# Definition:Unity (Abstract Algebra)/Field

< Definition:Unity (Abstract Algebra)(Redirected from Definition:Unity of Field)

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

## Contents

## Definition

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

## Sources

- 1944: Emil Artin and Arthur N. Milgram:
*Galois Theory*(2nd ed.) (translated by Arthur N. Milgram) ... (previous) ... (next): $\text I$. Linear Algebra: $\text A$. Fields - 1955: John L. Kelley:
*General Topology*... (previous) ... (next): Chapter $0$: Algebraic Concepts