# Differences

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magma [2015/04/12 15:58] nikolaj |
magma [2015/04/12 17:48] (current) nikolaj |
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===== Magma ===== | ===== Magma ===== | ||

==== Set ==== | ==== Set ==== | ||

- | | @#55CCEE: context | @#55CCEE: $M$ | | + | | @#55CCEE: context | @#55CCEE: $M$ ... set | |

- | | @#FFBB00: definiendum | @#FFBB00: $ \langle M,* \rangle \in \text{Magma}(M)$ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \langle\!\langle M,* \rangle\!\rangle \in$ magma | |

- | | @#55EE55: postulate | @#55EE55: $*$ ... binary operation | | + | | @#AAFFAA: inclusion | @#AAFFAA: $* \in$ binary operation (M) | |

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The binary operation is often called //multiplication//. | The binary operation is often called //multiplication//. | ||

- | The axioms | + | The axiom '$* \in$ binary operation (M)' above means that a magma is closed with respect to the multiplication. |

- | | + | |

- | $*\in \mathrm{BinaryOp}(M)$ | + | |

- | | + | |

- | above means that a magma is closed with respect to the multiplication. | + | |

One generally calls $M$ the Magma, i.e. the set where the operation "$*$" is defined on. | One generally calls $M$ the Magma, i.e. the set where the operation "$*$" is defined on. |