Definition:Algebraic Closure/Also defined as
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Algebraic Closure: Also defined as
Some sources define an algebraic closure of a field $K$ as the smallest algebraically closed algebraic field extension of $K$.
From Algebraic Closure of Field is Unique, it is clear that defining it as the smallest such algebraic field extension is redundant.
Sources
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): algebraically closed (algebraic closure)