Noether Normalization and Applications

Gert-Martin Greuel () and Gerhard Pfister ()
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Gert-Martin Greuel: University of Kaiserslautern, Department of Mathematics
Gerhard Pfister: University of Kaiserslautern, Department of Mathematics

Chapter 3 in A Singular Introduction to Commutative Algebra, 2002, pp 191-237 from Springer

Abstract: Abstract Integral extension of a ring means adjoining roots of monic polynomials over the ring. This is an important tool for studying affine rings, and it is used in many places, for example, in dimension theory, ring normalization and primary decomposition. Integral extensions are closely related to finite maps which, geometrically, can be thought of as projections with finite fibres plus some algebraic conditions. We shall give a constructive introduction with explicit algorithms to these subjects.

Keywords: Prime Ideal; Maximal Ideal; Integral Domain; Polynomial Ring; Noetherian Ring (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-3-662-04963-1_3

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