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- Algebraic number field : A field extension of the rational numbers of finite degree; a principal object of study in algebraic number theory.
- Conductor of a number field : Used in algebraic number theory; a modulus which determines the splitting of prime ideals.
- Field automorphism : An invertible function from a field onto itself which respects the field operations of addition and multiplication.
- Field extension : A field containing a given field as a subfield.
- Field theory (mathematics) : A subdiscipline of abstract algebra that studies fields, which are mathematical constructs that generalize on the familiar concepts of real number arithmetic.
- Monogenic field : An algebraic number field for which the ring of integers is a polynomial ring.
- Ordered field : A field with a total order which is compatible with the algebraic operations.
- Quadratic equation : An equation of the form ax2 + bx + c = 0 where a, b and c are constants.
- Root of unity : An algebraic quantity some power of which is equal to one.