Simple algebra

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In mathematics, an algebra is simple if it contains no non-trivial ideals.

Simple algebras (and semi-simple algebras) were completely classified in 1907 by Joseph Wedderburn in his doctoral thesis with the title On hypercomplex numbers which appeared in the Proceedings of the London Mathematical Society. In his thesis he showed that any simple algebra is isomorphic to a matrix algebra over some division ring. This result was later generalized to semisimple rings in the Artin–Wedderburn theorem

Examples

See also

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