HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC

Let K be a field of characteristicp>۰, K[[x]], the ring of formal power series over K,K((x)), the quotient field of K[[x]], and K(x) the fieldof rational functions over K. We shall give somecharacterizations of an algebraic function f\in K((x)) over K.Let L be a field of characteristic zero. The power series f\inL[[x]] is called differentially algebraic, if it satisfies adifferential equation of the form P(x, y, y',...)=۰, where Pis a non-trivial polynomial. This notion is defined over fields ofcharacteristic zero and is not so significant over fields ofcharacteristic p>۰, since f^{(p)}=۰. We shall define ananalogue of the concept of a differentially algebraic power seriesover K and we shall find some more related results.

کلیدواژه ها:

Formal Power Series ، Algebraic Formal Power Series ، Differentially Algebraic Formal Power Series