Abstract
In this section we shall prove Theorems A and A1, explained in Chapter 8. Theorem A1 is a form of the Noether normalization theorem, due to Nagata [1962]. It gives a kind of universal tool for the solution of many problems about affine rings. We shall illustrate this assertion by proving three other famous results: Hilbert’s Nullstellensatz, Noether’s theorem on the finiteness of the integral closure of an affine domain, and, in the next chapter, Grothendieck’s lemma of generic freeness, with its applications to the semi-continuity of fiber dimensions.
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© 1995 Springer-Verlag New York, Inc.
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Eisenbud, D. (1995). The Dimension of Affine Rings. In: Commutative Algebra. Graduate Texts in Mathematics, vol 150. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5350-1_15
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DOI: https://doi.org/10.1007/978-1-4612-5350-1_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-3-540-78122-6
Online ISBN: 978-1-4612-5350-1
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