Last updated 3 years ago
A setFFFwith two binary operations +,⋅:F×F→F+,\cdot:F\times F\to F+,⋅:F×F→Fis a field if the following holds:
R,+R,+R,+is a commutative group with identity 000
R−{0},⋅R-\{0\},\cdotR−{0},⋅is a commutative group with identity111.
Distributivity: a(b+c)=ab+ac,(a+b)c=ac+bca(b+c)=ab+ac,(a+b)c=ac+bca(b+c)=ab+ac,(a+b)c=ac+bc
// field extensions, algebraic elements
