##  [Socle](/socle) 

  ##  [Socle](https://puremath.quantumdictionary.io/socle-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The socle of a module or ring is the sum of all its minimal nonzero submodules (or minimal ideals); it is the largest semisimple subobject contained in the module and equals the direct sum of all simple submodules.