# Field extension/Related Articles

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- Algebraic number field [r]: A field extension of the rational numbers of finite degree; a principal object of study in algebraic number theory.
^{[e]} - Artin-Schreier polynomial [r]: A type of polynomial whose roots generate extensions of degree
*p*in characteristic*p*.^{[e]} - Complex number [r]: Numbers of the form
*a+bi*, where*a*and*b*are real numbers and*i*denotes a number satisfying .^{[e]} - Conductor of a number field [r]: Used in algebraic number theory; a modulus which determines the splitting of prime ideals.
^{[e]} - Cyclotomic field [r]: An algebraic number field generated over the rational numbers by roots of unity.
^{[e]} - Discriminant of an algebraic number field [r]: An invariant attached to an extension of algebraic number fields which describes the geometric structure of the ring of integers and encodes ramification data.
^{[e]} - Elliptic curve [r]: An algebraic curve of genus one with a group structure; a one-dimensional abelian variety.
^{[e]} - Field (mathematics) [r]: An algebraic structure with operations generalising the familiar concepts of real number arithmetic.
^{[e]} - Field automorphism [r]: An invertible function from a field onto itself which respects the field operations of addition and multiplication.
^{[e]} - Field theory (mathematics) [r]: A subdiscipline of abstract algebra that studies fields, which are mathematical constructs that generalize on the familiar concepts of real number arithmetic.
^{[e]} - Galois theory [r]: Algebra concerned with the relation between solutions of a polynomial equation and the fields containing those solutions.
^{[e]} - Matroid [r]: Structure that captures the essence of a notion of 'independence' that generalizes linear independence in vector spaces.
^{[e]} - Minimal polynomial [r]: The monic polynomial of least degree which a square matrix or endomorphism satisfies.
^{[e]} - Normal extension [r]: A field extension which contains all the roots of an irreducible polynomial if it contains one such root.
^{[e]} - Quadratic equation [r]: An equation of the form
*ax*^{2}+*bx*+*c*= 0 where*a*,*b*and*c*are constants.^{[e]} - Quadratic field [r]: A field which is an extension of its prime field of degree two.
^{[e]} - Splitting field [r]: A field extension generated by the roots of a polynomial.
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