Abstract algebra/Related Articles
From Citizendium, the Citizens' Compendium
- See also changes related to Abstract algebra, or pages that link to Abstract algebra or to this page or whose text .
- Algebra : A branch of mathematics concerning the study of structure, relation and quantity.
Disciplines within abstract algebra
- Category theory : 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.
- Commutative algebra : Branch of mathematics studying commutative rings and related structures.
- Field theory : A subdiscipline of abstract algebra that studies fields, which are mathematical constructs that generalize on the familiar concepts of real number arithmetic.
- Galois theory : Algebra concerned with the relation between solutions of a polynomial equation and the fields containing those solutions.
- Group theory : Branch of mathematics concerned with groups and the description of their properties.
- Linear algebra : Branch of mathematics that deals with the theory of systems of linear equations, matrices, vector spaces, determinants, and linear transformations.
- Ring theory : The mathematical theory of algebraic structures with binary operations of addition and multiplication.
- Universal algebra : Add brief definition or description
- Field : An algebraic structure with operations generalising the familiar concepts of real number arithmetic.
- Group : 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.
- Lattice (order) : An ordered set in which any two element set has a supremum and an infimum.
- Module : Mathematical structure of which abelian groups and vector spaces are particular types.
- Monoid : An algebraic structure with an associative binary operation and an identity element.
- Ring : Algebraic structure with two operations, combining an abelian group with a monoid.
- Scheme : Topological space together with commutative rings for all its open sets, which arises from 'glueing together' spectra (spaces of prime ideals) of commutative rings.
- Semigroup : An algebraic structure with an associative binary operation.
- Vector space : A set of vectors that can be added together or scalar multiplied to form new vectors
- Algebraic geometry : Discipline of mathematics that studies the geometric properties of the objects defined by algebraic equations.
- Algebraic topology : Add brief definition or description
- Combinatorics : Branch of mathematics concerning itself, at the elementary level, with counting things.
- Number theory : The study of integers and relations between them.