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Scarcity of finite polynomial orbits. (English) Zbl 0961.11005
Summary: Let \(R\) be a finitely generated integral domain of zero characteristic. If the index of the group of units of \(R\) in the group of the integral closure of \(R\) is finite then \(R\) contains only finitely many inequivalent finite nonlinear polynomial orbits. This applies in particular to all integrally closed domains.

MSC:
11C08 Polynomials in number theory
11R09 Polynomials (irreducibility, etc.)
12E05 Polynomials in general fields (irreducibility, etc.)
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