime filtrations of $R/I^n$ such that the set of primes appearing in these filtrations is finite.