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Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and real or complex numbers, often now called elementary algebra. The distinction is rarely made in more recent writings.

Attributes	Values
rdf:type	place
rdfs:label	List of abstract algebra topics (en)
rdfs:comment	Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and real or complex numbers, often now called elementary algebra. The distinction is rarely made in more recent writings. (en)
sameAs	Cubic function
dbp:wikiPageUsesTemplate	dbt:Main dbt:Short_description dbt:Wiktionary dbt:Algebra
Subject	Abstract algebra Outlines of mathematics and logic Wikipedia outlines Mathematics-related lists
gold:hypernym	Area
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/List_of_abstract_algebra_topics?oldid=1057037113&ns=0
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Wikipage revision ID	1057037113 (xsd:integer)
Link from a Wikipage to another Wikipage	Flexible algebra Formal power series Formally real field Green's relations Group (mathematics) Local analysis Local field Local ring Localization (commutative algebra) Locally cyclic group Magma (algebra) Noetherian module Noetherian ring Non-associative algebra Noncommutative ring Normal closure (group theory) Normal extension Normal subgroup Product of rings Projective cover Projective module Projective representation Prüfer domain Skolem–Noether theorem Unary operation Unique factorization domain Unit (ring theory) Wreath product Abelian extension Abelian group Abel–Ruffini theorem Abstract algebra Additive inverse Affine representation Algebra homomorphism Algebra over a field Algebra representation Algebraic closure Algebraic element Algebraic extension Algebraic geometry Algebraic number field Algebraic structure Algebraically closed field Algebraically compact module Alternating group Alternative algebra Annihilator (ring theory) Aperiodic semigroup Arity Artinian module Artinian ring Artin–Rees lemma Associative property Associator Auto magma object Automorphism group Baer ring Banach algebra Bialgebra Bimodule Binary operation Monoid Monoid (category theory) Monoid factorisation Monoid ring Monoidal category Monomorphism Morita equivalence Radical of a module Radical of an ideal Semi-local ring Semidirect product Semigroup Semiprime ring Semiprimitive ring Semiring Semisimple algebra Semisimple module Separable extension Separable polynomial Universal algebra Universal enveloping algebra

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