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semiring [2013/08/31 18:27] 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: $(b+c)*a=(b*a)+(c*a)$ | | ||
- | |||
- | ==== Ramifications ==== | ||
- | === Discussion === | ||
- | ==== Reference ==== | ||
- | Wikipedia: [[https://en.wikipedia.org/wiki/Semiring|Semiring]] | ||
- | ==== Context ==== | ||
- | === Requirements === | ||
- | [[Abelian monoid]] |