This is a preview of subscription content, log in via an institution to check access.
References
[Ab1] Aberbach, I.: Finite phantom projective dimension. (Preprint 1990)
[Ab2] Aberbach, I.: Test elements in excellent rings with an application to the uniform Artin-Rees property (Preprint)
[A] Abhyankar, S.S.: Resolution of singularities of algebraic surfaces. In: Algebraic Geometry, pp. 1–11. London: Oxford University Press
[BM] Bierstone, E., Milman, P.D.: Relations among analytic functions. Ann. Inst. Fourier37, 187–239 (1987)
[BS] Briançon, J., Skoda, H.: Sur la clôture intégrale d'un idéal de germes de fonctions holomorphes en un point de ℂ. C.R. Acad. Sci., Paris, Sér.,278, 949–951 (1974)
[Br] Brodmann, M.: Einige Ergebnisse aus der lokalen Kohomologietheorie und ihre Anwendung. Osnabrucker Schriften zur Mathematik5, (1983)
[BV] Bruns, W., Vetter, U.: Determinantal rings. (Lect. Notes Math., vol. 1327) Berlin Heidelberg New York: Springer 1988
[BE] Buchsbaum, D., Eisenbud, D.: What makes a complex exact? J. Algebra25, (1973)
[DO1] Duncan, A.J., O'Carroll, L.: A full uniform Artin-Rees theorem. J. Reine Angew. Math.394, 203–207 (1989)
[DO2] Duncan, A.J., O'Carroll, L.: On Zariski regularity, the vanishing of Tor, and a uniform Artin-Rees theorem, Topics in Algebra. Banach Cent. Publ.26, 49–55 (1990)
[EH] Eisenbud, D., Hochster, M.: A Nullstellensatz with nilpotents and Zariski's main lemma on holomorphic functions. J. Algebra58, 157–161 (1979)
[Fa] Faltings, G.: Über die Annulatoren lokaler Kohomologiegruppen. Arch. Math.30, 473–476 (1978)
[G] Goto, S.: Vanishing of Ext i A (M, A). J. Math. Kyoto Univ.22, 481–484 (1982/83)
[H] Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic 0. Ann. Math.79, 205–326 (1964)
[HH1] Hochster, M., Huneke, C.: Tight closure, invariant theory, and the Briançon-Skoda theorem. J. Am. Math. Soc.3, 31–116 (1990)
[HH2] Hochster, M., Huneke, C.: Tight closure and strong F-regularity. Mém. Soc. Math. Fr.38, 119–133 (1989)
[HH3] Hochster, M., Huneke, C.: F-regularity, test elements, and smooth base change. (In preparation)
[HH4] Hochster, M., Huneke, C.: Tight closures of parameter ideals and splitting in modulefinite extensions. (In preparation)
[HH5] Hochster, M., Huneke, C.: Infinite integral extensions and big Cohen-Macaulay algebras. Ann. Math. (to appear)
[Hu] Huneke, C.: Hilbert functions and symbolic powers. Mich. Math. J.34, 293–318 (1987)
[KT1] El Khadiri, A., Tougeron, J.-C.: Familles noethériennes de sous-modules dek[[x]] p et applications I. C. R. Acad. Sci., Paris, Sér. I301, no 9 423–426 (1985)
[KT2] El Khadiri, A., Tougeron, J.-C.: Familles noethériennes de sous-modules dek[[x]] p et applications II. C.R. Acad. Sci., Paris, Sér. I.301 (no. 10) 475–478 (1985)
[Ko] Kollár, J.: Sharp effective Nullstellensatz. J. Am. Math. Soc.1, 963–975 (1988)
[K] Kunz, E.: On noetherian rings of characteristicp. Am. J. Math.98, 999–1013 (1976)
[L1] Lipman, J.: Rational singularities... Publ. Math, Inst. Hautes Étud. Sci.36, 195–279 (1969)
[L2] Lipman, J.: Relative Lipschitz saturation. Am. J. Math.,97, 791–813 (1975)
[L3] Lipman, J.: Desingularization of two-dimensional schemes. Ann. Math.107, 151–207 (1978)
[LS] Lipman, J., Sathaye, A.: Jacobian ideals and a theorem of Briançon-Skoda. Mich. Math. J.28, 199–222 (1981)
[LT] Lipman, J., Teissier, B.: Pseudo-rational local rings and a theorem of Briançon-Skoda about integral closures of ideals. Mich. Math. J.28, 97–116 (1981)
[Ly] Lyubeznik, G.: A property of ideals in polynomial rings. Proc. Am. Math. Soc.98, 399–400 (1986)
[Mat] Matsumura, H.: Commutative Algebra. New York: Benjamin 1970
[Mat 1] Matsumura, H.: Commutative Ring Theory. Cambridge, New York: Cambridge University Press 1980
[NR] Northcott, D.G., Rees, D.: Reductions of ideals in local rings. Proc. Cambridge Philos. Soc. 50 (1954), pp. 145–158
[O1] O'Carroll, L.: A uniform Artin-Rees theorem and Zariski's main lemma on holomorphic functions. Invent. Math.90, 674–682 (1987)
[O2] O'Carroll, L.: A note on Artin-Rees numbers. Bull. Lond. Math. Soc. (to appear)
[Ra] Raghavan, K.N.: Uniform annihilation of local cohomology and of Koszul homology, preprint 1991
[R1] Rees, D.: Two classical theorems of ideal theory. Proc. Camb. Phil. Soc.52, 155–157 (1956)
[R2] Rees, D.: A note on analytically unramified local rings. J. Lond. Math. Soc.36, 24–28 (1961)
[R3] Rees, D.: Lectures on the asymptotic theory of ideals. (Lond. Math. Soc. Lect. Note Ser., vol. 113), Cambridge: Cambridge University Press 1989
[R4] Rees, D.: Hilbert functions and pseudo-rational local rings of dimension two. J. Lon. Math. Soc.24, 467–479 (1981)
[Ro] Roberts, P.: Two applications of dualizing complexes over local rings. Ann. Sci. Ec. Norm. Supér.9, 103–106 (1976)
[Sc] Schenzel, P.: Cohomological annihilators. Math. Proc. Camb. Philos. Soc.91, 345–350 (1982)
[Sw] Swanson, I.: Joint reductions, tight closure, and the Briançon-Skoda theorem. J. Algebra (to appear)
[Z] Zariski, O.: A fundamental lemma from the theory of holomorphic functions on an algebraic variety. Ann. Mat. Pura Appl., IV. Ser.429, 187–198 (1949)
Author information
Authors and Affiliations
Additional information
Oblatum 25-III-1990 & 10-VI-1991
Partially supported by the NSF
Rights and permissions
About this article
Cite this article
Huneke, C. Uniform bounds in noetherian rings. Invent Math 107, 203–223 (1992). https://doi.org/10.1007/BF01231887
Issue Date:
DOI: https://doi.org/10.1007/BF01231887