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Reduced algebraSimple ringZero divisorDivision ringPrime ringFactor ringMinimal idealQuotient ringOrdered ringPrincipal ideal ringNoetherian ringCommutative ringUnique factorization ringPrimary idealDomainProduct ringRegular elementRingPolynomial ringIntegral domainPrimitive polynomialLocal ringRadicalFactor idealBoolean ringRadical idealTotal ring of fractionsCharacteristicRing of fractionsRight idealPolynomial algebraSimple algebraValuation ringCentral simple algebraIdealSubringSemiringFree moduleNilradicalRingoidRing theoryModuleGroup ringNear-ringSkew fieldRing isomorphismCommutatorPrincipal idealField of fractionsK-algebraMaximal idealNullstellensatzPolynomial basisDivision algebraPseudoringLeft idealVanishing idealIdeal numberDirect productSocleResidue fieldNilpotentRing homomorphismOverorderFractional idealRing sum normal formCenterMatrix algebraLocalizationPrime idealDedekind domainRing theoristPseudoradicalKummer ringNon-associative algebraAlgebra over a ringCommutative algebraNearringZeroR-moduleSimple rootTwo-sided idealIntegral elementMinimal polynomialNormal extensionAlgebraic number fieldReductivityUnique factorization domainComposition algebraField of quotientsMultiplicative subsetReductionAlgebraPerfect fieldK-theorySplitting fieldAdeleSuperringCycleNoetherian domain