| 单词 | Semisimple Algebra |
| 释义 | Semisimple AlgebraAn Algebra with no nontrivial nilpotent Ideals. In the 1890s, Cartan, Frobenius, and Molienindependently proved that any finite-dimensional semisimple algebra over the Real orComplex numbers is a finite and unique Direct Sum of SimpleAlgebras. This result was then extended to algebras over arbitrary fields by Wedderburn in 1907 (Kleiner1996). See also Ideal, Nilpotent Element, Simple Algebra
Kleiner, I. ``The Genesis of the Abstract Ring Concept.'' Amer. Math. Monthly 103, 417-424, 1996. |
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