Powers of sums and their associated primes

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.

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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

Authors

Hop D. Nguyen
Institute of Mathematics VAST Hanoi Vietnam

Quang Hoa Tran
University of Education Hue University Hue Vietnam

Vol. 316, No. 1, 2022

Hop D. Nguyen and Quang Hoa Tran

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors