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monoid [2015/03/28 20:15] nikolaj |
monoid [2015/03/28 20:17] nikolaj |
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===== Monoid ===== | ===== Monoid ===== | ||
==== Set ==== | ==== Set ==== | ||
- | | @#55CCEE: context | @#55CCEE: $M$ | | + | | @#55CCEE: context | @#55CCEE: $M$ ... set | |
| @#FFBB00: definiendum | @#FFBB00: $ \langle\!\langle M,*\rangle\!\rangle \in$ it | | | @#FFBB00: definiendum | @#FFBB00: $ \langle\!\langle M,*\rangle\!\rangle \in$ it | | ||
| @#AAFFAA: inclusion | @#AAFFAA: $*$ ... binary operation | | | @#AAFFAA: inclusion | @#AAFFAA: $*$ ... binary operation | | ||
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=== Discussion === | === Discussion === | ||
- | The binary operation is often called //multiplication// and $e$ is called the identity, identity element of 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 === |