Abstract algebra > Related Articles
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Contents |
Parent topics
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]
Other related topics
- Algebraic geometry [r]: Discipline of mathematics that studies the geometric properties of the objects defined by algebraic equations. [e]
- Algebraic topology [r]: Add brief definition or description
- Combinatorics [r]: Branch of mathematics concerning itself, at the elementary level, with counting things. [e]
- Number theory [r]: The study of integers and relations between them. [e]
