# 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

## Parametric decomposition of powers of ideals versus regularity of sequencesHTML articles powered by AMS MathViewer

by Shiro Goto and Yasuhiro Shimoda
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 $\Lambda _{s,n} = \{(\alpha _{1}, \alpha _{2}, \cdots , \alpha _{s}) \in {\mathbb {Z}}^{s} \mid \alpha _{i} \geq 1 \ \text {for all} \ 1 \leq i \leq s \ \text {and} \ \sum _{i=1}^{s}\alpha _{i} = s + n - 1\}$.
Similar Articles
• Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13H99
• Retrieve articles in all journals with MSC (2000): 13H99
• 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