A Remark on Hilbert Reciprocity
نویسنده
چکیده
Hilbert’s law of quadratic reciprocity, as reformulated by Hasse, states that for a quaternion algebra D over a number field K, the number of ramified places of D is even. In general a number field has three kinds of places: finite, real, and complex. The complex places are never ramified. If D is assumed unramified at all finite places, it follows that D is ramified at an even number of real places. In other words, if S(R) denotes the set of embeddings K ↪→ R and H denotes Hamilton’s quaternions, then
منابع مشابه
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