Kyoto Journal of Mathematics

When are the Rees algebras of parameter ideals almost Gorenstein graded rings?

Shiro Goto, Mehran Rahimi, Naoki Taniguchi, and Hoang Le Truong

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Abstract

Let A be a Cohen–Macaulay local ring with dimA=d3, possessing the canonical module KA. Let a1,a2,,ar (3rd) be a subsystem of parameters of A, and set Q=(a1,a2,,ar). We show that if the Rees algebra R(Q) of Q is an almost Gorenstein graded ring, then A is a regular local ring and a1,a2,,ar is a part of a regular system of parameters of A.

Article information

Source
Kyoto J. Math., Volume 57, Number 3 (2017), 655-666.

Dates
Received: 2 February 2016
Accepted: 17 May 2016
First available in Project Euclid: 14 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1492194851

Digital Object Identifier
doi:10.1215/21562261-2017-0010

Mathematical Reviews number (MathSciNet)
MR3685059

Zentralblatt MATH identifier
06774051

Subjects
Primary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
Secondary: 13H15: Multiplicity theory and related topics [See also 14C17] 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics

Keywords
Cohen–Macaulay ring Gorenstein ring almost Gorenstein ring parameter ideal Rees algebra

Citation

Goto, Shiro; Rahimi, Mehran; Taniguchi, Naoki; Le Truong, Hoang. When are the Rees algebras of parameter ideals almost Gorenstein graded rings?. Kyoto J. Math. 57 (2017), no. 3, 655--666. doi:10.1215/21562261-2017-0010. https://projecteuclid.org/euclid.kjm/1492194851


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References

  • [1] V. Barucci and R. Fröberg, One-dimensional almost Gorenstein rings, J. Algebra 188 (1997), 418–442.
  • [2] J. P. Brennan, J. Herzog, and B. Ulrich, Maximally generated Cohen-Macaulay modules, Math. Scand. 61 (1987), 181–203.
  • [3] J. A. Eagon and D. G. Northcott, Ideals defined by matrices and a certain complex associated with them, Proc. Roy. Soc. London Ser. A 269 (1962), 188–204.
  • [4] S. Goto, N. Matsuoka, and T. T. Phuong, Almost Gorenstein rings, J. Algebra 379 (2013), 355–381.
  • [5] S. Goto, N. Matsuoka, N. Taniguchi, and K.-i. Yoshida, The almost Gorenstein Rees algebras of parameters, J. Algebra 452 (2016), 263–278.
  • [6] S. Goto, R. Takahashi, and N. Taniguchi, Almost Gorenstein rings—towards a theory of higher dimension, J. Pure Appl. Algebra 219 (2015), 2666–2712.
  • [7] J. Herzog and E. Kunz, Der kanonische Modul eines Cohen-Macaulay-Rings (Sem. Lokale Kohomologietheorie von Grothendieck, Univ. Regensburg, Regensburg, 1970/1971), Lecture Notes in Math. 238, Springer, Berlin, 1971.