Axiomatic characterization of fields by the product formula for valuations
Axiomatic characterization of fields by the product formula for valuations
复制标题
通过估值的乘积公式对字段进行公理化表征
DOI：
10.1090/s0002-9904-1945-08383-9
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发表时间：
1945
影响因子：
1.3
通讯作者：
G. Whaples
中科院分区：
文献类型：
--
作者：
E. Artin;G. Whaples
导论.已知类域理论的定理适用于两种域：有理域的代数扩张和常数域上的单变量函数域的代数扩张。我们将把这些域分别称为数域和函数域。对于类域论，函数域确实必须限制为以伽罗瓦域作为常数域的函数域;然而，我们只在§5中作了这种限制，在此之前，我们考虑具有任意常数域的域。在证明这些定理时，赋值的乘积公式起着重要的作用。这个公式表明，对于一组合适的不等价估值，||p，
Introduction. The theorems of class field theory are known to hold for two kinds of fields: algebraic extensions of the rational field and algebraic extensions of a field of functions of one variable over a field of constants. We shall refer to these fields as number fields and function fields, respectively. For class field theory, the function fields must indeed be restricted to those with a Galois field as field of constants; however, we make this restriction only in §5, and until then consider fields with an arbitrary field of constants. In proving these theorems, the product formula for valuations plays an important rôle. This formula states that, for a suitable set of inequivalent valuations | | p,