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Proceedings of the American Mathematical Society

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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$.


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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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