##  [Semiring](/semiring) 

  ##  [Semiring](https://puremath.quantumdictionary.io/semiring-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A semiring is an algebraic structure (S, +, ·) with two binary operations: addition (+) forming a commutative monoid with identity 0, and multiplication (·) forming a monoid with identity 1 (possibly the same as 0 only in the trivial case), where multiplication distributes over addition from both sides and 0 annihilates S under multiplication. Additive inverses need not exist.