| context | ⟨X,+,∗⟩∈ring(X) |
| definiendum | ⟨X,+,∗⟩∈it |
| postulate | ⟨X,∗⟩∈monoid(X) |
The second requirement implies that there is an identiy for the binary operation ∗.
One generally (also) calls X the unital ring, i.e. the set where the operations “+” and “∗” are defined on.
Wikipedia: Ring