# Field theory (mathematics)/Related Articles

From Citizendium, the Citizens' Compendium

*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]}

- 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]}