The field of Nash functions and factorization of polynomials

Stanisław Spodzieja

Annales Polonici Mathematici (1996)

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

Abstract

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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.

How to cite

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Stanisław 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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  1. [K] W. Krull, Über einen Irreduzibilitätssatz von Bertini, J. Reine Angew. Math. 177 (1937), 94-104. 
  2. [Ł] S. Łojasiewicz, Introduction to Complex Analytic Geometry, Birkhäuser, Basel, 1991. Zbl0747.32001
  3. [M] D. Mumford, Algebraic Geometry I, Complex Projective Varieties, Springer, Berlin, 1976. Zbl0356.14002
  4. [N] R. Narasimhan, Several Complex Variables, Chicago Lectures in Mathematics, Chicago-London 1971. Zbl0223.32001
  5. [Sc] A. Schinzel, Selected Topics on Polynomials, The University of Michigan Press, Ann Arbor, 1982. 
  6. [Sp] S. Spodzieja, On multi-valued algebraic mappings, Bull. Soc. Sci. Lett. Łódź 44 (1994), 95-109. Zbl0885.14007
  7. [St] Y. Stein, The total reducibility order of a polynomial in two variables, Israel J. Math. 68 (1989), 109-122. Zbl0716.12001
  8. [T] P. Tworzewski, Intersection of analytic sets with linear subspaces, Ann. Scuola Norm. Sup. Pisa (4) 17 (1990), 227-271. Zbl0717.32006
  9. [W] R. J. Walker, Algebraic Curves, Dover, New York, 1950. Zbl0039.37701

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