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Principal ideal ringPrimary idealCommutative ringNoetherian moduleNoetherian domainSimple ringUnique factorization ringLocal ringIntegral domainReduced ringFactor ringRadical idealQuotient ringFactor idealMinimal idealRight idealPrime idealPolynomial ringCharacteristicPrime ringRadicalRing of fractionsCommutative algebraZero divisorOrdered ringReduced algebraDivision ringIdeal numberIdealRegular elementTotal ring of fractionsTwo-sided idealPrincipal idealLeft idealAlgebraic number fieldDedekind domainMaximal idealProduct ringPrimitive polynomialHilbert's basis theoremPolynomial algebraBoolean ringAbelian groupRing isomorphismNon-associative algebraFractional idealUnique factorization domainDomainMatrix algebraCommutatorAbelian algebraNumber fieldGroup ringLocalizationNear-ringCentral simple algebraOverorderRingK-algebraLeibniz algebraIntegral elementValuation ringRing theoryVanishing idealJordan algebraAnabelian geometryIdealizerAlgebra over a ringField of fractionsRing theoristSubringRing homomorphismNearringSemiringField of quotientsWeyl algebraFrobenius endomorphismRingoidNullstellensatzAdditive groupCenterAlgebraPrincipal ideal domainAlgebraic numberResidue fieldSplitting fieldSimple algebraEuclidean domainConductorModuleCombinatorial commutative algebraKummer ringNormal extensionAlgebraic normal formDivision algebraAdeleNilradicalPerfect fieldPolynomial basisAlgebraic closure