Axiomatic characterization of fields by the product formula for valuations
Emil Artin,George Whaples +1 more
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In this paper, the product formula for valuations plays an important role in proving these theorems, and it is shown that, for a suitable set of inequivalent valuations | | p,Abstract:
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,read more
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