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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.
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.
In the situation that is a prime number, = is the second Hilbert p-class field of , that is the maximal metabelian unramified extension of of degree a power of , varies over the intermediate field between and its first Hilbert p-class field (), and = (() /) = (() /) correspondingly varies over the intermediate groups between and ...
United States Office of Personnel Management notification that Federal agencies in the Washington, D.C. area would be closed on December 21, 2009, due to the North American blizzard of 2009. A snow day in the United States and Canada is a day that school classes are cancelled or delayed by snow, heavy ice, or extremely low temperatures.
As with the Hilbert problems, one of the prize problems (the Poincaré conjecture) was solved relatively soon after the problems were announced. The Riemann hypothesis is noteworthy for its appearance on the list of Hilbert problems, Smale's list, the list of Millennium Prize Problems, and even the Weil conjectures, in its geometric guise.
Hilbert served as Economic Affairs Officer of the United Nations Secretariat for 15 years (), where he created the Information Society Program for Latin America and the Caribbean [6] He conceptualized the design of the eLAC Action Plans, which has led to six consecutive generations of digital development agendas for Latin America and the Caribbean (2005–2025).
At the start of summer, the White House swore in more than 9,000 members of the inaugural class of the American Climate Corps. The corps members are now serving across the country stifling ...
The origin of the Entscheidungsproblem goes back to Gottfried Leibniz, who in the seventeenth century, after having constructed a successful mechanical calculating machine, dreamt of building a machine that could manipulate symbols in order to determine the truth values of mathematical statements. [3]