Category:Ring theory

• Glossary of ring theory

*

• Quasiregular element
• Ring theory

0

• Zero object (algebra)

A

• Additive identity
• Algebra (ring theory)
• Algebra homomorphism
• Annihilator (ring theory)
• Arithmetical ring
• Artin algebra
• Artinian ideal
• Artinian ring
• Artin–Rees lemma
• Artin–Wedderburn theorem
• Artin–Zorn theorem
• Ascending chain condition on principal ideals
• Azumaya algebra

B

• Baer ring
• Balanced module
• Bézout domain
• Binomial ring
• Biquaternion
• Boolean ring
• Brauer group
• Brauer–Cartan–Hua theorem

C

• C-semiring
• Category of rings
• Central simple algebra
• Centralizer and normalizer
• Characteristic (algebra)
• Classification of Clifford algebras
• Clifford algebra
• Coherent ring
• Commutative ring
• Composition algebra
• Composition ring
• Connected ring

D

• Dedekind–Hasse norm
• Dense submodule
• Depth of noncommutative subrings
• Divisibility (ring theory)
• Division algebra
• Division ring
• Domain (ring theory)
• Double centralizer theorem

E

• Endomorphism ring
• Euclidean domain

F

• Finite ring
• Flat map
• Formal power series
• Free algebra
• Free ideal ring

G

• GCD domain
• Generalized Clifford algebra
• Geometric algebra
• Global dimension
• Goldie's theorem
• Goldman domain
• Graded algebra

G cont.

• Group algebra
• Group ring

H

• Height (ring theory)
• Hereditary ring
• Hermite ring
• Hochschild homology
• Hopfian object
• Hopkins–Levitzki theorem

I

• Idealizer
• Integer
• Integral domain
• Invariant basis number
• Inversive ring geometry
• Irreducible element
• Irreducible ideal
• Irreducible ring

J

• Jacobson density theorem
• Jacobson radical
• Jacobson ring
• Jaffard ring
• User:Jheald/sandbox/Geometric algebra

K

• Kaplansky's conjecture
• Kasch ring
• Köthe conjecture
• Krull ring
• Kummer ring
• Kurosh problem

L

• Laurent polynomial
• Levitzky's theorem
• Local ring
• Localization of a ring
• Loewy ring

M

• Matrix ring
• Maximal ideal
• Minimal ideal
• Monoid ring
• Morita equivalence

N

• Nakayama algebra
• Nakayama's conjecture
• Necklace ring
• Nilpotent
• Noetherian ring
• Noncommutative ring
• Noncommutative unique factorization domain
• Numerical polynomial

O

• Opposite ring
• Order (ring theory)
• Ore condition
• Ore extension
• Overring

P

• Partially ordered ring
• Perfect field
• Perfect ring
• Poisson ring
• Polynomial identity ring
• Polynomial ring
• Prime element
• Prime ring
• Primitive ring

P cont.

• Principal ideal domain
• Principal ideal ring
• Product of rings

Q

• Quadratic integer
• Quasi-Frobenius ring
• Quotient ring

R

• Radical of a ring
• Rank ring
• Real closed ring
• Reduced ring
• Regev's theorem
• Regular ideal
• Regular local ring
• Regular ring
• Ring (mathematics)
• Ring extension
• Ring homomorphism
• Ring of integers
• Pseudo-ring

S

• Schreier domain
• Semi-local ring
• Semiperfect ring
• Semiprime ring
• Semiprimitive ring
• Semiring
• Semisimple module
• Serial module
• Severi–Brauer variety
• Simple algebra
• Simple ring
• Singular submodule
• Skolem–Noether theorem
• Square-free
• Stably finite ring
• Subring
• Subring test
• Sylvester domain
• Symmetric algebra

T

• Tensor product of algebras
• Quasisymmetric function
• Topological ring
• Total quotient ring
• Triangular matrix ring

U

• Uniform module
• Unipotent
• Unique factorization domain
• Unit (ring theory)
• Unit ring
• Universal enveloping algebra

V

• Valuation ring
• Von Neumann regular ring

W

• Wedderburn's little theorem
• Weyl algebra
• Witt vector

Z

• Zero divisor
• Zero ring
• Zero-product property
• Zorn ring

Λ

• Λ-ring