# Abstract algebra/Related Articles  Main Article Discussion Related Articles  [?] Bibliography  [?] External Links  [?] Citable Version  [?] A list of Citizendium articles, and planned articles, about Abstract algebra.

## Parent topics

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

## Subtopics

### Disciplines within abstract algebra

• Category theory [r]: Loosely speaking, a class of objects and a collection of morphisms which act upon them; the morphisms can be composed, the composition is associative and there are identity objects and rules of identity. [e]
• Commutative algebra [r]: Branch of mathematics studying commutative rings and related structures. [e]
• Field theory [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]
• Group theory [r]: Branch of mathematics concerned with groups and the description of their properties. [e]
• Linear algebra [r]: Branch of mathematics that deals with the theory of systems of linear equations, matrices, vector spaces, determinants, and linear transformations. [e]
• Ring theory [r]: The mathematical theory of algebraic structures with binary operations of addition and multiplication. [e]
• Universal algebra [r]: Add brief definition or description

### Algebraic structures

• Field [r]: An algebraic structure with operations generalising the familiar concepts of real number arithmetic. [e]
• Group [r]: Set with a binary associative operation such that the operation admits an identity element and each element of the set has an inverse element for the operation. [e]
• Lattice (order) [r]: An ordered set in which any two element set has a supremum and an infimum. [e]
• Module [r]: Mathematical structure of which abelian groups and vector spaces are particular types. [e]
• Monoid [r]: An algebraic structure with an associative binary operation and an identity element. [e]
• Ring [r]: Algebraic structure with two operations, combining an abelian group with a monoid. [e]
• Scheme [r]: Topological space together with commutative rings for all its open sets, which arises from 'glueing together' spectra (spaces of prime ideals) of commutative rings. [e]
• Semigroup [r]: An algebraic structure with an associative binary operation. [e]
• Vector space [r]: A set of vectors that can be added together or scalar multiplied to form new vectors [e]