# 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