Under multiplication, a ring is a monoid; this means that multiplication is associative and has an identity called the multiplicative identity and denoted . An invertible element for multiplication is called a unit. The inverse or multiplicative inverse (for avoiding confusion with additive inverses) of a unit is denoted or, when the multiplication is commutative,
Under multiplication a ring is a monoid; this means that multiplication is associative and has an identity called the multiplicative identity and denoted  An invertible element for multiplication is called a unit The inverse or multiplicative inverse (for avoiding confusion with additive inverses) of a unit is denoted or when the multiplication is commutative