Definition:Unity (Abstract Algebra)/Ring

Let $$\left({R, +, \circ}\right)$$ be a ring.

If the semigroup $$\left({R, \circ}\right)$$ has an identity, this identity is referred to as the unity of the ring $$\left({R, +, \circ}\right)$$.

It is (usually) denoted $$1_R$$, where the subscript denotes the particular ring to which $$1_R$$ belongs (or often $$1$$ if there is no danger of ambiguity).

The ring itself is then referred to as a ring with unity.