# Field theory (mathematics)/Related Articles  Main Article Discussion Related Articles  [?] Bibliography  [?] External Links  [?] Citable Version  [?] A list of Citizendium articles, and planned articles, about Field theory (mathematics).
See also changes related to Field theory (mathematics), or pages that link to Field theory (mathematics) or to this page or whose text contains "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]