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Albert's main work was on associative and non-associative algebras and Riemann matrices. He worked on classifying division algebras building on the work of Wedderburn but Brauer, Hasse and Emmy Noether got the result first. Albert's major contribution is, however, detailed in a joint paper with Hasse.
Albert's book Structure of Algebras published in 1939 remains a classic. The work on Riemann matrices was prompted by Lefschetz. Albert received the Cole prize for this work.
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