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monoid [2015/03/28 20:17] nikolaj |
monoid [2015/04/12 16:05] nikolaj |
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| | @#55EE55: postulate | @#55EE55: $(a*b)*c=a*(b*c)$ | | | @#55EE55: postulate | @#55EE55: $(a*b)*c=a*(b*c)$ | | ||
| | @#FFFDDD: exists | @#FFFDDD: $e\in M$ | | | @#FFFDDD: exists | @#FFFDDD: $e\in M$ | | ||
| - | | @#FFFDDD: for all | @#FFFDDD: $a\in M$ | | + | | @#55EE55: postulate | @#55EE55: $e$ ... unit element $\langle\!\langle M,*\rangle\!\rangle$ | |
| - | | @#55EE55: postulate | @#55EE55: $a*e=e*a=a$ | | + | |
| ----- | ----- | ||
| === Discussion === | === Discussion === | ||
| - | The binary operation is often called //multiplication// and $e$ is called the identity, identity element or unit. | + | The binary operation is often called //multiplication// and $e$ is called the //identity//, //identity element// or //unit//. |
| - | One generally calls $M$ the monoid, i.e. the set where the operation "$*$" is defined on. | + | One generally calls $M$ the monoid, i.e. the set where the operation "$*$" is defined on. |
| + | |||
| + | Like above, one often uses infix notion for $*$. | ||
| === Reference === | === Reference === | ||
| Line 19: | Line 20: | ||
| ----- | ----- | ||
| + | === Requirements === | ||
| + | [[Unit element]] | ||
| === Subset of === | === Subset of === | ||
| [[Semigroup]] | [[Semigroup]] | ||
