Comments On " Orbits of automorphism groups of fields"

Details Comments On " Orbits of automorphism groups of fields" Comments On " Orbits of automorphism groups of fields"

2007-09-18

arxiv.org/abs/0709.2797v1

Mathematics

Commutative Algebra

6 pages

Scientific paper

Let $R$ be a commutative $k-$algebra over a field $k$. Assume $R$ is a Noetherian integral domain and $|R|=\infty$. The group of $k-$automorphisms of $R$,i.e., $Aut_k(R)$ acts in a natural way on $(R-k)$. We study the structure of $R$ when orbit space $(R-k)/Aut_k(R)$ is finite, and note that most of the results proved in $[1,\S2]$ hold in this case as well. We also give an elementary proof of [1,Theorem 1.1] in case $k$ is finitely generated over its prime subfield.

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