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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Parametric decomposition of powers of ideals versus regularity of sequences
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by Shiro Goto and Yasuhiro Shimoda PDF
Proc. Amer. Math. Soc. 132 (2004), 929-933 Request permission

Abstract:

Let $Q = (a_{1}, a_{2}, \cdots , a_{s}) \ (\subsetneq A)$ be an ideal in a Noetherian local ring $A$. Then the sequence $a_{1}, a_{2}, \cdots , a_{s}$ is $A$-regular if every $a_{i}$ is a non-zerodivisor in $A$ and if $Q^{n} = \bigcap _{\alpha } (a_{1}^{\alpha _{1}}, a_{2}^{\alpha _{2}}, \cdots , a_{s}^{\alpha _{s}})$ for all integers $n \geq 1$, where $\alpha = (\alpha _{1}, \alpha _{2}, \cdots , \alpha _{s})$ runs over the elements of the set $\Lambda _{s,n} = \{(\alpha _{1}, \alpha _{2}, \cdots , \alpha _{s}) \in {\mathbb {Z}}^{s} \mid \alpha _{i} \geq 1 \ \text {for all} \ 1 \leq i \leq s \ \text {and} \ \sum _{i=1}^{s}\alpha _{i} = s + n - 1\}$.
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Additional Information
  • Shiro Goto
  • Affiliation: Department of Mathematics, School of Science and Technology, Meiji University, 214-8571 Japan
  • MR Author ID: 192104
  • Email: goto@math.meiji.ac.jp
  • Yasuhiro Shimoda
  • Affiliation: Department of Mathematics, Faculty of General Education, Kitasato University, 228-8555 Japan
  • Email: shimoda@clas.kitasato-u.ac.jp
  • Received by editor(s): May 28, 2002
  • Published electronically: October 29, 2003
  • Additional Notes: The first author is supported by the Grant-in-Aid for Scientific Research in Japan (C(2), No. 13640044)
  • Communicated by: Bernd Ulrich
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 929-933
  • MSC (2000): Primary 13H99
  • DOI: https://doi.org/10.1090/S0002-9939-03-07160-0
  • MathSciNet review: 2045406