Powers of sums and their associated primes

Hop D. Nguyen and Quang Hoa Tran

Vol. 316 (2022), No. 1, 217–235

DOI: 10.2140/pjm.2022.316.217

Abstract

Let $A$ and $B$ be polynomial rings over a field $k$, and let $I\subseteq A$ and $J\subseteq B$ be proper homogeneous ideals. We analyze the associated primes of powers of $I+J\subseteq A{\otimes }_{k}B$ given the data on the summands. The associated primes of large enough powers of $I+J$ are determined. We then answer positively a question due to I. Swanson and R. Walker about the persistence property of $I+J$ in many new cases.

Keywords

associated prime, powers of ideals, persistence property

Mathematical Subject Classification

Primary: 13A15, 13F20

Milestones

Received: 6 March 2021

Revised: 26 June 2021

Accepted: 5 November 2021

Published: 26 February 2022