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Kummer's theoremFactor ringPrincipal ideal ringQuotient ringTotal ring of fractionsProduct ringRing of fractionsDivision ringPolynomial ringSimple ringPrime ringValuation ringPolynomial algebraUnique factorization ringRingCommutative ringSubringReduced ringAlgebraic numberCoringRegular elementLocalizationLocal ringPrimitive polynomialIntegral elementSuperringDomainPseudoringNoetherian ringIntegral domainK-algebraGroup ringPrimary idealIdealizerOrdered ringPell numberDedekind domainMatrix algebraConjugateReduced algebraRingoidSemiringMultiple rootSkew fieldFactor idealRadical idealComposite numberRadicalRing theoryCircle groupZero divisorIdeal numberHyperalgebraDivision algebraAlgebraic integerRight idealRoot of unitySimple rootIdealSchur functionFiberingOverorderOverringPrincipal rootCentral simple algebraCyclotomic fieldFrobenius endomorphismSupernumberPseudoradicalCullen primeCharacteristicNear-ringComplexBoolean ringJacobi symbolPlurigenusPrime idealFractional idealCunningham chainRing theoristRational functionFree modulePolynomial basisModulePrimitive rootHurwitz algebraResidue fieldHerbrand-ribet theoremContentCommutative algebraPrimeRational root theoremNumber fieldPrimitive elementDedekind ringSeparable polynomialUnique factorization domainQuadratic surdAdeleSturm's theorem