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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Depth functions of powers of homogeneous ideals
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by Huy Tài Hà, Hop Dang Nguyen, Ngo Viet Trung and Tran Nam Trung PDF
Proc. Amer. Math. Soc. 149 (2021), 1837-1844 Request permission

Abstract:

We settle a conjecture of Herzog and Hibi, which states that the function $\mathrm {depth} S/Q^n$, $n \ge 1$, where $Q$ is a homogeneous ideal in a polynomial ring $S$, can be any convergent numerical function. We also give a positive answer to a longstanding open question of Ratliff on the associated primes of powers of ideals.
References
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Additional Information
  • Huy Tài Hà
  • Affiliation: Department of Mathematics, Tulane University. 6823 St. Charles Avenue, New Orleans, Louisiana 70118
  • ORCID: 0000-0002-6002-3453
  • Email: tha@tulane.edu
  • Hop Dang Nguyen
  • Affiliation: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam
  • MR Author ID: 981901
  • Email: ngdhop@gmail.com
  • Ngo Viet Trung
  • Affiliation: International Centre for Research and Postgraduate Training, Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam
  • MR Author ID: 207806
  • Email: nvtrung@math.ac.vn
  • Tran Nam Trung
  • Affiliation: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam
  • Email: tntrung@math.ac.vn
  • Received by editor(s): April 17, 2019
  • Received by editor(s) in revised form: February 24, 2020
  • Published electronically: March 2, 2021
  • Additional Notes: The first author was partially supported by the Simons Foundation (grant #279786) and Louisiana Board of Regents (grant #LEQSF(2017-19)-ENH-TR-25).
    The third author was partially supported by Vietnam National Foundation for Science and Technology Development under grant number 101.04-2019.313.
    The second and fourth authors were partially funded by International Centre for Research and Postgraduate Training in Mathematics (ICRTM) under grant numbers ICRTM01_2020.05 and ICRTM01_2020.04.
  • Communicated by: Claudia Polini
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 1837-1844
  • MSC (2020): Primary 13C15, 13D02, 14B05
  • DOI: https://doi.org/10.1090/proc/15083
  • MathSciNet review: 4232180