Tensor-multinomial sums of ideals: Primary decompositions and persistence of associated primes
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- by Irena Swanson and Robert M. Walker PDF
- Proc. Amer. Math. Soc. 147 (2019), 5071-5082 Request permission
Abstract:
Given a Noetherian tensor product of two Noetherian algebras over a field and proper ideals $I$ and $J$ in the two algebras, we determine the associated primes of each power of $I+J$ in terms of the associated primes of lower powers of $I$ and of $J$. We record two applications. First, in case the field is algebraically closed, we construct primary decompositions for powers of $I+J$ from primary decompositions for powers of $I$ and $J$. Separately, we attack the persistence problem for associated primes of powers of an ideal in case one of $I$ or $J$ is a non-zero normal ideal.References
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Additional Information
- Irena Swanson
- Affiliation: Department of Mathematics, Reed College, 3203 SE Woodstock Boulevard, Portland, Oregon 97202
- MR Author ID: 320892
- Email: iswanson@reed.edu
- Robert M. Walker
- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
- MR Author ID: 1031098
- Email: robmarsw@umich.edu
- Received by editor(s): July 1, 2018
- Received by editor(s) in revised form: March 5, 2019
- Published electronically: June 10, 2019
- Additional Notes: In the course of completing this work, the second author acknowledges support from NSF RTG grant DMS-0943832, NSF DMS-1501625, a 2017–18 Ford Foundation Dissertation Fellowship, and a 2018–19 Rackham Science Award from the Rackham Graduate School at UM-Ann Arbor and partial support from NSF grant 1501625.
- Communicated by: Claudia Polini
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 5071-5082
- MSC (2010): Primary 13C05; Secondary 13B22, 14B05
- DOI: https://doi.org/10.1090/proc/14630
- MathSciNet review: 4021070