Almost Gorenstein Rees algebras of pg-ideals, good ideals, and powers of the maximal ideals

Shiro Goto, Naoyuki Matsuoka, Naoki Taniguchi, Ken Ichi Yoshida

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 K ≅ A/m, and I is a pg-ideal; (2) (A, m) is a two-dimensional almost Gorenstein local ring having minimal multiplicity, and I =ml for all l ≥ 1; (3) (A,m) is a regular local ring of dimension d ≥ 2, and I = md-1. Conversely, if R(ml) is an almost Gorenstein graded ring for some l ≥ 2 and d ≥ 3, then l = d - 1.

Original languageEnglish
Pages (from-to)159-174
Number of pages16
JournalMichigan Mathematical Journal
Volume67
Issue number1
Publication statusPublished - 2018 Mar 1

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Rees Algebra
Gorenstein Ring
Maximal Ideal
Gorenstein
Local Ring
Regular Local Ring
Cohen-Macaulay Ring
Graded Ring
Algebraically closed
Multiplicity

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Almost Gorenstein Rees algebras of pg-ideals, good ideals, and powers of the maximal ideals. / Goto, Shiro; Matsuoka, Naoyuki; Taniguchi, Naoki; Yoshida, Ken Ichi.

In: Michigan Mathematical Journal, Vol. 67, No. 1, 01.03.2018, p. 159-174.

Research output: Contribution to journalArticle

Goto, Shiro ; Matsuoka, Naoyuki ; Taniguchi, Naoki ; Yoshida, Ken Ichi. / Almost Gorenstein Rees algebras of pg-ideals, good ideals, and powers of the maximal ideals. In: Michigan Mathematical Journal. 2018 ; Vol. 67, No. 1. pp. 159-174.
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