The algebraic closure of the power series field in positive characteristic
The algebraic closure of the power series field in positive characteristic
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正特性幂级数场的代数闭包
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
K. Kedlaya
中科院分区：
文献类型：
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作者：
K. Kedlaya
对于K是一个代数闭域，设K（(t)）表示幂级数环K上的商域。“Newton-Puiseux定理”指出，如果K具有特征0，则K（(t)）的代数闭包是n∈n上K（(t1/n)）域的并。我们通过构造一个K（(t)）的代数闭包来回答Abhyankar的一个问题。
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.