### Abstract

Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by δ_{R}^{n}(M) for each module M and for each integer n. We propose a conjecture asking if δ_{R}^{n}(R/m^{ℓ}) = 0 for any positive integers n and ℓ. We prove that this is true provided the associated graded ring of R has depth not less than dim R - 1. Furthermore we show that there are only finitely many possibilities for a pair of positive integers (n, ℓ) for which δ_{R}^{n}(R/m^{ℓ}) > 0.

Original language | English |
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Pages (from-to) | 2641-2647 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 124 |

Issue number | 9 |

Publication status | Published - Dec 1 1996 |

Externally published | Yes |

### Keywords

- Cohen-Macaulay approximations
- Cohen-Macaulay modules
- Gorenstein ring

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Yoshino, Y. (1996). On the higher delta invariants of a Gorenstein local ring.

*Proceedings of the American Mathematical Society*,*124*(9), 2641-2647.