# Fields

A set$$F$$with two binary operations $$+,\cdot:F\times F\to F$$is a **field** if the following holds:

* $$R,+$$is a commutative group with identity $$0$$
* $$R-{0},\cdot$$is a commutative group with identity$$1$$.
* Distributivity: $$a(b+c)=ab+ac,(a+b)c=ac+bc$$

// field extensions, algebraic elements