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A New Class of Invertible Polynomial Maps

✍ Scribed by Arno van den Essen; Engelbert Hubbers

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
175 KB
Volume
187
Category
Article
ISSN
0021-8693

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✦ Synopsis

In this paper we present a new large class of polynomial maps F s X q H : A n n Ε½ . Βͺ A Definition 1.1 on every commutative ring A for which the Jacobian Conjecture is true. In particular H does not need to be homogeneous. We also Ε½ . show that for all H in this class satisfying H 0 s 0 the nth iterate H ( ΠΈΠΈΠΈ ( H s 0.

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Generalizing the norm and trace mappings for % O P /% O , we introduce an interesting class of polynomials over "nite "elds and study their properties. These polynomials are then used to construct curves over "nite "elds with many rational points.