### 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 p_{g}-ideal; (2) (A, m) is a two-dimensional almost Gorenstein local ring having minimal multiplicity, and I =m^{l} for all l ≥ 1; (3) (A,m) is a regular local ring of dimension d ≥ 2, and I = m^{d-1}. Conversely, if R(m^{l}) is an almost Gorenstein graded ring for some l ≥ 2 and d ≥ 3, then l = d - 1.

Original language | English |
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Pages (from-to) | 159-174 |

Number of pages | 16 |

Journal | Michigan Mathematical Journal |

Volume | 67 |

Issue number | 1 |

Publication status | Published - 2018 Mar 1 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

_{g}-ideals, good ideals, and powers of the maximal ideals.

*Michigan Mathematical Journal*,

*67*(1), 159-174.

**Almost Gorenstein Rees algebras of p _{g}-ideals, good ideals, and powers of the maximal ideals.** / Goto, Shiro; Matsuoka, Naoyuki; Taniguchi, Naoki; Yoshida, Ken Ichi.

Research output: Contribution to journal › Article

_{g}-ideals, good ideals, and powers of the maximal ideals',

*Michigan Mathematical Journal*, vol. 67, no. 1, pp. 159-174.

_{g}-ideals, good ideals, and powers of the maximal ideals. Michigan Mathematical Journal. 2018 Mar 1;67(1):159-174.

}

TY - JOUR

T1 - Almost Gorenstein Rees algebras of pg-ideals, good ideals, and powers of the maximal ideals

AU - Goto, Shiro

AU - Matsuoka, Naoyuki

AU - Taniguchi, Naoki

AU - Yoshida, Ken Ichi

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85043514890&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043514890&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85043514890

VL - 67

SP - 159

EP - 174

JO - Michigan Mathematical Journal

JF - Michigan Mathematical Journal

SN - 0026-2285

IS - 1

ER -