field
commutative ring in which every nonzero element is inversible
local field
non-discrete locally compact topological field
complete field
algebraic structure that is complete relative to a metric
finite field
field that contains a finite number of elements
algebraic number field
a finite degree (and hence algebraic) field extension of the field of rational numbers
splitting field
minimal field in which every polynomial in a given set decomposes into linear factors
perfect field
a field that is either of characteristic 0, or of positive characteristic p such that every element admits a p-th root
subfield
mathematical concept
real closed field
Non algebraically closed field whose extension by sqrt(–1) is algebraically closed
residue field
field arising from a quotient ring by a maximal ideal
valued field
mathematical concept
function field of an algebraic variety
the field of ratios of polynomial functions on a variety
topological field
field endowed with a topology which makes the field operations continuous
formally real field
field that can be equipped with an ordering
field extension
pair of a mathematical field and its subfield
Hardy field
field consisting of germs of real-valued functions at infinity that are closed under differentiation
Pythagorean field
field in which every sum of two squares is a square
set of real numbers
set whose elements are the real numbers
field of rational numbers
smallest field of characteristic zero