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Spring 2007 Field degrees and multiplicities for non-integral extensions
Bernd Ulrich, Clarence W. Wilkerson
Illinois J. Math. 51(1): 299-311 (Spring 2007). DOI: 10.1215/ijm/1258735337

Abstract

Let $R$ be a graded subalgebra of a polynomial ring $S$ over a field so that $S$ is algebraic over $R$. The goal of this paper is to relate the generator degrees of $R$ to the degree $[S:R]$ of the underlying quotient field extension, and to provide a numerical criterion for $S$ to be integral over $R$ that is based on this relationship. As an application we obtain a condition guaranteeing that a ring of invariants of a finite group is a polynomial ring.

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Bernd Ulrich. Clarence W. Wilkerson. "Field degrees and multiplicities for non-integral extensions." Illinois J. Math. 51 (1) 299 - 311, Spring 2007. https://doi.org/10.1215/ijm/1258735337

Information

Published: Spring 2007
First available in Project Euclid: 20 November 2009

zbMATH: 1141.13007
MathSciNet: MR2346199
Digital Object Identifier: 10.1215/ijm/1258735337

Subjects:
Primary: 13B21
Secondary: 13A50

Rights: Copyright © 2007 University of Illinois at Urbana-Champaign

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Vol.51 • No. 1 • Spring 2007
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