The algebraically closed field of Nash functions is introduced. It is shown that this field is an algebraic closure of the field of rational functions in several variables. We give conditions for the irreducibility of polynomials with Nash coefficients, a description of factors of a polynomial over the field of Nash functions and a theorem on continuity of factors.
@article{bwmeta1.element.bwnjournal-article-apmv65z1p81bwm,
author = {Stanis\l aw Spodzieja},
title = {The field of Nash functions and factorization of polynomials},
journal = {Annales Polonici Mathematici},
volume = {63},
year = {1996},
pages = {81-94},
zbl = {0909.12002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv65z1p81bwm}
}
Stanisław Spodzieja. The field of Nash functions and factorization of polynomials. Annales Polonici Mathematici, Tome 63 (1996) pp. 81-94. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv65z1p81bwm/
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