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March 2018 Almost Gorenstein Rees Algebras of pg-Ideals, Good Ideals, and Powers of the Maximal Ideals
Shiro Goto, Naoyuki Matsuoka, Naoki Taniguchi, Ken-ichi Yoshida
Michigan Math. J. 67(1): 159-174 (March 2018). DOI: 10.1307/mmj/1516330972

Abstract

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.

Citation

Download Citation

Shiro Goto. Naoyuki Matsuoka. Naoki Taniguchi. Ken-ichi Yoshida. "Almost Gorenstein Rees Algebras of pg-Ideals, Good Ideals, and Powers of the Maximal Ideals." Michigan Math. J. 67 (1) 159 - 174, March 2018. https://doi.org/10.1307/mmj/1516330972

Information

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

zbMATH: 06965594
MathSciNet: MR3770858
Digital Object Identifier: 10.1307/mmj/1516330972

Subjects:
Primary: 13A30, 13H10, 13H15

Rights: Copyright © 2018 The University of Michigan

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Vol.67 • No. 1 • March 2018
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