Zeros of differentials along one-fibered ideals
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- by R. Fedder, C. Huneke and R. Hübl PDF
- Proc. Amer. Math. Soc. 108 (1990), 319-325 Request permission
Abstract:
Let $\left ( {R,m} \right )$ be a complete local domain containing the rationals. If $I \subseteq R$ is a one-fibered ideal then there is a constant $l$, depending only on $R$ and $I$, such that if $f \in m$ and $f \notin {I^n}$, then there exists a derivation $d$ such that $d\left ( f \right ) \notin {I^{n + l}}$.References
-
D. Cutkosky, On unique and almost unique factorization of complete ideals II, (to appear in Inventiones Math.).
R. Fedder, Rational singularity implies $F$-injective type for graded Cohen-Macaulay rings of dimension 2, (in preparation).
- Melvin Hochster and Craig Huneke, Tight closure, Commutative algebra (Berkeley, CA, 1987) Math. Sci. Res. Inst. Publ., vol. 15, Springer, New York, 1989, pp. 305–324. MR 1015524, DOI 10.1007/978-1-4612-3660-3_{1}5
- Ernst Kunz, Kähler differentials, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1986. MR 864975, DOI 10.1007/978-3-663-14074-0
- Ernst Kunz and Rolf Waldi, Regular differential forms, Contemporary Mathematics, vol. 79, American Mathematical Society, Providence, RI, 1988. MR 971502, DOI 10.1090/conm/079
- Stephen McAdam, Asymptotic prime divisors, Lecture Notes in Mathematics, vol. 1023, Springer-Verlag, Berlin, 1983. MR 722609, DOI 10.1007/BFb0071575
- D. G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145–158. MR 59889, DOI 10.1017/s0305004100029194 H. Prüfer, Untersuchungen über Teilbarkeitseigenschaften in Körpern, J. Reine Angew. Math. 168 (1932), 1-36.
- 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
- D. Rees, Valuations associated with ideals. II, J. London Math. Soc. 31 (1956), 221–228. MR 78971, DOI 10.1112/jlms/s1-31.2.221
- Judith D. Sally, One-fibered ideals, Commutative algebra (Berkeley, CA, 1987) Math. Sci. Res. Inst. Publ., vol. 15, Springer, New York, 1989, pp. 437–442. MR 1015533, DOI 10.1007/978-1-4612-3660-3_{2}4
- P. Samuel, Some asymptotic properties of powers of ideals, Ann. of Math. (2) 56 (1952), 11–21. MR 49166, DOI 10.2307/1969764
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 319-325
- MSC: Primary 13H10
- DOI: https://doi.org/10.1090/S0002-9939-1990-0990421-4
- MathSciNet review: 990421