##  [Non-Semisimplicity](/non-semisimplicity) 

  ##  [Non-Semisimplicity](https://puremath.quantumdictionary.io/non-semisimplicity-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The property of an algebra, module, object, or category that it cannot be written as a direct sum (or categorical equivalent) of simple (semisimple) constituents; equivalently, there exist nontrivial extensions or a nonzero radical obstructing complete decomposition.