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semigroup [2014/03/21 11:11] 127.0.0.1 external edit |
semigroup [2016/01/20 12:52] nikolaj |
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| ===== Semigroup ===== | ===== Semigroup ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#55CCEE: context | @#55CCEE: $S$ | | + | | @#55CCEE: context | @#55CCEE: $S$ ... set | |
| + | | @#FFBB00: definiendum | @#FFBB00: $\langle\!\langle S,* \rangle\!\rangle \in $ semigroup(S) | | ||
| + | | @#AAFFAA: inclusion | @#AAFFAA: $\langle\!\langle S,* \rangle\!\rangle\in $ magma(S) | | ||
| + | | @#55EE55: postulate | @#55EE55: $(a*b)*c=a*(b*c)$ | | ||
| - | | @#FFBB00: definiendum | @#FFBB00: $ \langle S,* \rangle \in \text{Semigroup}(S)$ | | + | ----- |
| - | | @#55EE55: postulate | @#55EE55: $\langle S,* \rangle\in \mathrm{Magma}(S)$ | | + | === Discussion === |
| - | + | ||
| - | | @#DDDDDD: range | @#DDDDDD: $a,b,c\in S$ | | + | |
| - | + | ||
| - | | @#55EE55: postulate | @#55EE55: $\forall a,b,c.\ (a*b)*c=a*(b*c)$ | | + | |
| - | + | ||
| - | ==== Discussion ==== | + | |
| The binary operation is often called //multiplication//. | The binary operation is often called //multiplication//. | ||
| Line 18: | Line 15: | ||
| One generally calls $S$ the semigroup, i.e. the set where the operation "$*$" is defined on. | One generally calls $S$ the semigroup, i.e. the set where the operation "$*$" is defined on. | ||
| - | ==== Reference ==== | + | === Reference === |
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Semigroup|Semigroup]] | + | Wikipedia: |
| - | ==== Parents ==== | + | [[http://en.wikipedia.org/wiki/Semigroup | Semigroup]], |
| + | [[https://en.wikipedia.org/wiki/Special_classes_of_semigroups | Special classes of semigroups]] | ||
| + | |||
| + | ----- | ||
| === Subset of === | === Subset of === | ||
| [[Magma]] | [[Magma]] | ||
