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
Famous quotes containing the words ring and/or theory:
“I like well the ring of your last maxim, “It is only the fear of death makes us reason of impossibilities.” And but for fear, death itself is an impossibility.”
—Henry David Thoreau (1817–1862)
“Psychotherapy—The theory that the patient will probably get well anyway, and is certainly a damned ijjit.”
—H.L. (Henry Lewis)