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A note on higher derivations and integral dependence


Author: William C. Brown
Journal: Proc. Amer. Math. Soc. 35 (1972), 367-371
MSC: Primary 13B10
DOI: https://doi.org/10.1090/S0002-9939-1972-0302627-7
MathSciNet review: 0302627
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Abstract: In this note we prove the following: Theorem. Let R' be an associative commutative ring with identity. Suppose R' is an integral extension of R, and $ \delta = \{ {\delta _i}\} $ is a higher derivation on R' which restricts to a higher derivation on R. Suppose p is a prime ideal in R which is differential under $ \delta $. Then there exists a prime ideal p' in R' such that p' is $ \delta $-differential and $ p' \cap R = p$.


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

  • [1] W. C. Brown and W. E. Kuan, Ideals and higher derivations in commutative rings, Canad. J. Math. (to appear). MR 0294319 (45:3388)
  • [2] S. Sato, On rings with a higher derivation, Proc. Amer. Math. Soc. 30 (1971), 63-69. MR 0279139 (43:4865)
  • [3] A. Seidenberg, Differential ideals in rings of finitely generated type, Amer. J. Math. 89 (1967), 22-42. MR 35 #2902. MR 0212027 (35:2902)
  • [4] O. Zariski and P. Samuel, Commutative algebra. Vol. 1, University Series in Higher Math., Van Nostrand, Princeton, N.J., 1958. MR 19, 833. MR 0090581 (19:833e)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0302627-7
Keywords: Higher derivations, differential ideals
Article copyright: © Copyright 1972 American Mathematical Society

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