In mathematics, given a local field K, such as the fields of reals or p-adic numbers, whose multiplicative group of non-zero elements is K×, the Hilbert symbol is an algebraic construction, extracted from reciprocity laws, and important in the formulation of local class field theory. As the name suggests, it was in some sense introduced by David Hilbert, although it would be anachronistic to say that of the local field formulation.
Explicitly, it is the function (–, –) from K× × K× to {−1,1} defined by
Read more about Hilbert Symbol: Properties, Interpretation As An Algebra, Hilbert Symbols Over The Rationals, Kaplansky Radical
Famous quotes containing the word symbol:
“A symbol is indeed the only possible expression of some invisible essence, a transparent lamp about a spiritual flame; while allegory is one of many possible representations of an embodied thing, or familiar principle, and belongs to fancy and not to imagination: the one is a revelation, the other an amusement.”
—William Butler Yeats (1865–1939)