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Krull dimension of polynomial rings

Part of the Lecture Notes in Mathematics book series (LNM,volume 311)

Abstract

Let Q be a prime ideal of R[X1, ..., Xn] and let P=Q ∩ R. This paper investigates the relationship between the ranks of Q and P[X1, ..., Xn]. The results are used to recover some well-known results concerning the Krull dimension of R[X1, ..., Xn]. The paper also contains a number of examples related to questions which arose in connection with the above investigation.

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References

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© 1973 Springer-Verlag

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Brewer, J.W., Montgomery, P.R., Rutter, E.A., Heinzer, W.J. (1973). Krull dimension of polynomial rings. In: Brewer, J.W., Rutter, E.A. (eds) Conference on Commutative Algebra. Lecture Notes in Mathematics, vol 311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068916

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  • DOI: https://doi.org/10.1007/BFb0068916

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06140-3

  • Online ISBN: 978-3-540-38340-6

  • eBook Packages: Springer Book Archive