\begin{definition}[Definition:Commutative and Unitary Ring]
A '''commutative and unitary ring''' $\struct {R, +, \circ}$ is a ring with unity which is also commutative.
That is, it is a ring such that the ring product $\struct {R, \circ}$ is commutative and has an identity element.
That is, such that the multiplicative semigroup $\struct {R, \circ}$ is a commutative monoid.
The identity element is usually denoted by $1_R$ or $1$ and called a unity.
\end{definition}