A binary operation on a nonempty set X is a mapping of the Cartesian product of X with itself into X, say, ⋆: X×X → X. It is usual to write x ⋆ y instead of ⋆(x, y) to indicate the value in X of the mapping ⋆ at the point (x, y) in X×X. In this context it is convenient to interpret the binary operation ⋆ multiplicatively, so that x ⋆ y is interpreted as the product of x and y, and it is written in a simplified form as x y.