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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On polynomials which commute with a given polynomial


Author: William M. Boyce
Journal: Proc. Amer. Math. Soc. 33 (1972), 229-234
MSC: Primary 12D99
DOI: https://doi.org/10.1090/S0002-9939-1972-0291138-3
MathSciNet review: 0291138
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Abstract: By extending a theorem of Jacobsthal, the following result is obtained: if g is a nonlinear polynomial, there is an integer $ J(g) \geqq 1$ such that for each $ m > 0$ there are either $ J(g)$ or zero distinct polynomials of degree m which commute with g. A formula is given for computing $ J(g)$ from the coefficients of g.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0291138-3
Keywords: Commuting functions, commuting polynomials, common fixed point, Tchebycheff polynomials, functional composition
Article copyright: © Copyright 1972 American Mathematical Society

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