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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Rees algebras of ideals having small analytic deviation
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by Sam Huckaba and Craig Huneke PDF
Trans. Amer. Math. Soc. 339 (1993), 373-402 Request permission

Abstract:

In this article we identify two large families of ideals of a Cohen-Macaulay (sometimes Gorenstein) local ring whose Rees algebras are Cohen-Macaulay. Our main results imply, for example, that if $(R,M)$ is a regular local ring and $P$ is a prime ideal of $R$ such that ${P^n}$ is unmixed for all $n \geq 1$, then the Rees algebra $R[Pt]$ is Cohen-Macaulay if either $\dim (R/P) = 2$, or $\dim (R/P) = 3,R/P$ is Cohen-Macaulay, and $R/P$ is integrally closed.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 339 (1993), 373-402
  • MSC: Primary 13A30; Secondary 13H10
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1123455-7
  • MathSciNet review: 1123455