### 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 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Almost Gorenstein Rees algebras of p<sub>g</sub>-ideals, good ideals, and powers of the maximal ideals'. Together they form a unique fingerprint.

## Cite this

Goto, S., Matsuoka, N., Taniguchi, N., & Yoshida, K. I. (2018). Almost Gorenstein Rees algebras of p

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