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Algebraic Closure


The field F^_ is called an algebraic closure of F if F^_ is algebraic over F and if every polynomial f(x) in F[x] splits completely over F^_, so that F^_ can be said to contain all the elements that are algebraic over F.

For example, the field of complex numbers C is the algebraic closure of the field of reals R.


See also

Algebraically Closed, Splitting Field

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References

Dummit, D. S. and Foote, R. M. Abstract Algebra, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 455, 1998.

Referenced on Wolfram|Alpha

Algebraic Closure

Cite this as:

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

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