Abstract
Let $R$ be an integral domain. We study the structure of $R$ under the condition that the orbit space $R/\mathit{Aut}(R)$ is finite. It is proved that if $R$ is Noetherian, then $ |R/\mathit{Aut}(R)|= \infty$ unless $R$ is a finite field (Theorem 15 and Corollary 16). Furthermore, we give an example of an infinite integral domain with $|R/\mathit{Aut}(R)|< \infty$.
Citation
Pramod K. Sharma. "Orbits of automorphisms of integral domains." Illinois J. Math. 52 (2) 645 - 652, Summer 2008. https://doi.org/10.1215/ijm/1248355355
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