Quasigroup
Set
| context | X |
| postulate | ⟨X,∗⟩∈Quasigroup(X) |
| context | ⟨X,∗⟩∈Magma(X) |
| range | a,b,x,y∈X |
| postulate | ∀a. ∀b. ∃x. a∗x=b |
| postulate | ∀a. ∀b. ∃y. y∗a=b |
Here we used infix notation for “∗”.
Ramifications
Discussion
The binary operation is often called multiplication.
The axioms ∗∈binaryOp(X) above means that a monoid is closed with respect to the multiplication.
One generally calls X the quasigroup, i.e. the set where the operation “∗” is defined on.
Reference
Wikipedia: Quasigroup
Parents
Subset of
