A general reciprocity theorem for all orders which covered all other known reciprocity theorems when proved by E. Artin in 1927. If is a number field and a finite integral extension, then there is a surjection from the group of fractional ideals prime to the discriminant, given by the Artin symbol. For some cycle , the kernel of this surjection contains each principal fractional ideal generated by an element congruent to 1 mod .
Artin's Reciprocity Theorem
See alsoLanglands Program
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Cite this as:
Weisstein, Eric W. "Artin's Reciprocity Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ArtinsReciprocityTheorem.html