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E-Algebraic Functions over Fields of Positive Characteristic—An Analogue of Differentially Algebraic Functions

✍ Scribed by Habib Sharif

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
158 KB
Volume
207
Category
Article
ISSN
0021-8693

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✦ Synopsis

A function or a power series f is called differentially algebraic if it satisfies a Ž X Ž n. . differential equation of the form P x, y, y , . . . , y s 0, where P is a nontrivial polynomial. This notion is usually defined only over fields of characteristic zero and is not so significant over fields of characteristic p ) 0 as f Ž p. ' 0. For a formal power series over a perfect field K of positive characteristic we shall define an analogue of the concept of a differentially algebraic power series. We shall show that these series together with ordinary addition and multiplication of series form a field ⌫ with some natural properties. We also show that ⌫ is not closed under

the Hadamard product operation.

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