Extensions of A Field
An extension of a field k is just a field K containing k as a subfield. One distinguishes between extensions having various qualities. For example, an extension K of a field k is called algebraic, if every element of K is a root of some polynomial with coefficients in k. Otherwise, the extension is called transcendental.
The aim of Galois theory is the study of algebraic extensions of a field.
Read more about this topic: Field Theory (mathematics)
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