#### Vol. 316, No. 1, 2022

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Powers of sums and their associated primes

### Hop D. Nguyen and Quang Hoa Tran

Vol. 316 (2022), No. 1, 217–235
##### 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