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arXiv · 2101.06583

Powers of sums and their associated primes

Hop D. Nguyen·Quang Hoa Tran
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Abstract

Let $A, B$ be polynomial rings over a field $k$, and $I\subseteq A, J\subseteq B$ 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 about the persistence property of $I+J$ in many new cases.

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Hop D. Nguyen, Quang Hoa Tran. 2021-01-17. Powers of sums and their associated primes. https://doi.org/10.2140/pjm.2022.316.217

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