The Michigan Mathematical Journal

Almost Gorenstein Rees Algebras of pg-Ideals, Good Ideals, and Powers of the Maximal Ideals

Shiro Goto, Naoyuki Matsuoka, Naoki Taniguchi, and Ken-ichi Yoshida

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Let (A,m) be a Cohen–Macaulay local ring, and let I be an ideal of A. We prove that the Rees algebra R(I) is an almost Gorenstein ring in the following cases:

(1) (A,m) is a two-dimensional excellent Gorenstein normal domain over an algebraically closed field KA/m, and I is a pg-ideal;

(2) (A,m) is a two-dimensional almost Gorenstein local ring having minimal multiplicity, and I=m for all 1;

(3) (A,m) is a regular local ring of dimension d2, and I=md1. Conversely, if R(m) is an almost Gorenstein graded ring for some 2 and d3, then =d1.

Article information

Michigan Math. J., Volume 67, Issue 1 (2018), 159-174.

Received: 22 August 2016
Revised: 20 June 2017
First available in Project Euclid: 19 January 2018

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Zentralblatt MATH identifier

Primary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] 13H15: Multiplicity theory and related topics [See also 14C17] 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics


Goto, Shiro; Matsuoka, Naoyuki; Taniguchi, Naoki; Yoshida, Ken-ichi. Almost Gorenstein Rees Algebras of $p_{g}$ -Ideals, Good Ideals, and Powers of the Maximal Ideals. Michigan Math. J. 67 (2018), no. 1, 159--174. doi:10.1307/mmj/1516330972.

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