Rational functions with linear relations

We find all polynomials f,g,h over a field K such that g and h are linear and f(g(x))=h(f(x)). We also solve the same problem for rational functions f,g,h, in case the field K is algebraically closed.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2008-04, Vol.136 (4), p.1403-1408
Main Authors: Masuda, Ariane M., Zieve, Michael E.
Format: Article
Language:English
Subjects:
Algebra
Coefficients
Commuting
Exact sciences and technology
General mathematics
General, history and biography
Julia sets
Mathematical analysis
Mathematics
Polynomials
Rational functions
Real functions
Sciences and techniques of general use
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Description
Summary:We find all polynomials f,g,h over a field K such that g and h are linear and f(g(x))=h(f(x)). We also solve the same problem for rational functions f,g,h, in case the field K is algebraically closed.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-07-09246-5