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semigroup [2014/03/21 11:11] 127.0.0.1 external edit |
semigroup [2014/12/18 18:56] nikolaj |
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| ==== Set ==== | ==== Set ==== | ||
| | @#55CCEE: context | @#55CCEE: $S$ | | | @#55CCEE: context | @#55CCEE: $S$ | | ||
| - | |||
| | @#FFBB00: definiendum | @#FFBB00: $ \langle S,* \rangle \in \text{Semigroup}(S)$ | | | @#FFBB00: definiendum | @#FFBB00: $ \langle S,* \rangle \in \text{Semigroup}(S)$ | | ||
| - | |||
| | @#55EE55: postulate | @#55EE55: $\langle S,* \rangle\in \mathrm{Magma}(S)$ | | | @#55EE55: postulate | @#55EE55: $\langle S,* \rangle\in \mathrm{Magma}(S)$ | | ||
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| | @#DDDDDD: range | @#DDDDDD: $a,b,c\in S$ | | | @#DDDDDD: range | @#DDDDDD: $a,b,c\in S$ | | ||
| - | |||
| | @#55EE55: postulate | @#55EE55: $\forall a,b,c.\ (a*b)*c=a*(b*c)$ | | | @#55EE55: postulate | @#55EE55: $\forall a,b,c.\ (a*b)*c=a*(b*c)$ | | ||
| - | ==== Discussion ==== | + | ----- |
| + | |||
| + | === Discussion === | ||
| The binary operation is often called //multiplication//. | The binary operation is often called //multiplication//. | ||
| Line 18: | Line 16: | ||
| 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: [[http://en.wikipedia.org/wiki/Semigroup|Semigroup]] | ||
| - | ==== Parents ==== | + | |
| + | ----- | ||
| === Subset of === | === Subset of === | ||
| [[Magma]] | [[Magma]] | ||
