통합자연과학논문집 (Journal of Integrative Natural Science)

조선대학교 기초과학연구원 (The Basic Science Institute Chosun University)
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Numerical Invariants on a Ring F[[X,Y]]/ for a Field F

  • Jung, Soyeun (Department of Mathematics, Indiana University Bloomington) ;
  • Lee, Kisuk (Department of Mathematics, Sookmyung Women's University)
  • 투고 : 2013.10.18
  • 심사 : 2013.12.20
  • 발행 : 2013.12.30
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초록

We provide a complete proof that the existence of a system of parameters, which is a reduction of the maximal ideal, is essential in Koh-Lee's conjecture.

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참고문헌

  1. K. Lee, "Computation of numerical invariants col(-), row(-) for a ring ${\kappa}[[t^{e},t^{e+1},t^{e-1}^{e-1}]]$," J. Korea Math. Soc., Vol.37, pp.521-530, 2000.
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  3. J. Koh and K. Lee, "New invariants of Noetherian local rings," J. Alg., Vol.235, pp.431-452, 2001. https://doi.org/10.1006/jabr.2000.8506
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  5. S. Ding, "Auslander's ${\delta}$-invariants of Gorenstein local rings," Proc. Amer. Math. Soc., Vol.122, pp. 649-656, 1994.
  6. J. Koh and K. Lee, "On column invariant and index of Cohen-Macaulay local rings," J. Korean Math. Soc., Vol.43, pp.871-883, 2006. https://doi.org/10.4134/JKMS.2006.43.4.871
  7. M. Hashmoto and A. Shida, "Some remarks on index and generalized Loewy length of a Gorenstein local ring," J. Alg., Vol.187, pp.150-162, 1997. https://doi.org/10.1006/jabr.1997.6770
  8. D. G. Northcott and D. Rees, "Reductions of ideals in local rings," Proc. Camb. Phil. Soc., Vol.50, pp.145-158, 1954. https://doi.org/10.1017/S0305004100029194