On the approximate roots of polynomials

Janusz Gwoździewicz; Arkadiusz Płoski

Annales Polonici Mathematici (1995)

  • Volume: 60, Issue: 3, page 199-210
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Janusz Gwoździewicz, and Arkadiusz Płoski. "On the approximate roots of polynomials." Annales Polonici Mathematici 60.3 (1995): 199-210. <http://eudml.org/doc/262335>.

@article{JanuszGwoździewicz1995,
abstract = {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.},
author = {Janusz Gwoździewicz, Arkadiusz Płoski},
journal = {Annales Polonici Mathematici},
keywords = {approximate root; semigroup of an analytic curve; irreducibility criterion; approximable roots of polynomials; field of meromorphic series},
language = {eng},
number = {3},
pages = {199-210},
title = {On the approximate roots of polynomials},
url = {http://eudml.org/doc/262335},
volume = {60},
year = {1995},
}

TY - JOUR
AU - Janusz Gwoździewicz
AU - Arkadiusz Płoski
TI - On the approximate roots of polynomials
JO - Annales Polonici Mathematici
PY - 1995
VL - 60
IS - 3
SP - 199
EP - 210
AB - 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.
LA - eng
KW - approximate root; semigroup of an analytic curve; irreducibility criterion; approximable roots of polynomials; field of meromorphic series
UR - http://eudml.org/doc/262335
ER -

References

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  1. [1] S. S. Abhyankar, Expansion Techniques in Algebraic Geometry, Tata Inst. Fund. Research, Bombay, 1977. Zbl0818.14001
  2. [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. Zbl0272.12102
  3. [3] S. S. Abhyankar and T. Moh, Embeddings of the line in the plane, ibid. 276 (1975), 148-166. Zbl0332.14004
  4. [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. [5] J. Gwoździewicz and A. Płoski, On the Merle formula for polar invariants, Bull. Soc. Sci. Lettres Łódź 41 (7) (1991), 61-67. Zbl0893.32006
  6. [6] M. Merle, Invariants polaires des courbes planes, Invent. Math. 41 (1977), 103-111. Zbl0371.14003
  7. [7] T. T. Moh, On the concept of approximate roots for algebra, J. Algebra 65 (1980), 347-360. Zbl0437.13004
  8. [8] T. T. Moh, On two fundamental theorems for the concept of approximate roots, J. Math. Soc. Japan 34 (1982), 637-652. Zbl0528.12015
  9. [9] A. Płoski, Bézout's theorem for affine curves with one branch at infinity, Univ. Iagell. Acta Math. 28 (1991), 77-80. Zbl0759.14023
  10. [10] O. Zariski, Le problème des modules pour les branches planes, Centre de Mathématiques de l'Ecole Polytechnique, 1973. Zbl0317.14004

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