There also are
nullary operations.
n-ary operations for integers n > 2.
These are
distinguished elements. For instance, the null element and the unit
element in Z, Z/nZ, R[X] and
R[X]/(f) as well as the identity in
Sn.
These elements are special elements with respect to an operation. Most of the time such elements will have special names, like unit element.
For each natural number n one can define the notion
of an n-ary operation: a map Vn -> V.
+(3,5,7) = 3 + 5 + 7.
The + operator for example, can be viewed as a 3-ary operator in the following interpretation