# The field of Nash functions and factorization of polynomials

Annales Polonici Mathematici (1996)

- Volume: 65, Issue: 1, page 81-94
- ISSN: 0066-2216

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topStanisław Spodzieja. "The field of Nash functions and factorization of polynomials." Annales Polonici Mathematici 65.1 (1996): 81-94. <http://eudml.org/doc/269956>.

@article{StanisławSpodzieja1996,

abstract = {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.},

author = {Stanisław Spodzieja},

journal = {Annales Polonici Mathematici},

keywords = {Nash function; field; decomposition of polynomial; algebraic closure; holomorphic function; Nash functions; factorization of polynomials},

language = {eng},

number = {1},

pages = {81-94},

title = {The field of Nash functions and factorization of polynomials},

url = {http://eudml.org/doc/269956},

volume = {65},

year = {1996},

}

TY - JOUR

AU - Stanisław Spodzieja

TI - The field of Nash functions and factorization of polynomials

JO - Annales Polonici Mathematici

PY - 1996

VL - 65

IS - 1

SP - 81

EP - 94

AB - 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.

LA - eng

KW - Nash function; field; decomposition of polynomial; algebraic closure; holomorphic function; Nash functions; factorization of polynomials

UR - http://eudml.org/doc/269956

ER -

## References

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- [St] Y. Stein, The total reducibility order of a polynomial in two variables, Israel J. Math. 68 (1989), 109-122. Zbl0716.12001
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- [W] R. J. Walker, Algebraic Curves, Dover, New York, 1950. Zbl0039.37701

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