Definition:Adjoined Number

Definition

Let $F$ be a field.

Let $E / F$ be a field extension of $F$.

An adjoined number to $F$ is an element of $E / F$ which is not in $F$.

That is, it has been adjoined to $F$.

Examples

Adjoining $\sqrt 2$ to $\Q$

Consider the example of a field extension:

Real Numbers of Type $a + b \sqrt 2: a, b \in \Q$

where $\Q \sqbrk {\sqrt 2}$ forms a finite field extension over the rational numbers $\Q$ of degree $2$.

The element $\sqrt 2$ is an example of an adjoined number on $\Q$.

Also see

• Results about adjoined numbers can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): adjoined number
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): adjoined number