Science Fair Project 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 homological algebra 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
Semigroups and monoids
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)
- Order (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)
- Semi-local ring
- Algebra (ring theory)
- Cohen-Macaulay ring
- Gorenstein ring
- Monoid ring
- Group ring
- Group algebra
- Dual number
- Derivation (abstract algebra)
- Artinian ring
- Noetherian ring
- Von Neumann regular ring
- Banach algebra
- Associative algebra
- Hypercomplex number
- Rig (algebra)
Field theory
- Subfield (mathematics)
- Field extension
- Multiplicative group
- 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
- Formally real field
- Real closed field
- 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
- Pure submodule
- Algebraically compact module
- Bimodule
- Annihilator
- Regular sequence (algebra), depth (algebra)
- Localization of a module
- Fractional ideal
- Length of a module
- Fitting lemma
- Artinian module
Representation theory
- Representation of an algebra
- Group representation
- Maschke's theorem
- Schur's lemma
- Intertwining map
- Affine representation
- Projective representation
- Modular representation theory
- Quiver (mathematics)
- Representation of a Hopf algebra
- Algebra representation of a Hopf algebra
- Algebra representation of a Lie algebra
- Algebra representation of a Lie superalgebra
Non-associative systems
- Nonassociative ring
- Associator
- Lie algebra (see also list of Lie group topics)
- Jordan algebra
- Magma (algebra)
- Loop (algebra)
- Quasigroup
- Alternative algebra
- Power associativity
- Cayley-Dickson construction
Generalities
- Algebraic structure
- Universal algebra
- Kernel of a function
- Universal property
- Filtration (abstract algebra)
- Category theory
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
- Ginac 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
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details