##  [Near-Ring](/near-ring) 

  ##  [Near-Ring](https://puremath.quantumdictionary.io/near-ring-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A near-ring is a set N equipped with two operations, addition (+) making (N, +) a (usually noncommutative) group or at least a group-like structure, and a multiplication (·) that is associative, where one distributive law holds (typically right distributivity: (a + b)·c = a·c + b·c) but the other may fail; definitions vary on whether additively the structure must be a group or just a monoid.