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semiring [2013/08/31 18:26] nikolaj |
semiring [2014/03/21 11:11] (current) |
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===== Semiring ===== | ===== Semiring ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $X$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
- | $\langle X,+,* \rangle \in \mathrm{SemiRing}(X)$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\langle X,+,* \rangle \in \mathrm{Semiring}(X)$ | |
- | | @#88DDEE: $\langle X,+ \rangle \in \mathrm{AbelianMonoid}(X)$ | | + | | @#55CCEE: context | @#55CCEE: $\langle X,+ \rangle \in \mathrm{AbelianMonoid}(X)$ | |
| $a,b,c\in X$ | | | $a,b,c\in X$ | | ||
- | | @#55EE55: $(a*b)*c=a*(b*c)$ | | + | | @#55EE55: postulate | @#55EE55: $(a*b)*c=a*(b*c)$ | |
- | | @#55EE55: $a*(b+c)=(a*b)+(a*c)$ | | + | | @#55EE55: postulate | @#55EE55: $a*(b+c)=(a*b)+(a*c)$ | |
- | | @#55EE55: $(b+c)*a=(b*a)+(c*a)$ | | + | | @#55EE55: postulate | @#55EE55: $(b+c)*a=(b*a)+(c*a)$ | |
- | ==== Ramifications ==== | + | ==== Discussion ==== |
- | === Discussion === | + | === Reference === |
- | ==== Reference ==== | + | |
Wikipedia: [[https://en.wikipedia.org/wiki/Semiring|Semiring]] | Wikipedia: [[https://en.wikipedia.org/wiki/Semiring|Semiring]] | ||
- | ==== Context ==== | + | ==== Parents ==== |
- | === Requirements === | + | === Context === |
[[Abelian monoid]] | [[Abelian monoid]] |