Ulrich ideals and almost gorenstein rings

Shiro Goto, Ryo Takahashi, Naoki Taniguchi

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The structure of the complex RHomR(R/I, R) is explored for an Ulrich ideal I in a Cohen–Macaulay local ring R. As a consequence, it is proved that in a one-dimensional almost Gorenstein but non-Gorenstein local ring, the only possible Ulrich ideal is the maximal ideal. It is also studied when Ulrich ideals have the same minimal number of generators.

Original languageEnglish
Pages (from-to)2811-2823
Number of pages13
JournalProceedings of the American Mathematical Society
Volume144
Issue number7
DOIs
Publication statusPublished - 2016 Jul 1
Externally publishedYes

Fingerprint

Gorenstein Ring
Local Ring
Cohen-Macaulay Ring
Maximal Ideal
Gorenstein
Generator

Keywords

  • Almost Gorenstein ring
  • Cohen–Macaulay ring
  • Ulrich ideal

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Ulrich ideals and almost gorenstein rings. / Goto, Shiro; Takahashi, Ryo; Taniguchi, Naoki.

In: Proceedings of the American Mathematical Society, Vol. 144, No. 7, 01.07.2016, p. 2811-2823.

Research output: Contribution to journalArticle

Goto, Shiro ; Takahashi, Ryo ; Taniguchi, Naoki. / Ulrich ideals and almost gorenstein rings. In: Proceedings of the American Mathematical Society. 2016 ; Vol. 144, No. 7. pp. 2811-2823.
@article{9a171343cbca49abb7f6e4bf9c5ec8d9,
title = "Ulrich ideals and almost gorenstein rings",
abstract = "The structure of the complex RHomR(R/I, R) is explored for an Ulrich ideal I in a Cohen–Macaulay local ring R. As a consequence, it is proved that in a one-dimensional almost Gorenstein but non-Gorenstein local ring, the only possible Ulrich ideal is the maximal ideal. It is also studied when Ulrich ideals have the same minimal number of generators.",
keywords = "Almost Gorenstein ring, Cohen–Macaulay ring, Ulrich ideal",
author = "Shiro Goto and Ryo Takahashi and Naoki Taniguchi",
year = "2016",
month = "7",
day = "1",
doi = "10.1090/proc/12970",
language = "English",
volume = "144",
pages = "2811--2823",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "7",

}

TY - JOUR

T1 - Ulrich ideals and almost gorenstein rings

AU - Goto, Shiro

AU - Takahashi, Ryo

AU - Taniguchi, Naoki

PY - 2016/7/1

Y1 - 2016/7/1

N2 - The structure of the complex RHomR(R/I, R) is explored for an Ulrich ideal I in a Cohen–Macaulay local ring R. As a consequence, it is proved that in a one-dimensional almost Gorenstein but non-Gorenstein local ring, the only possible Ulrich ideal is the maximal ideal. It is also studied when Ulrich ideals have the same minimal number of generators.

AB - The structure of the complex RHomR(R/I, R) is explored for an Ulrich ideal I in a Cohen–Macaulay local ring R. As a consequence, it is proved that in a one-dimensional almost Gorenstein but non-Gorenstein local ring, the only possible Ulrich ideal is the maximal ideal. It is also studied when Ulrich ideals have the same minimal number of generators.

KW - Almost Gorenstein ring

KW - Cohen–Macaulay ring

KW - Ulrich ideal

UR - http://www.scopus.com/inward/record.url?scp=84964039913&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964039913&partnerID=8YFLogxK

U2 - 10.1090/proc/12970

DO - 10.1090/proc/12970

M3 - Article

AN - SCOPUS:84964039913

VL - 144

SP - 2811

EP - 2823

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 7

ER -