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Ring (mathematics), Algebraic structure, Binary operation, Closure (mathematics), Associativity, Identity element, Inverse element, Commutativity, Commutative ring, Ideal (ring theory), Quotient ring, Localization of a ring, Prime ideal, Spectrum of a ring, Ring homomorphism, Module (mathematics), Noetherian ring, Krull dimension, Division ring, Graded algebra, Ring theory, Elementary group theory, Binomial theorem, Unit (ring theory), Subring, Product of rings, Boolean ring, Endomorphism ring, Tensor product of algebras, Number system, Set-theoretic definition of natural numbers, Rational number, Polynomial ring, Topological ring, Topological group, Integral domain, Field (mathematics)