He was one of the leading algebraists of the century, with an influence larger than might be guessed from the one volume of his Collected Papers edited by his students Serge Lang[?] and John Tate. He worked in algebraic number theory, contributing largely to class field theory and a new construction of Lfunction. He also contributed to the pure theories of rings, groups and fields. He developed the theory of braids as a branch of algebraic topology.
He was also an important expositor: of Galois theory, and of the group cohomology approach to class field theory (with John Tate), to mention two theories where his formulations became standard. The influential treatment of abstract algebra by van der Waerden is said to derive in part from Artin's ideas, as well as those of Emmy Noether. He wrote a book on geometric algebra that may well have originated the term.
He left two conjectures, both known as Artin's conjecture. The first concerns Artin's Lfunction for a linear representation of a Galois group; and the second the frequency with which a given integer a is a primitive root modulo primes p, when a is fixed and p varies. These are unproven; Hooley proved a result for the second conditional on the first.
Emil Artin died in 1962, in Hamburg, Germany.
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