# Definition:Algebraic Closure

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## Definition

Let $K$ be a field.

An **algebraic closure** of $K$ is an algebraically closed algebraic field extension of $K$.

An **algebraic closure** of $K$ can be denoted $\overline K$.

## Also see

from which every field has exactly one **algebraic closure**, up to isomorphism. Consequently we may refer to ** the algebraic closure** of $K$.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**algebraic closure** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**algebraic closure**

- Weisstein, Eric W. "Algebraic Closure." From
*MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/AlgebraicClosure.html