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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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On the depth of the associated graded ring
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by Anna Guerrieri PDF
Proc. Amer. Math. Soc. 123 (1995), 11-20 Request permission

Abstract:

Let (R, m) be a Cohen-Macaulay local ring of positive dimension d, let I be an $m -$ primary ideal of R. In this paper we individuate some conditions on I that allow us to determine a lower bound for depth ${\text {gr}_I}(R)$. It is proved that if $J \subseteq I$ is a minimal reduction of I such that $\lambda ({I^2} \cap J/IJ) = 2$ and ${I^n} \cap J = {I^{n - 1}}J$ for all $n \geq 3$, then depth ${\text {gr}_I}(R) \geq d - 2$; let us remark that $\lambda$ denotes the length function.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 11-20
  • MSC: Primary 13A30; Secondary 13C15, 13H10
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1211580-9
  • MathSciNet review: 1211580