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