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

â€‹$R,+$is a commutative group with identity $0$â€‹

â€‹$R-\{0\},\cdot$is a commutative group with identity$1$.

Distributivity: $a(b+c)=ab+ac,(a+b)c=ac+bc$â€‹

// field extensions, algebraic elements