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semiring [2013/09/02 22:55]
nikolaj
semiring [2014/03/21 11:11]
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-===== Semiring ===== 
-==== Definition ==== 
-| @#88DDEE: $X$ | 
  
-| @#FFBB00: $\langle X,+,* \rangle \in \mathrm{SemiRing}(X)$ | 
- 
-| @#88DDEE: $\langle X,+ \rangle \in \mathrm{AbelianMonoid}(X)$ | 
-| $a,b,c\in X$ | 
- 
-| @#55EE55: $(a*b)*c=a*(b*c)$ | 
-| @#55EE55: $a*(b+c)=(a*b)+(a*c)$ | 
-| @#55EE55: $(b+c)*a=(b*a)+(c*a)$ | 
- 
-==== Discussion ==== 
-=== Reference === 
-Wikipedia: [[https://​en.wikipedia.org/​wiki/​Semiring|Semiring]] 
-==== Context ==== 
-=== Requirements === 
-[[Abelian monoid]] 
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