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monoid_kernel [2013/09/05 20:22] nikolaj created |
monoid_kernel [2014/03/21 11:11] (current) |
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| ===== Monoid kernel ===== | ===== Monoid kernel ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $ X $ | | + | | @#55CCEE: context | @#55CCEE: $ X $ | |
| - | | @#88DDEE: $ M $ ... monoid | | + | | @#55CCEE: context | @#55CCEE: $ M $ ... monoid | |
| - | | @#88DDEE: $ f:X\to M $ | | + | | @#55CCEE: context | @#55CCEE: $ f:X\to M $ | |
| - | | @#FFBB00: $ x\in\mathrm{ker}(f) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ x\in\mathrm{ker}(f) $ | |
| - | | @#55EE55: $ f(x)=e $ | | + | | @#55EE55: postulate | @#55EE55: $ f(x)=e $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | $\mathrm{ker}(f)$ is $\mathrm{ker}(f)$ w.r.t. the unit of the monoid. | + | $\mathrm{ker}(f)$ is $\mathrm{sol}(f)$ w.r.t. the unit of the monoid. |
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Solution_set|Solution set]] | Wikipedia: [[http://en.wikipedia.org/wiki/Solution_set|Solution set]] | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| === Subset of === | === Subset of === | ||
| [[Solution set]] | [[Solution set]] | ||
| - | === Requirements === | + | === Context === |
| [[Monoid]] | [[Monoid]] | ||
