Ulrich ideals and almost Gorenstein rings
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- by Shiro Goto, Ryo Takahashi and Naoki Taniguchi
- Proc. Amer. Math. Soc. 144 (2016), 2811-2823
- DOI: https://doi.org/10.1090/proc/12970
- Published electronically: December 3, 2015
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Abstract:
The structure of the complex $\mathrm {\textbf {R}Hom}_R(R/I,R)$ 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.References
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Bibliographic 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
- MR Author ID: 192104
- Email: goto@math.meiji.ac.jp
- Ryo Takahashi
- Affiliation: Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8602, Japan
- MR Author ID: 674867
- 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
- MR Author ID: 1086482
- ORCID: 0000-0001-9343-7161
- Email: taniguti@math.meiji.ac.jp
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2811-2823
- MSC (2010): Primary 13H10, 13H15, 13D07
- DOI: https://doi.org/10.1090/proc/12970
- MathSciNet review: 3487216