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Ulrich ideals and almost Gorenstein rings


Authors: Shiro Goto, Ryo Takahashi and Naoki Taniguchi
Journal: Proc. Amer. Math. Soc. 144 (2016), 2811-2823
MSC (2010): Primary 13H10, 13H15, 13D07
DOI: https://doi.org/10.1090/proc/12970
Published electronically: December 3, 2015
MathSciNet review: 3487216
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Abstract: The structure of the complex $ \mathrm {{\bf R}Hom}_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.


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Additional Information

Shiro Goto
Affiliation: Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki 214-8571, Japan
Email: goto@math.meiji.ac.jp

Ryo Takahashi
Affiliation: Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8602, Japan
Email: takahashi@math.nagoya-u.ac.jp

Naoki Taniguchi
Affiliation: Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki 214-8571, Japan
Email: taniguti@math.meiji.ac.jp

DOI: https://doi.org/10.1090/proc/12970
Keywords: Almost Gorenstein ring, Cohen--Macaulay ring, Ulrich ideal
Received by editor(s): July 16, 2015
Received by editor(s) in revised form: September 3, 2015
Published electronically: December 3, 2015
Additional Notes: The first author was partially supported by JSPS Grant-in-Aid for Scientific Research 25400051
The second author was partially supported by JSPS Grant-in-Aid for Scientific Research 25400038
The third author was partially supported by Grant-in-Aid for JSPS Fellows 26-126 and by JSPS Research Fellow
Communicated by: Irena Peeva
Article copyright: © Copyright 2015 American Mathematical Society

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