Abstract
The concept of an integral ring extension is a generalization of the concept of an algebraic field extension. In the first section of this chapter, we develop the algebraic theory of integral extensions, and introduce the concept of a normal ring. Section 8.2 studies the morphism Spec(S) → Spec(R) induced from an integral extension R ⊆ S. In Sect. 8.3, we turn our attention to affine algebras again. We prove the Noether normalization theorem, and use it to prove, among other results, that all maximal ideals of an affine domain have equal height.
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© 2011 Springer-Verlag Berlin Heidelberg
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Kemper, G. (2011). Integral Extensions. In: A Course in Commutative Algebra. Graduate Texts in Mathematics, vol 256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03545-6_9
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DOI: https://doi.org/10.1007/978-3-642-03545-6_9
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03544-9
Online ISBN: 978-3-642-03545-6
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