Ulrich ideals and almost gorenstein rings

Shiro Goto; Ryo Takahashi; Naoki Taniguchi

doi:10.1090/proc/12970

Ulrich ideals and almost gorenstein rings

Shiro Goto, Ryo Takahashi, Naoki Taniguchi

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

The structure of the complex RHom_R(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 language	English
Pages (from-to)	2811-2823
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	7
DOIs	https://doi.org/10.1090/proc/12970
Publication status	Published - 2016 Jul 1
Externally published	Yes

Keywords

Almost Gorenstein ring
Cohen–Macaulay ring
Ulrich ideal

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/proc/12970

Cite this

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AU - Goto, Shiro

AU - Takahashi, Ryo

AU - Taniguchi, Naoki

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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

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JF - Proceedings of the American Mathematical Society

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ER -

Ulrich ideals and almost gorenstein rings

Abstract

Keywords

ASJC Scopus subject areas

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