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Semisimple Algebra


An algebra with no nontrivial nilpotent ideals. In the 1890s, Cartan, Frobenius, and Molien independently proved that any finite-dimensional semisimple algebra over the real or complex numbers is a finite and unique direct sum of simple algebras. This result was then extended to algebras over arbitrary fields by Wedderburn in 1907 (Kleiner 1996).


See also

Ideal, Nilpotent Element, Simple Algebra

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References

Kleiner, I. "The Genesis of the Abstract Ring Concept." Amer. Math. Monthly 103, 417-424, 1996.

Referenced on Wolfram|Alpha

Semisimple Algebra

Cite this as:

Weisstein, Eric W. "Semisimple Algebra." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SemisimpleAlgebra.html

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