The field is called an algebraic closure of if is algebraic over and if every polynomial splits completely over , so that can be said to contain all the elements that are algebraic over .
For example, the field of complex numbers is the algebraic closure of the field of reals .
See alsoAlgebraically Closed,
Splitting Field Explore with Wolfram|AlphaMore things to try:
ReferencesDummit, D. S. and Foote, R. M. Abstract Algebra, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 455, 1998. Referenced on Wolfram|AlphaAlgebraic Closure Cite this as:Weisstein, Eric W. "Algebraic Closure." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AlgebraicClosure.html
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