DOI QR코드

DOI QR Code

Invariants of Local Rings under Completion

  • Lee, Kisuk (Department of Mathematics, Sookmyung Women's University)
  • Received : 2017.10.24
  • Accepted : 2017.11.17
  • Published : 2017.12.30

Abstract

We study the behavior of some invariants under completion. We also give a counterexample, which is the same as a counterexample to Ding's Conjecture, to Koh-Lee's Conjecture.

Keywords

References

  1. J. Koh and K. Lee, "Some restrictions on the maps in the minimal resolutions", J. Algebra, Vol. 202, pp. 671-689, 1998. https://doi.org/10.1006/jabr.1997.7310
  2. J. Koh and K. Lee, "New invariants of noetherian local rings", J. Algebra, Vol. 235, pp. 431-452, 2001. https://doi.org/10.1006/jabr.2000.8506
  3. M. Hashimoto and A. Shida, "Some remarks on index and generalized Loewy length of a Gorenstein local ring", J. Algebra, Vol. 187, pp. 150-162, 1997. https://doi.org/10.1006/jabr.1997.6770
  4. A. D. Stefani, "A counterexample to conjecture of Ding", J. Algebra, Vol. 452, pp. 324-337, 2016.
  5. S. Ding, "Cohen-Macaulay approximation and multiplicity", J. Algebra, Vol. 153, pp. 271-288, 1992. https://doi.org/10.1016/0021-8693(92)90156-G
  6. S. Ding, "A note on the index of cohen-macaulay local ring", Commun. Algebra, Vol. 21, pp. 53-71, 1993. https://doi.org/10.1080/00927879208824550
  7. S. Ding, "The associated graded ring and the index of a Gorenstein local rings", Proc. Am. Math. Soc., Vol. 120, pp. 1029-1033, 1994. https://doi.org/10.1090/S0002-9939-1994-1181160-1
  8. M. Auslander and R.O. Buchweitz, "The homological theory of maximal cohen-macaulay approximations", Memoires De La S. M. F., Vol. 38, pp. 5-37, 1989.
  9. M. Auslander, "Minimal cohen-macaulay approximations", unpublished paper.
  10. J. Koh and K. Lee, "On column invariant and index of cohen-macaulay local rings", Journal of the Korean Mathematical Society, Vol. 43, pp. 871-883, 2006. https://doi.org/10.4134/JKMS.2006.43.4.871
  11. M. Artin, "Algebraic approximation of structures over complete local rings", Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques, Vol. 36, pp. 23-58, 1969. https://doi.org/10.1007/BF02684596
  12. C. Peskine and L. Szpiro, "Dimension projective finie et cohomologie locale", Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques, Vol. 42, pp. 47-119, 1973. https://doi.org/10.1007/BF02685877
  13. K. Lee, "Computation of numerical invariants col(-), row(-) for a ring k[te,te+1,t(e-1)e-1]", Journal of the Korean Mathematical Society, Vol. 3, pp. 521-530, 2000.
  14. J. Herzog, "On the index of a homogeneous Gorenstein ring", Contemporary Mathematics, Vol. 159, pp. 95-102, 1994.
  15. K. Lee, "Some remarks on numerical invariants of local rings", J. Natural Sciences Sookmyung Women's, University, pp. 79-83, 1998.