### 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 |
---|---|

Pages (from-to) | 2641-2647 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 124 |

Issue number | 9 |

Publication status | Published - 1996 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*124*(9), 2641-2647.

**On the higher delta invariants of a Gorenstein local ring.** / Yoshino, Yuji.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 124, no. 9, pp. 2641-2647.

}

TY - JOUR

T1 - On the higher delta invariants of a Gorenstein local ring

AU - Yoshino, Yuji

PY - 1996

Y1 - 1996

N2 - Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by δR n(M) for each module M and for each integer n. We propose a conjecture asking if δR n(R/mℓ) = 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 δR n(R/mℓ) > 0.

AB - Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by δR n(M) for each module M and for each integer n. We propose a conjecture asking if δR n(R/mℓ) = 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 δR n(R/mℓ) > 0.

KW - Cohen-Macaulay approximations

KW - Cohen-Macaulay modules

KW - Gorenstein ring

UR - http://www.scopus.com/inward/record.url?scp=21444458353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21444458353&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21444458353

VL - 124

SP - 2641

EP - 2647

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -