Introduction to Fields
Definition of a Field
Examples
Example 1: are fields (infinite fields).
Example 2: is a field for prime (finite fields).
Example 3: is a field.
Properties
Characteristic of a Field
Field Extensions
We say is an extension field of .
Algebraic Elements
Minimal Polynomial
Degree of Extension
Tower Law
Algebraic Extensions
An extension is algebraic if every element of is algebraic over .
Examples of Extensions
Example 1: has degree with basis .
Example 2: has degree with basis .
Example 3: has degree with basis .