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Artin made major contributions to the theory of noncommutative rings.
Artin attended the University of Göttingen for one year (1922-23) before becoming a lecturer at the University of Hamburg.
Artin was not a Jew but his wife was a Jew so when the 'New Official's Law' (1937) affected those related to Jews by marriage he was forced to leave Germany.
In 1937 he emigrated to the USA and taught at various universities. He was at Notre Dame for the year 1937-38, spent eight years at Indiana from 1938 to 1946 and then was 12 years at Princeton from 1946 to 1958.
In 1958 Artin returned to Germany, being appointed to his first university at Hamburg.
Artin's first work was on quadratic number fields, working on the analytic and arithmetic theory. In 1927 he made a major contribution to the theory of noncommutative rings, called hypercomplex numbers at this time. In particular he worked in the theory of associative algebras.
In 1944 he did important work on rings with the minimum condition on right ideals, now called Artinian rings. He presented new insight into semi-simple algebras over the rationals.
Another important piece of work done by Artin during his first period in Hamburg was the theory of braids which he presented in 1925. These have proved important to both algebra and topology.
In 1955 he produced two important papers on finite simple groups, proving that the only coincidences in orders of the known (in 1955) finite simple groups were those given by Dickson in his Linear groups .
Among Artin's main books are Geometric algebra (1957) and Class field theory (1961).
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