Emil Artin created modern general algebra (together with E. Noether). The works of Emil Artin constitute a significant part of the famous “Modern algebra” (now simply “Algebra”) of van der Waerden.
Particularly important is Artin’s contribution to field theory, where he co-developed the theory of real fields with O. Schreyer, and then solved the famous 17th problem of Hilbert.
No less important are Artin’s works in algebraic number theory, mainly in class field theory, where he applied the Galois cohomology apparatus.
He formulated the law of reciprocity. Among the students of Emil Artin were Serge Leng and John Tate. His son Michael Artin is also a well-known mathematician.
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