##  [Wedderburn–Malcev Decomposition](/wedderburn-malcev-decomposition) 

  ##  [Wedderburn–Malcev Decomposition](https://puremath.quantumdictionary.io/wedderburn-malcev-decomposition-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A structural theorem for finite-dimensional associative algebras stating that, under a splitting condition, an algebra A decomposes as a semidirect (or vector-space) sum A = S ⊕ R where R is the Jacobson radical and S is a semisimple subalgebra isomorphic to the semisimple quotient A/R; the decomposition provides a semisimple complement to the radical when a splitting exists.