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In algebraic number theory, the Hilbert class field E of a number field K is the maximal abelian unramified extension of K.Its degree over K equals the class number of K and the Galois group of E over K is canonically isomorphic to the ideal class group of K using Frobenius elements for prime ideals in K.
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1896 David Hilbert gives the first complete proof of the Kronecker–Weber theorem. 1897 Weber introduces ray class groups and general ideal class groups. 1897 Hilbert publishes his Zahlbericht. 1897 Hilbert rewrites the law of quadratic reciprocity as a product formula for the Hilbert symbol. 1897 Kurt Hensel introduced p-adic numbers.
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28,864 (confirmed by DOH 9/20/21) Government website; www.health.pa.gov /topics /disease /Pages /Coronavirus.aspx ‡ Suspected cases have not been confirmed by laboratory tests as being due to this strain, although some other strains may have been ruled out.
The commutative diagram in the previous section, which connects the number theoretic class extension homomorphism / with the group theoretic Artin transfer ,, enabled Furtwängler to prove the principal ideal theorem by specializing to the situation that = is the (first) Hilbert class field of , that is the maximal abelian unramified extension ...