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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