COMPUTATION OF NUMERICAL INVARIANTS col(-), row(-) FOR A RING k[$t^2$,$t^e+1$, $t^(e-1)e-1$]

  • Lee, Ki-Suk
  • Published : 2000.07.01

Abstract

We find the values of numerical invariants col(R) and row (R) for R=k[te, te+1, t(e-1)e-1] where k is a field and e$\geq$4. We also show that col(R) = crs (R) and row (R) = drs(R), but they are strictly less than the reduction number of R plus 1.

Keywords

invariants;reduction number;Loewy length;Cohen-Macaulay ring

References

  1. Proc. Camb. Phil. Soc. v.50 Reductions of ideals in local rings D.G. Northcott;D. Rees
  2. J. Math. Kyoto Univ. v.17 On the associated graded ring of a local Cohen-Macaulay ring J. Sally
  3. J. Alg. (to appear) New invariants of Noetherian local rings
  4. J. Alg. v.202 Some restrictions on the maps in minimal resolutions J. Koh and K. Lee
  5. J. Alg. v.108 Reduction numbers for ideals of analytic spread one, S. Huckaba
  6. J. Alg. v.58 On form rings which are Cohen-Macaulay G. Valla
  7. Proc. Amer. Math. Soc. v.122 Auslander's δ-invariants of Gorenstein local rings S. Ding