Definition:Unity (Abstract Algebra)/Field

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This page is about Unity of Field. For other uses, see Unity.


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

The identity of the multiplicative group $\struct {F, \times}$ is referred to as the unity of the field $\struct {F, +, \times}$.

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

Also known as

The term unit is often used for unity.

It is preferred that this is not used on $\mathsf{Pr} \infty \mathsf{fWiki}$ as it can be confused with a unit of a ring, which is a different thing altogether.

Also see