DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16

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The relative algebraic closure of $F$ in an extension $K$

Definition

For a field extension $K / F$ , the relative algebraic closure of $F$ in $K$ is

${acl}_{K} (F) : = {a \in K : a is algebraic over F} .$

By The elements of an extension algebraic over the base field form a subfield, this set is a subfield of $K$ containing $F$ .

Depends on

The elements of an extension algebraic over the base field form a subfield

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 20 results over 10 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources

A. W. Knapp, Basic Algebra, 2nd ed., Chapter IX, Section 1 (standard reference, not scraped)

The relative algebraic closure of FF in an extension KK