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).

**References**

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

© 1996-9

1999-05-26