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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The $D$-resultant, singularities
and the degree of unfaithfulness


Authors: Arno van den Essen and Jie-Tai Yu
Journal: Proc. Amer. Math. Soc. 125 (1997), 689-695
MSC (1991): Primary 13P99
DOI: https://doi.org/10.1090/S0002-9939-97-03639-3
MathSciNet review: 1353403
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Abstract: We introduce the $D$-resultant of two polynomials in one variable and show how it can be used to decide if $k(f(t),g(t))=k(t),k[f(t),g(t)]=k[t]$ and to find the singularities of the curve $x=f(t),y=g(t)$. The second criterion is used to give a very short proof of a special case of the epimorphism theorem of Abhyankar and Moh.


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Additional Information

Arno van den Essen
Affiliation: Department of Mathematics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands
Email: essen@sci.kun.nl

Jie-Tai Yu
Affiliation: Department of Mathematics, University of Hong Kong, Hong Kong
Email: yujt@hkusua.hku.hk

DOI: https://doi.org/10.1090/S0002-9939-97-03639-3
Received by editor(s): June 15, 1995
Received by editor(s) in revised form: September 21, 1995
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1997 American Mathematical Society