Illinois Journal of Mathematics

Field degrees and multiplicities for non-integral extensions

Bernd Ulrich and Clarence W. Wilkerson

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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.

Article information

Source
Illinois J. Math., Volume 51, Number 1 (2007), 299-311.

Dates
First available in Project Euclid: 20 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258735337

Digital Object Identifier
doi:10.1215/ijm/1258735337

Mathematical Reviews number (MathSciNet)
MR2346199

Zentralblatt MATH identifier
1141.13007

Subjects
Primary: 13B21: Integral dependence; going up, going down
Secondary: 13A50: Actions of groups on commutative rings; invariant theory [See also 14L24]

Citation

Ulrich, Bernd; Wilkerson, Clarence W. Field degrees and multiplicities for non-integral extensions. Illinois J. Math. 51 (2007), no. 1, 299--311. doi:10.1215/ijm/1258735337. https://projecteuclid.org/euclid.ijm/1258735337


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