In
mathematics, a
field is one of the fundamental
algebraic structures used in
abstract algebra. It is a
nonzero commutative division ring, or equivalently a
ring whose nonzero elements form an
abelian group under multiplication. As such it is an
algebraic structure with notions of
addition,
subtraction,
multiplication, and
division satisfying the appropriate abelian group equations and
distributive law. The most commonly used fields are the field of
real numbers, the field of
complex numbers, and the field of
rational numbers, but there are also
finite fields,
algebraic function fields,
algebraic number fields,
p-adic fields, and so forth.