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quasigroup [2013/08/06 21:39]
nikolaj created
quasigroup [2014/03/21 11:11]
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-===== Quasigroup ===== 
-==== Definition ==== 
-| @#88DDEE: $X$ | 
  
-| @#55EE55: $ \langle X,* \rangle \in \text{Quasigroup}(X)$ | 
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-| @#88DDEE: $*\in \mathrm{magma}(X)$ | 
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-| @#DDDDDD: $a,b,x,y\in X$ | 
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-| @#55EE55: $ \forall a.\ \forall b.\ \exists x.\ a*x=b $ | 
-| @#55EE55: $ \forall a.\ \forall b.\ \exists y.\ y*a=b $ | 
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-Here we used infix notation for "​$*$"​. 
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-==== Ramifications ==== 
-=== Discussion === 
- 
-The binary operation is often called //​multiplication//​. 
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-The axioms $*\in \mathrm{binaryOp}(X)$ above means that a monoid is closed with respect to the multiplication. ​ 
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-One generally calls $X$ the quasigroup, i.e. the set where the operation "​$*$"​ is defined on. 
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-==== Reference ==== 
-Wikipedia: [[http://​en.wikipedia.org/​wiki/​Quasigroup|Quasigroup]] 
-==== Context ==== 
-=== Subset of === 
-[[Magma]] 
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