In
abstract algebra,
field extensions are the main object of study in
field theory. The general idea is to start with a base
field and construct in some manner a larger field that contains the base field and satisfies additional properties. For instance, the set
Q(√2) = {
a +
b√2 |
a,
b ∈
Q} is the smallest extension of
Q that includes every real solution to the equation
x2 = 2.