Almost Gorenstein rings - towards a theory of higher dimension

Shiro Goto; Ryo Takahashi; Naoki Taniguchi

doi:10.1016/j.jpaa.2014.09.022

Almost Gorenstein rings - towards a theory of higher dimension

Shiro Goto^*, Ryo Takahashi, Naoki Taniguchi

^*Corresponding author for this work

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

46 Citations (Scopus)

Abstract

The notion of almost Gorenstein local ring introduced by V. Barucci and R. Fröberg for one-dimensional Noetherian local rings which are analytically unramified has been generalized by S. Goto, N. Matsuoka and T.T. Phuong to one-dimensional Cohen-Macaulay local rings, possessing canonical ideals. The present purpose is to propose a higher-dimensional notion and develop the basic theory. The graded version is also posed and explored.

Original language	English
Pages (from-to)	2666-2712
Number of pages	47
Journal	Journal of Pure and Applied Algebra
Volume	219
Issue number	7
DOIs	https://doi.org/10.1016/j.jpaa.2014.09.022
Publication status	Published - 2015 Jul 1
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2014.09.022

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abstract = "The notion of almost Gorenstein local ring introduced by V. Barucci and R. Fr{\"o}berg for one-dimensional Noetherian local rings which are analytically unramified has been generalized by S. Goto, N. Matsuoka and T.T. Phuong to one-dimensional Cohen-Macaulay local rings, possessing canonical ideals. The present purpose is to propose a higher-dimensional notion and develop the basic theory. The graded version is also posed and explored.",

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AU - Takahashi, Ryo

AU - Taniguchi, Naoki

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AB - The notion of almost Gorenstein local ring introduced by V. Barucci and R. Fröberg for one-dimensional Noetherian local rings which are analytically unramified has been generalized by S. Goto, N. Matsuoka and T.T. Phuong to one-dimensional Cohen-Macaulay local rings, possessing canonical ideals. The present purpose is to propose a higher-dimensional notion and develop the basic theory. The graded version is also posed and explored.

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Almost Gorenstein rings - towards a theory of higher dimension

Abstract

ASJC Scopus subject areas

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