On function compositions that are polynomials

Erhard Aichinger

doi:10.48550/arXiv.1601.01779

On function compositions that are polynomials

Erhard Aichinger

Institute for Algebra

Research output: Working paper and reports › Preprint

Abstract

For a polynomial map f:k^n→k^m (k a field), we investigate those polynomials g∈k[t1,…,tn] that can be written as a composition g=h∘f, where h:k^m→k is an arbitrary function. In the case that k is algebraically closed of characteristic 0 and f is surjective, we will show that g=h∘f implies that h is a polynomial.

Original language	English
Number of pages	11
DOIs	https://doi.org/10.48550/arXiv.1601.01779
Publication status	Published - Jan 2016

Publication series

Name	arXiv.org
No.	arXiv:1601.01779
ISSN (Print)	2331-8422

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101013 Mathematical logic
102031 Theoretical computer science

JKU Focus areas

Computation in Informatics and Mathematics
Engineering and Natural Sciences (in general)

Access to Document

10.48550/arXiv.1601.01779

Algebraic approaches to the description of Mal'cev clones
Aichinger, E. (PI)
01.01.2012 → 31.10.2015
Project: Funded research › FWF - Austrian Science Fund

Cite this

@techreport{f6c6a4d0b99b4066abe70626879cee2d,

title = "On function compositions that are polynomials",

abstract = "For a polynomial map f:k\textasciicircum{}n→k\textasciicircum{}m (k a field), we investigate those polynomials g∈k[t1,…,tn] that can be written as a composition g=h∘f, where h:k\textasciicircum{}m→k is an arbitrary function. In the case that k is algebraically closed of characteristic 0 and f is surjective, we will show that g=h∘f implies that h is a polynomial.",

author = "Erhard Aichinger",

year = "2016",

month = jan,

doi = "10.48550/arXiv.1601.01779",

language = "English",

series = "arXiv.org",

number = "arXiv:1601.01779",

type = "WorkingPaper",

}

TY - UNPB

T1 - On function compositions that are polynomials

AU - Aichinger, Erhard

PY - 2016/1

Y1 - 2016/1

N2 - For a polynomial map f:k^n→k^m (k a field), we investigate those polynomials g∈k[t1,…,tn] that can be written as a composition g=h∘f, where h:k^m→k is an arbitrary function. In the case that k is algebraically closed of characteristic 0 and f is surjective, we will show that g=h∘f implies that h is a polynomial.

AB - For a polynomial map f:k^n→k^m (k a field), we investigate those polynomials g∈k[t1,…,tn] that can be written as a composition g=h∘f, where h:k^m→k is an arbitrary function. In the case that k is algebraically closed of characteristic 0 and f is surjective, we will show that g=h∘f implies that h is a polynomial.

U2 - 10.48550/arXiv.1601.01779

DO - 10.48550/arXiv.1601.01779

M3 - Preprint

T3 - arXiv.org

BT - On function compositions that are polynomials

ER -

On function compositions that are polynomials

Abstract

Publication series

Fields of science

JKU Focus areas

Access to Document

Projects

Algebraic approaches to the description of Mal'cev clones

Cite this