Ring Theory
- General
- Ring (mathematics)
- Commutative algebra, Commutative ring
- Ring theory, Noncommutative ring
- Algebra over a field
- Non-associative algebra
- Relatives to rings: Semiring, Nearring, Rig (algebra)
- Structure
- Subring, Subalgebra
- Center (algebra)
- Ring ideal
- Principal ideal
- Ideal quotient
- Maximal ideal, minimal ideal
- Primitive ideal, prime ideal, semiprime ideal
- Radical of an ideal
- Jacobson radical
- Socle of a ring
- unit (ring theory), Idempotent, Nilpotent, Zero divisor
- Characteristic (algebra)
- Ring homomorphism, Algebra homomorphism
- Ring epimorphism
- Ring monomorphism
- Ring isomorphism
- Skolem–Noether theorem
- Graded algebra
- Morita equivalence
- Brauer group
- Constructions
- Direct sum of rings, Product of rings
- Quotient ring
- Matrix ring
- Endomorphism ring
- Polynomial ring
- Formal power series
- Monoid ring, Group ring, Group algebra
- Localization of a ring
- Tensor algebra
- Symmetric algebra, Exterior algebra, Clifford algebra
- Free algebra
- Completion (ring theory)
- Types
- Field (mathematics), Division ring, division algebra
- Simple ring, Central simple algebra, Semisimple ring, Semisimple algebra
- Primitive ring, Semiprimitive ring
- Prime ring, Semiprime ring, Reduced ring
- Integral domain, Domain (ring theory)
- Field of fractions, Integral closure
- Euclidean domain, Principal ideal domain, Unique factorization domain, Dedekind domain, Prüfer domain
- Von Neumann regular ring
- Quasi-Frobenius ring
- Hereditary ring, Semihereditary ring
- Local ring, Semi-local ring
- Discrete valuation ring
- Regular local ring
- Cohen–Macaulay ring
- Gorenstein ring
- Artinian ring, Noetherian ring
- Perfect ring, semiperfect ring
- Baer ring, Rickart ring
- Lie ring, Lie algebra
- Ideal (Lie algebra)
- Jordan algebra
- Differential algebra
- Banach algebra
- Examples
- Rational number, Real number, Complex number, Quaternions, Octonions
- Hurwitz quaternion
- Gaussian integer
- Theorems and applications
- Algebraic geometry
- Hilbert's Nullstellensatz
- Hilbert's basis theorem
- Hopkins–Levitzki theorem
- Krull's principal ideal theorem
- Levitzky's theorem
- Galois theory
- Abel–Ruffini theorem
- Artin-Wedderburn theorem
- Jacobson density theorem
- Wedderburn's little theorem
- Lasker–Noether theorem
Read more about this topic: List Of Abstract Algebra Topics
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