Definition:Ring with Unity

Definition
A non-null ring $$\left({R, +, \circ}\right)$$ is a ring with unity iff the semigroup $$\left({R, \circ}\right)$$ has an identity.

It follows that such a $$\left({R, \circ}\right)$$ is a monoid.

A ring with unity is also referred to as a ring with a one, a ring with identity, or a unit ring.