The eventual index of reducibility of parameter ideals and the sequentially Cohen–Macaulay property

Abstract

In this paper, our purpose is to give a characterization of a sequentially Cohen–Macaulay module, which was introduced by Stanley (Combinatorics and Commutative Algebra, 2nd edn, Birkhäuser, Boston, 1996), in terms of its index of reducibility of parameter ideals, which was given by Noether in 1921 (Math Ann 83:24–66, 1921). This applies in particular to characterizing the Gorensteinness, Cohen–Macaulayness of local rings in terms of eventually the index of reducibility for parameter ideals.

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Acknowledgements

The author would like to thank the referee for the valuable comments to improve this article. This work is partially supported by a fund of NAFOSTED under Grant No. 101.04-2017.14 and the Alexander von Humboldt Foundation.

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Correspondence to Hoang Le Truong.

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Truong, H.L. The eventual index of reducibility of parameter ideals and the sequentially Cohen–Macaulay property. Arch. Math. 112, 475–488 (2019). https://doi.org/10.1007/s00013-018-1284-8

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Mathematics Subject Classification

  • 13H10
  • 13D45
  • 13A15
  • 13H15

Keywords

  • Index of reducibility
  • Sequentially Cohen–Macaulay
  • Distinguished ideal
  • Local cohomology