The field of Nash functions and factorization of polynomials

• Autorzy: Stanisław Spodzieja
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Nash function   field   decomposition of polynomial  

Kategorie tematyczne

• 12F99: None of the above, but in this section
• 12D99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996-1997
• Tom: 65
• Numer: 1
• Strony: 81-94

Daty

wydano

1996

otrzymano

1995-11-21

poprawiono

1996-04-02

Twórcy

autor

Stanisław Spodzieja

• Faculty of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Bibliografia

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