The Algebraic Closure of the Power Series Field in Positive Characteristic
نویسنده
چکیده
For K an algebraically closed field, let K((t)) denote the quotient field of the power series ring over K. The “Newton-Puiseux theorem” states that if K has characteristic 0, the algebraic closure of K((t)) is the union of the fields K((t1/n)) over n ∈ N. We answer a question of Abhyankar by constructing an algebraic closure of K((t)) for any field K of positive characteristic explicitly in terms of certain generalized power series.
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