# Field theory (mathematics)/Related Articles  Main Article Talk Related Articles  [?] Bibliography  [?] External Links  [?] Citable Version  [?] A list of Citizendium articles, and planned articles, about Field theory (mathematics).

## Parent topics

• Algebra [r]: A branch of mathematics concerning the study of structure, relation and quantity. [e]

## Subtopics

• Algebraic number field [r]: A field extension of the rational numbers of finite degree; a principal object of study in algebraic number theory. [e]
• Field automorphism [r]: An invertible function from a field onto itself which respects the field operations of addition and multiplication. [e]
• Field extension [r]: A field containing a given field as a subfield. [e]
• Finite field [r]: Field that contains only finitely many elements. [e]
• Galois theory [r]: Algebra concerned with the relation between solutions of a polynomial equation and the fields containing those solutions. [e]
• Genus field [r]: The maximal absolutely abelian unramified extension of a number field. [e]
• Monogenic field [r]: An algebraic number field for which the ring of integers is a polynomial ring. [e]
• Ordered field [r]: A field with a total order which is compatible with the algebraic operations. [e]
• Quadratic field [r]: A field which is an extension of its prime field of degree two. [e]

## Other related topics

• Division ring [r]: (or skew field), In algebra it is a ring in which every non-zero element is invertible. [e]
• Vector space [r]: A set of vectors that can be added together or scalar multiplied to form new vectors [e]