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AnnihilatorRadical of an idealMaximal idealPrincipal ideal ringRadical idealTorsion-free moduleRing of integersCommutative algebraRadicalDivision ringIdealMatrix ringLocal ringQuotient ringIdempotentArtinian ringSimple ringTotal ring of fractionsPrincipal idealInvariant basis numberNakayama's lemmaPrime elementIntegral domainCharacteristicLie algebraIdeal class groupJacobian matrix and determinantFinite ringZero divisorNoetherian ringDedekind domainRingCyclotomic fieldSpecial linear lie algebraRing theoryAlgebraic integerCommutator subgroupHarmonic polynomialCommutative ringPrime ringLocalizationMutationCategory of modulesGraded ringPrimary idealResidue fieldKronecker symbolInner automorphismSemiringNilpotentProjective unitary groupModular groupDivision algebraCommutatorSemisimple lie algebraReduced ringNullstellensatzCasimir elementDiscrete valuation ringIdeal numberRinged spaceModuleEuclidean domainNoncommutative ringRadical axisCartan decompositionJacobi identityMonoidAbstract algebraRegular local ringRing homomorphismNilradicalAffine groupAlgebraic numberClass field theoryRational numberPrime idealAbsorbing elementAdele ringComposition algebraAlgebraic number theoryElementCartan subalgebraJacobi polynomialsMultiplicative subsetComplete measureCompletion of a ringRight idealLatticeAscending chain conditionSimple algebraCentral simple algebraFree algebraAssociative algebraInitial and terminal objectsSyzygantConstructible universeSimple lie algebraInclusion functionJacobi method