# algebraically closed field

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## algebraically closed field

[¦al·jə¦brā·ik·lē ¦klōzd ′fēld] (mathematics)

A field

*F*such that every polynomial of degree equal to or greater than 1 with coefficients in*F*has a root in*F*.A field

*F*is said to be algebraically closed in an extension field*K*if any root in*K*of a polynominal with coefficients in*F*also lies in*F*. Also known as algebraically complete field.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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