Online Encyclopedia
List of abstract algebra topics
This is a list of abstract algebra topics, by Wikipedia page. See also:
- list of commutative algebra topics
- list of group theory topics
- list of linear algebra topics.
- glossary of field theory
- glossary of group theory
- glossary of ring theory
- glossary of tensor theory.
Contents |
Basic language
- Unary operator
- Binary operation
- Closure (mathematics)
- Arity
- Commutative operation
- Identity element
- Additive inverse, multiplicative inverse, inverse element
- Cancellation property
- Magma object
- Associativity
- Distributivity
- Semigroup
- monoid
- Coimage
Group theory
- Group (mathematics)
- Finite group
- Coset
- Lagrange's theorem
- Abelian group
- Cyclic group
- Klein four-group
- Elementary group theory
- Normal subgroup
- Characteristic subgroup
- Derived group
- Centralizer and normalizer
- Automorphism group
- Sylow theorem
- Group action
- Free group
- Presentation of a group
- Free product
- Word problem for groups
- Burnside's problem
Ring theory
- Ring (mathematics)
- Subring
- Ring homomorphism
- Ring ideal
- Simple ring
- Product of rings
- Unit (ring theory)
- Idempotent
- Nilpotent, reduced (ring theory)
- Zero divisor
- Integral domain
- Euclidean domain
- Principal ideal domain
- Domain (ring theory)
- Prime ring
- Primitive ring
- Primitive ideal
- Semiprimitive ring
- Matrix ring
- Jacobson density theorem
- Field (mathematics)
- Field of quotients
- Commutative algebra
- Polynomial, monomial
- Polynomial ring, symmetric algebra
- Center (algebra)
- Integral closure
- Dedekind domain
- Unique factorization domain
- Formal power series
- Characteristic
- Boolean algebra, Boolean ring, Boolean homomorphism
- Division ring, division algebra
- Quaternions
- Local ring
- Valuation (mathematics)
- Algebra (ring theory)
- Cohen-Macaulay ring
- Gorenstein ring
- Monoid ring
- Group ring
- Group algebra
- Dual number
- Derivation
- Artinian ring
- Noetherian ring
- Banach algebra
- Associative algebra
- Hypercomplex number
- Rig (algebra)
Field theory
- Subfield (mathematics)
- Field extension
- Algebraic number field
- Global field
- Local field
- Finite field
- Algebraic element
- Algebraic extension
- Symmetric function
- Splitting field
- Separable polynomial
- Separable extension
- Primitive element (field theory)
- Algebraic closure
- Algebraically closed field
- Transcendence degree
- Normal extension
- Galois extension
- Galois theory
- Field norm
- Field trace
- Tensor product of fields
- Inverse Galois problem
Module theory
- Free module
- Finitely-generated module
- Finitely-presented module
- Projective module
- Injective module
- Flat module
- Direct sum
- Simple module
- Indecomposable module
- Algebraically compact module
- Annihilator
- Regular sequence (algebra), depth (algebra)
- Localization of a module
- Fractional ideal
- Length of a module
- Fitting lemma
- Artinian module
- Representation theory
- Quiver (mathematics)
Homological algebra
- Cokernel
- Exact sequence
- Chain complex
- Five lemma
- Short five lemma
- Snake lemma
- Nine lemma
- Extension (algebra)
- Koszul complex
- Exact functor
- Derived functor
- Ext functor
- Tor functor
- Spectral sequence
- Whitehead problem
- Homological conjectures in commutative algebra
Non-associative systems
- Lie algebra (see also list of Lie group topics)
- Magma (algebra)
- Loop (algebra)
- Quasigroup
- Alternative algebra
- Power associativity
- Cayley-Dickson construction
Generalities
Computer algebra
See Computer_algebra_system#List_of_Computer_algebra_systems for a list.
- Symbolic mathematics
- Axiom computer algebra system, Axiom (algebra software)
- GAP computer algebra system
- Gimac computer algebra system
- Macaulay computer algebra system
- Magma computer algebra system
- Maple computer algebra system
- Mathematica
- Maxima computer algebra system
- PARI-GP computer algebra system
- Reduce computer algebra system
- SINGULAR computer algebra system
- Yacas
Last updated: 01-22-2005 01:20:16