# Abstract algebra/Related Articles

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A list of Citizendium articles, and planned articles, about Abstract algebra.
See also changes related to Abstract algebra, or pages that link to Abstract algebra or to this page or whose text contains "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]