在Q_p 上維度為2 和 3 的體擴張
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2005
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大家都知道對於Q_p來說, 給定一個維度n必只存在有限多個在Q_p上擴張體維度是n的. 對於每個正整數n, 我們觀察係數在Q_p這個體上的多項式而且最高次是n次它的根的行為. 我們在這篇論文中主要是要研究多項式的係數和體擴張之間的關係.
It is well-known that for a p-adic field there exists only finite many extensions of a given degree. For a polynomial f with coefficients satisfying some conditions in Qp of given degree and let alpha be any root of f, we want to discuss the connection between coefficients of f and types of extensions Qp(alpha). In this paper we present a method for discussing the relation.
It is well-known that for a p-adic field there exists only finite many extensions of a given degree. For a polynomial f with coefficients satisfying some conditions in Qp of given degree and let alpha be any root of f, we want to discuss the connection between coefficients of f and types of extensions Qp(alpha). In this paper we present a method for discussing the relation.
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維度, 擴張