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Noetherian ringAscending chain conditionSimple ringDivision ringFinite ringIntegral domainMatrix ringPrime elementRing of integersGraded ringNoncommutative ringSemiringCharacteristicRingMaximal idealRinged spacePrincipal ideal ringEuclidean domainUnique factorization domainTotal ring of fractionsRing theoryPrime ringDedekind domainIdealDiscrete valuation ringJacobson radicalFree algebraNullstellensatzNoetherian moduleLocal ringInvariant basis numberIrreducible representationAdele ringCommutative algebraIdempotentSimple algebraRegular sequenceZero divisorAlgebraic number fieldMonomial orderAnnihilatorPolynomial ringUnique factorization ringDifferential graded algebraPrincipal idealReduced ringArchimedean propertyAlgebraic independenceRing homomorphismFinite field arithmeticNilpotentTranscendental equationQuotient ringInner automorphismMaximal independent setDivergent seriesIdeal class groupConstructible universeChain complexIrreducible elementDiophantine equationRadical idealLatticeCommutative ringAlgebraic structureDedekind cutAlgebraic number theoryConstant-recursive sequenceIsogenyDivision algebraAlgebraic riccati equationDifferential algebraSemisimple lie algebraAlgebraic numberPrimary idealCommutatorGenerating set of a groupTauberian theoremRadical of an idealAbstract algebraTorsion-free moduleSequence spaceAlgebraic integerAlgebraic closureMonoidAxiom of infinityLower setMonotone convergence theoremTranscendental functionAxiom of extensionalityAffine groupMinimal idealCongruence subgroupAnalytic number theoryAdelic algebraic groupIndicator functionAlternating series testRegular local ringFormal power seriesSimple lie algebra