Fields

A setFFwith two binary operations +,:F×FF+,\cdot:F\times F\to Fis a field if the following holds:

  • R,+R,+is a commutative group with identity 00

  • R{0},R-\{0\},\cdotis a commutative group with identity11.

  • Distributivity: a(b+c)=ab+ac,(a+b)c=ac+bca(b+c)=ab+ac,(a+b)c=ac+bc

// field extensions, algebraic elements