In the case of a group for example, the identity element is sometimes simply denoted by the symbol
The distinction between additive and multiplicative identity is used most often for sets that support both binary operations, such as rings, integral domains, and fields.
[10][11][12] This should not be confused with a unit in ring theory, which is any element having a multiplicative inverse.
[3] Another common example is the cross product of vectors, where the absence of an identity element is related to the fact that the direction of any nonzero cross product is always orthogonal to any element multiplied.
Yet another example of structure without identity element involves the additive semigroup of positive natural numbers.