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Algebraic Closure -- from Wolfram MathWorld

TOPICS Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld Algebraic Closure

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

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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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