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| Authors: | Arno van den Essen Jie-Tai Yu |
| Affiliation: | Department of Mathematics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands ; Department of Mathematics, University of Hong Kong, Hong Kong |
| Abstract: | We introduce the  -resultant of two polynomials in one variable and show how it can be used to decide if ![$k(f(t),g(t))=k(t),k[f(t),g(t)]=k[t]$](http://www.ams.org/proc/1997-125-03/S0002-9939-97-03639-3/gif-abstract/img5.gif) and to find the singularities of the curve  . 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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