This is a glossary of some terms of the subject.
(See field theory (physics) for the unrelated field theories in physics.)
A field is a commutative ring (F, +, *) in which 0 ≠ 1 and every nonzero element has a multiplicative inverse.
In a field we thus can perform the operations addition, subtraction, multiplication, and division.
The non-zero elements of a field F form an abelian group under multiplication; this group is typically denoted by F×; The ring of polynomials in the variable x with coefficients in F is denoted by F[x].