Derivations and the integral closure of ideals
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- by Reinhold Hübl and Appendix by Irena Swanson PDF
- Proc. Amer. Math. Soc. 127 (1999), 3503-3511 Request permission
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
- R. Berger, R. Kiehl, E. Kunz, and Hans-Joachim Nastold, Differentialrechnung in der analytischen Geometrie, Lecture Notes in Mathematics, No. 38, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224870
- Richard Fedder, A Frobenius characterization of rational singularity in $2$-dimensional graded rings, Trans. Amer. Math. Soc. 340 (1993), no. 2, 655–668. MR 1116312, DOI 10.1090/S0002-9947-1993-1116312-3
- R. Fedder, C. Huneke, and R. Hübl, Zeros of differentials along one-fibered ideals, Proc. Amer. Math. Soc. 108 (1990), no. 2, 319–325. MR 990421, DOI 10.1090/S0002-9939-1990-0990421-4
- Craig Huneke, Uniform bounds in Noetherian rings, Invent. Math. 107 (1992), no. 1, 203–223. MR 1135470, DOI 10.1007/BF01231887
- Craig Huneke and Karen E. Smith, Tight closure and the Kodaira vanishing theorem, J. Reine Angew. Math. 484 (1997), 127–152. MR 1437301
- Ernst Kunz, Kähler differentials, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1986. MR 864975, DOI 10.1007/978-3-663-14074-0
- Joseph Lipman, On complete ideals in regular local rings, Algebraic geometry and commutative algebra, Vol. I, Kinokuniya, Tokyo, 1988, pp. 203–231. MR 977761
- Joseph Lipman and Avinash Sathaye, Jacobian ideals and a theorem of Briançon-Skoda, Michigan Math. J. 28 (1981), no. 2, 199–222. MR 616270
- Joseph Lipman and Bernard Teissier, Pseudorational local rings and a theorem of Briançon-Skoda about integral closures of ideals, Michigan Math. J. 28 (1981), no. 1, 97–116. MR 600418
- David Rees, Izumi’s theorem, Commutative algebra (Berkeley, CA, 1987) Math. Sci. Res. Inst. Publ., vol. 15, Springer, New York, 1989, pp. 407–416. MR 1015531, DOI 10.1007/978-1-4612-3660-3_{2}2
- D. Rees, A note on analytically unramified local rings, J. London Math. Soc. 36 (1961), 24–28. MR 126465, DOI 10.1112/jlms/s1-36.1.24
- Günter Scheja and Uwe Storch, Differentielle Eigenschaften der Lokalisierungen analytischer Algebren, Math. Ann. 197 (1972), 137–170 (German). MR 306172, DOI 10.1007/BF01419591
- Günter Scheja and Uwe Storch, Über differentielle Abhängigkeit bei Idealen analytischer Algebren, Math. Z. 114 (1970), 101–112 (German). MR 263808, DOI 10.1007/BF01110319
- Günter Scheja and Hartmut Wiebe, Über Derivationen von lokalen analytischen Algebren, Symposia Mathematica, Vol. XI (Convegno di Algebra Commutativa, INDAM, Rome, 1971) Academic Press, London, 1973, pp. 161–192 (German). MR 0338461
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
- 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
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1618698