Definition:Commutative and Unitary Ring

Definition
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.

Also known as
Other nomenclature includes:
 * Commutative and unital ring
 * Commutative ring with unity
 * Commutative ring with identity