# Field extension/Related Articles

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A list of Citizendium articles, and planned articles, about Field extension.
See also changes related to Field extension, or pages that link to Field extension or to this page or whose text contains "Field extension".

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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 ${\displaystyle i^{2}=-1}$. [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 ax2 + 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. [e]