Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 51, Number 1 (2007), 299-311.
Field degrees and multiplicities for non-integral extensions
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.
Illinois J. Math., Volume 51, Number 1 (2007), 299-311.
First available in Project Euclid: 20 November 2009
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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