Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Derivations and the integral closure of ideals


Authors: Reinhold Hübl and Appendix by Irena Swanson
Journal: Proc. Amer. Math. Soc. 127 (1999), 3503-3511
MSC (1991): Primary 13N05, 13J10
DOI: https://doi.org/10.1090/S0002-9939-99-04968-0
Published electronically: May 13, 1999
MathSciNet review: 1618698
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $(R, \mathfrak{m} )$ be a complete local domain containing the rationals. Then there exists an integer $l$ such that for any ideal $I \subseteq R$, if $f \in \mathfrak{m} $, $f \notin I^{n}$, then there exists a derivation $\delta $ of $R$ with $\delta (f) \notin I^{n+l}$.


References [Enhancements On Off] (What's this?)

  • [BKKN] Berger, R., Kiehl, R., Kunz, E., Nastold, H.J.: Differentialrechnung in der analytischen Geometrie. Lecture Notes in Mathematics 38. 1967 MR 37:469
  • [F] Fedder, R.: A Frobenius characterization of rational singularity in two-dimensional graded rings. Trans. Amer. Math. Soc. 340, (1993), 655-668. MR 94b:13003
  • [FHH] Fedder, R., Huneke, C., Hübl, R.: Zeros of Differential Forms along One-Fibered Ideals. Proc. Amer. Math. Soc. 108, (1990), 319 - 325. MR 90d:13020
  • [Hn] C. Huneke: Uniform bounds in Noetherian rings, Invent. Math., 107 (1992), 203-223. MR 93b:13027
  • [HS] Huneke, C., Smith, K.: Tight closure and the Kodaira Vanishing Theorem. J. reine angew. Math. 484 (1997), 127 - 152 MR 98e:13007
  • [KD] Kunz, E.: Kähler Differentials. Vieweg. Braunschweig, Wiesbaden, 1986. MR 88e:14025
  • [Li] Lipman J.: On Complete Ideals in Regular Local Rings. In: Algebraic Geometry and Commutative Algebra in Honor of Masayoshi NAGATA, (1988), 203-231. MR 90g:14003
  • [LiS] Lipman, J., Sathaye, A.: Jacobian Ideals and a Theorem of Briancon-Skoda. Michigan Math. J. 28 (1981), 199 -222. MR 83m:13001
  • [LiT] Lipman, J., Teissier, B.: Pseudo-Rational Local Rings and a Theorem of Briancon-Skoda about Integral Closures of Ideals. Michigan Math. J. 28 (1981), 97-116. MR 82f:14004
  • [R1] D. Rees: Izumi's Theorem, in ``Commutative Algebra'', editors M. Hochster, C. Huneke and J.D. Sally, Springer-Verlag, 1989, 407-416. MR 90g:13010
  • [R2] D. Rees: A note on analytically unramified local rings, J. London Math. Soc., 36 (1961), 24-28. MR 23:A3761
  • [SS1] Scheja, G., Storch, U.: Differentielle Eigenschaften der Lokalisierungen analytischer Algebren. Math. Annalen 197, (1972), 137-170. MR 46:5299
  • [SS2] Scheja, G., Storch, U.: Über differentielle Abhängigkeit bei Idealen analytischer Algebren. Math. Z. 114 (1970), 101-112. MR 41:8408
  • [SW] Scheja, G., Wiebe, H.: Über Derivationen von lokalen analytischen Algebren. Symp. Math. XI (1973), 161-192. MR 49:3225

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13N05, 13J10

Retrieve articles in all journals with MSC (1991): 13N05, 13J10


Additional Information

Reinhold Hübl
Affiliation: NWF I - Mathematik, Universität Regensburg, 93040 Regensburg, Germany
Email: Reinhold.Huebl@Mathematik.Uni-Regensburg.de

Appendix by Irena Swanson
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003
Email: iswanson@mnsu.edu

DOI: https://doi.org/10.1090/S0002-9939-99-04968-0
Keywords: K\"{a}hler differentials, derivations
Received by editor(s): November 20, 1997
Received by editor(s) in revised form: February 24, 1998
Published electronically: May 13, 1999
Additional Notes: The author was partially supported by a Heisenberg–Stipendium of the DFG
The author of the appendix was partially supported by the National Science Foundation.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society