List of abstract algebra topics
This is a list of abstract algebra topics, by Wikipedia page. See also the list of group theory topics, glossary of group theory, glossary of ring theory, glossary of field theory, glossary of tensor theory; and the list of linear algebra topics.| Table of contents |
|
2 Group theory 3 Ring theory 4 Field theory 5 Module theory 6 Non-associative systems 7 Generalities 8 Computer algebra |
Basic language
- Binary operation
- Commutative operation
- Identity element
- Additive inverse, multiplicative inverse
- Associativity
- Distributivity
- Semigroup, monoid
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
- Product of rings
- Idempotent
- Nilpotent
- Zero divisor
- Integral domain
- Euclidean domain
- Principal ideal domain
- Field (mathematics)
- Field of quotients
- Commutative algebra
- Polynomial, monomial
- Center (algebra)
- Integral closure
- Dedekind domain
- Unique factorization domain
- Formal power series
- Characteristic
- Boolean algebra, Boolean ring
- Division ring, division algebra
- Local ring
- Valuation (mathematics)
- Monoid ring
- Group ring
- Dual number
- Derivation
- Artinian
- Noetherian
- Banach algebra
- Associative algebra
- Hypercomplex number
- Rig (algebra)
Field theory
- Subfield (mathematics)
- Field extension
- Algebraic number field
- Global field
- Local field
- Finite field
- Algebraic extension
- Symmetric function
- Splitting field
- Separable polynomial
- Separable extension
- Primitive element (field theory)
- Algebraic closure
- Algebraically closed field
- Transcendence degree
- Galois theory
- Tensor product of fields
Module theory
- Free module
- Projective module
- Finitely-generated module
- Direct sum
- Simple module
- Annihilator
- Representation theory
- Quiver (mathematics)
- Homological algebra
Non-associative systems
- Lie algebra
- Magma (algebra)
- Loop (algebra)
- Quasigroup
- Alternative algebra
- Power associativity
- Cayley-Dickson construction
Generalities
Computer algebra
