algebraically closed
The term "algebraically closed" is crucial in understanding the structure and properties of fields in algebra and field theory.
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Definition
C2Field Theory
(technical, academic)A field where every non-constant polynomial with coefficients from the field has at least one root within the field.
Example
- The field of complex numbers is algebraically closed because every polynomial with complex coefficients has a root in the complex numbers.
- In algebra, proving that a field is algebraically closed can simplify solving polynomial equations.
Similar
Terms that have similar or relatively close meanings to "algebraically closed":
algebraic structureuniversal algebracommutative algebraalgebraic analysisassociative algebra