Differences
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semiring [2013/09/02 22:57] nikolaj |
semiring [2014/03/21 11:11] (current) |
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| ===== Semiring ===== | ===== Semiring ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $X$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
| - | | @#FFBB00: $\langle X,+,* \rangle \in \mathrm{Semiring}(X)$ | | + | | @#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: $(b+c)*a=(b*a)+(c*a)$ | |
| ==== 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]] | ||
