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A Simple Algorithm for Deciding Primes in K[[x,y]]

Published online by Cambridge University Press:  20 November 2018

Tzee Char kuo
Tzee Char kuo*
Affiliation:
School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia
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Abstract

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The well-known Tschirnhausen transformation, , eliminates the second term of the polynomial xn + axn-l + …. By a mere repeated application of this transformation, one can decide whether a given element of k[[x,y]] is prime (irreducible) or not. Here K is an algebraically closed field of characteristic 0. A generalised version of Hensel's Lemma is developed for the proofs. The entire paper can be understood by undergraduate students.

Keywords

13143268
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 4 , 01 August 1995 , pp. 801 - 816
Copyright
Copyright © Canadian Mathematical Society 1995

References

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2. Kuo, T.-C., Generalised Newton-Puiseux theory and Hensel's lemma in C[[x,y]], Canad. J. Math. (6) XLI(1989), 1101–1116.Google Scholar
3. Moh, T.T., On the approximate roots of a polynomial, Crelle 278(1974), 301–306.Google Scholar