# Definition:Unity (Abstract Algebra)

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*This page is about Unity in the context of Abstract Algebra. For other uses, see Unity.*

## Definition

### Unity of Ring

Let $\struct {R, +, \circ}$ be a ring.

If the semigroup $\struct {R, \circ}$ has an identity, this identity is referred to as **the unity of the ring $\struct {R, +, \circ}$**.

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).

### Unity of Field

Let $\struct {F, +, \times}$ be a field.

The identity element of the multiplicative group $\struct {F^*, \times}$ of $F$ is called the **multiplicative identity** of $F$.

It is often denoted $e_F$ or $1_F$, or, if there is no danger of ambiguity, $e$ or $1$.