# Differences

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 magma [2015/04/12 15:58]nikolaj magma [2015/04/12 17:48] (current)nikolaj Both sides previous revision Previous revision 2015/04/12 17:48 nikolaj 2015/04/12 15:58 nikolaj 2015/04/12 15:56 nikolaj 2015/04/12 15:55 nikolaj 2015/02/02 19:04 nikolaj 2014/03/21 11:11 external edit2013/09/05 19:27 nikolaj 2013/09/05 00:02 nikolaj 2013/08/07 14:37 nikolaj 2013/08/07 14:36 nikolaj 2013/08/07 14:34 nikolaj 2013/08/07 14:26 nikolaj 2013/08/06 21:45 nikolaj 2013/08/06 21:39 nikolaj 2013/08/06 21:36 nikolaj created 2015/04/12 17:48 nikolaj 2015/04/12 15:58 nikolaj 2015/04/12 15:56 nikolaj 2015/04/12 15:55 nikolaj 2015/02/02 19:04 nikolaj 2014/03/21 11:11 external edit2013/09/05 19:27 nikolaj 2013/09/05 00:02 nikolaj 2013/08/07 14:37 nikolaj 2013/08/07 14:36 nikolaj 2013/08/07 14:34 nikolaj 2013/08/07 14:26 nikolaj 2013/08/06 21:45 nikolaj 2013/08/06 21:39 nikolaj 2013/08/06 21:36 nikolaj created Line 1: Line 1: ===== 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) | ----- ----- Line 9: Line 9: 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.