Erschienen in:

1998 | OriginalPaper | Buchkapitel

Additive Polynomials

verfasst von : David Goss

Erschienen in: Basic Structures of Function Field Arithmetic

Verlag: Springer Berlin Heidelberg

Enthalten in: Professional Book Archive

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Let k be a field of finite characteristic p and let $$\bar k$$ be a fixed algebraic closure. Let $$P\left( x \right) \in k\left[ x \right] $$ be a polynomial in x with coefficients in k. We say that P(x) is additive if and only if $$ P\left( {\alpha + \beta } \right) = P\left( \alpha \right) + P\left( \beta \right)\,\,for\,\,\left\{ {\alpha ,\beta ,\alpha + \beta } \right\} \subseteq k $$. We say that P(x) is absolutely additive if and only if P(x) is additive over $$\bar k$$.

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