Algebraically closed field

This article defines a field property: a property that can be evaluated to true/false for any field.
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Definition

Symbol-free definition

A field is termed algebraically closed if it satisfies the following conditions:

• Every nonconstant polynomial with coefficients in the field has a root in the field.
• Every monic polynomial with coefficients in the field can be expressed as a product of linear polynomials with coefficients in the field.