Illinois Journal of Mathematics

Field degrees and multiplicities for non-integral extensions

Bernd Ulrich and Clarence W. Wilkerson

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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

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

First available in Project Euclid: 20 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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