Function field
The
function field of an irreducible algebraic variety
is the
field (mathematics) of
fractions of the
ring (mathematics) of regular functions. The ring of regular functions is an
integral domain if and only if the variety is irreducible, and in this case the field of fractions is
defined. It is a field extension of the ground field over which the
variety is defined. The transcendence degree is called the dimension
of the variety.
