ArticleOriginal scientific text
Title
On the approximate roots of polynomials
Authors 1, 1
Affiliations
- Department of Mathematics, Technical University, Al. Tysiąclecia 7, 25-314 Kielce, Poland
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.
Keywords
approximate root, semigroup of an analytic curve, irreducibility criterion
Bibliography
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- S. S. Abhyankar and T. Moh, Embeddings of the line in the plane, ibid. 276 (1975), 148-166.
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- J. Gwoździewicz and A. Płoski, On the Merle formula for polar invariants, Bull. Soc. Sci. Lettres Łódź 41 (7) (1991), 61-67.
- M. Merle, Invariants polaires des courbes planes, Invent. Math. 41 (1977), 103-111.
- T. T. Moh, On the concept of approximate roots for algebra, J. Algebra 65 (1980), 347-360.
- T. T. Moh, On two fundamental theorems for the concept of approximate roots, J. Math. Soc. Japan 34 (1982), 637-652.
- A. Płoski, Bézout's theorem for affine curves with one branch at infinity, Univ. Iagell. Acta Math. 28 (1991), 77-80.
- O. Zariski, Le problème des modules pour les branches planes, Centre de Mathématiques de l'Ecole Polytechnique, 1973.
Pages:
199-210
Main language of publication
English
Received
1993-05-17
Published
1995
Exact and natural sciences