Nikolai Chebotaryov
Nikolai Grigoryevich Chebotaryov (Russian Николай Григорьевич Чеботарёв, Ukrainian Микола Григорович Чеботарьов, English transcription Nikolai Chebotaryovs; * 3 Junijul / June 15 1894greg in Kamjanez - Podilskyj, .. † July 2, 1947 in Moscow) was a Soviet mathematician. He was known primarily named after him tschebotarjowschen tightness sentence, a main result of algebraic number theory.
Life
Chebotaryov studied 1912-1918 Mathematics at the University of Kiev and at first then worked as a private tutor and research assistant. In 1921 he moved to Odessa, to support his parents living there. During this time, in 1922, Chebotaryov found the known density theorem, the basis of his later Habilitation should be (Russian doctorate degrees). In 1924 he was given the post of contrasting political reasons Dmitri Fyodorovich Egorov in Moscow, but announced a little later and he returned to Odessa. In 1925 he attended a meeting of the German Mathematical Society in Gdansk, where he Emmy Noether, Helmut Hasse and Kurt Hensel met and then Berlin ( Isay Schur ) and Göttingen visited. 1927 awarded him the Ukrainian Academy of Sciences in Kiev Russian doctoral degrees. In 1928 he became a professor at the University of Kazan, which he held until his death. There he founded his own school of algebraists.
His 1923 published tightness set generalized Dirichlet's theorem of primes in arithmetic progressions and solves a 1896 excepted by Ferdinand Georg Frobenius problem. He served Emil Artin in 1927 in the proof of his reciprocity law, a main result of class field theory.
In later years he worked on Galois theory, about which he wrote a textbook in two volumes (1934, 1937), and the inverse Galoisproblem ( for a given Galois group to find the appropriate equations). He also dealt with the problem of the resolvent, which goes back to Felix Klein and the reduction ( by a rational transformation ) of an algebraic equation with coefficients dependent parameter has an equation to the destination whose coefficients depend on as few parameters. Chebotaryov turned the Galois theory also 1934 on going back to ancient times, and also adopted, among others, Leonard Euler and Thomas Clausen problem of constructability of Halfmoon. Chebotaryov also dealt with the theory of Lie groups, to he published in 1940 the first Russian textbook on Lie groups, with the geometry of swept surfaces and history of mathematics.
In 1932 he gave a plenary lecture at the International Congress of Mathematicians in Zurich ( The tasks of modern Galois theory ).
His students include Mark Grigoryevich Krein and Vladimir Vladimirovich Morozov. In 1929 he became a corresponding member of the Soviet Academy of Sciences. In 1948, he was posthumously awarded the Soviet State Prize for his work on Resolvententheorie. In 1943 he was Honoured Scientist of the Russian Republic.
Writings
- Collected Works (in Russian ), 3 volumes, Moscow, Leningrad, 1949-1950
The German translation of the 1923 Russian original published work on the leak rate appeared in 1925 in Mathematische Annalen:
- Tschebotareff N. The determination of the density of a set of prime numbers which belong to a given class of substitution. In: Annals of Mathematics 95 (1925 ), pp. 191-228 ( digitized ).
Literature and sources
- Steve P. Hagen, H. W. Lenstra: Chebotarev and his density theorem. In: The Mathematical Intelligencer 18 (1996 ), pp. 26-37 (PDF, 2.7 MB).
- Adolf Pavlovich Yushkevich, articles in the Dictionary of Scientific Biography Cheboaryov, online