Field degrees and multiplicities for non-integral extensions
Ulrich, Bernd ; Wilkerson, Clarence W.
Illinois J. Math., Tome 51 (2007) no. 3, p. 299-311 / Harvested from Project Euclid
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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.
Publié le : 2007-01-15
Classification:  13B21,  13A50 
@article{1258735337,
     author = {Ulrich, Bernd and Wilkerson, Clarence W.},
     title = {Field degrees and multiplicities for non-integral extensions},
     journal = {Illinois J. Math.},
     volume = {51},
     number = {3},
     year = {2007},
     pages = { 299-311},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258735337}
}

Ulrich, Bernd; Wilkerson, Clarence W. Field degrees and multiplicities for non-integral extensions. Illinois J. Math., Tome 51 (2007) no. 3, pp.  299-311. http://gdmltest.u-ga.fr/item/1258735337/