| context | M … set |
| definiendum | ⟨⟨M,∗⟩⟩∈ it |
| inclusion | ∗ … binary operation |
| exists | e |
| postulate | e … unit element ⟨⟨M,∗⟩⟩ |
| postulate | (a∗b)∗c=a∗(b∗c) |
The binary operation is often called multiplication and e is called the identity, identity element or unit.
One generally calls M the monoid, i.e. the set where the operation “∗” is defined on, not the pair. For example, not that “A monoid is non-empty”.
Like above, one often uses infix notion for ∗.
Wikipedia: Monoid