Loop
Set
| context | X |
| postulate | ⟨X,∗⟩∈Loop(X) |
| context | ⟨X,∗⟩∈Quasigroup(X) |
| range | e,a∈X |
| postulate | ∃e. ∀a. (a∗e=e∗a=a) |
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 loop, i.e. the set where the operation “∗” is defined on.
Reference
Wikipedia: Quasigroup
Parents
Subset of
