Field extension/Related Articles

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A list of Citizendium articles, and planned articles, about 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]