On the approximate roots of polynomials

• Autorzy: Janusz Gwoździewicz , Arkadiusz Płoski
• Języki publikacji: EN

Abstrakty

EN

We give a simplified approach to the Abhyankar-Moh theory of approximate roots. Our considerations are based on properties of the intersection multiplicity of local curves.

Słowa kluczowe

EN

approximate root; semigroup of an analytic curve; irreducibility criterion

Kategorie tematyczne

• 14B05: Singularities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994-1995
• Tom: 60
• Numer: 3
• Strony: 199-210

Daty

wydano

1995

otrzymano

1993-05-17

Twórcy

autor

Janusz Gwoździewicz

• Department of Mathematics, Technical University, Al. Tysiąclecia 7, 25-314 Kielce, Poland

autor

Arkadiusz Płoski

• Department of Mathematics, Technical University, Al. Tysiąclecia 7, 25-314 Kielce, Poland

Bibliografia

• [1] S. S. Abhyankar, Expansion Techniques in Algebraic Geometry, Tata Inst. Fund. Research, Bombay, 1977.
• [2] S. S. Abhyankar and T. Moh, Newton-Puiseux expansion and generalized Tschirnhausen transformation, J. Reine Angew. Math. 260 (1973), 47-83; 261 (1973), 29-54.
• [3] S. S. Abhyankar and T. Moh, Embeddings of the line in the plane, ibid. 276 (1975), 148-166.
• [4] R. Ephraim, Special polars and curves with one place at infinity, in: Proc. Sympos. Pure Math. 40, Part I, Amer. Math. Soc., 1985, 353-359.
• [5] J. Gwoździewicz and A. Płoski, On the Merle formula for polar invariants, Bull. Soc. Sci. Lettres Łódź 41 (7) (1991), 61-67.
• [6] M. Merle, Invariants polaires des courbes planes, Invent. Math. 41 (1977), 103-111.
• [7] T. T. Moh, On the concept of approximate roots for algebra, J. Algebra 65 (1980), 347-360.
• [8] T. T. Moh, On two fundamental theorems for the concept of approximate roots, J. Math. Soc. Japan 34 (1982), 637-652.
• [9] A. Płoski, Bézout's theorem for affine curves with one branch at infinity, Univ. Iagell. Acta Math. 28 (1991), 77-80.
• [10] O. Zariski, Le problème des modules pour les branches planes, Centre de Mathématiques de l'Ecole Polytechnique, 1973.