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 | References | Similar Articles | Additional Information
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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Keywords:
Commuting functions,
commuting polynomials,
common fixed point,
Tchebycheff polynomials,
functional composition
Article copyright:
© Copyright 1972
American Mathematical Society
