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FALL 2015 On function compositions that are polynomials
Erhard Aichinger
J. Commut. Algebra 7(3): 303-315 (FALL 2015). DOI: 10.1216/JCA-2015-7-3-303


For a polynomial map $\tupBold{f} : k^n \to k^m$ ($k$ a field), we investigate those polynomials $g \in k[t_1,\ldots, t_n]$ that can be written as a composition $g = h \circ \tupBold{f}$, where $h: k^m \to k$ is an arbitrary function. In the case that $k$ is algebraically closed of characteristic~$0$ and $\tupBold{f}$ is surjective, we will show that $g = h \circ \tupBold{f}$ implies that $h$ is a polynomial.


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Erhard Aichinger. "On function compositions that are polynomials." J. Commut. Algebra 7 (3) 303 - 315, FALL 2015.


Published: FALL 2015
First available in Project Euclid: 14 December 2015

zbMATH: 1330.13009
MathSciNet: MR3433983
Digital Object Identifier: 10.1216/JCA-2015-7-3-303

Primary: 13B25
Secondary: 12E05

Keywords: Polynomial composition , polynomial maps

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

Vol.7 • No. 3 • FALL 2015
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