979: Extended Field of Field

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definition of extended field of field

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Topics

About: field

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Note

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Starting Context

• The reader knows a definition of field.

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Target Context

• The reader will have a definition of extended field of field.

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Orientation

There is a list of definitions discussed so far in this site.

There is a list of propositions discussed so far in this site.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$F$: $\in \{\text{ the fields }\}$
$\ast F^{\prime }$: $\in \{\text{ the fields }\}$
//

Conditions:
$F\subseteq F^{\prime }$
//

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2: Note

There can be some multiple extended fields of $F$.

For example, for $F=\mathbb{Q}$, $\mathbb{R}$ and $\mathbb{C}$ are some extended fields of $\mathbb{Q}$ among possible others.

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References

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