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Primary idealPrincipal ideal domainPrincipal idealPrime idealRadical idealPrime ringSimple ringFactor idealLocal ringIdealNoetherian ringCommutative ringProduct ringRadicalIdeal numberFactor ringDedekind domainMaximal idealUnique factorization ringRight idealMinimal idealIntegral domainQuotient ringPolynomial ringPrimitive polynomialReduced ringTwo-sided idealCommutative algebraLeft idealPolynomial algebraFractional idealCentral simple algebraReduced algebraValuation ringVanishing idealDivision ringPseudoradicalPrimeOrdered ringIdeleIdealizerIntegral elementRing theoryMatrix algebraPerfect fieldUnique factorization domainDirect productBoolean ringPrime fieldLocalizationRing of fractionsKummer ringRing isomorphismCharacteristicTotal ring of fractionsAbelian groupRingResidue fieldSubringPolynomial basisSpectrumCenterRing theoristField of fractionsK-algebraConductorRegular elementGroup ringSemiringRingoidDomainFrobenius endomorphismSuperringHyperidealNoetherian domainAbelian algebraCommutatorWeyl algebraZero divisorMaximalNilradicalAdeleNullstellensatzNear-ringRing homomorphismLeibniz algebraPrimorialEuclid's lemmaHyperalgebraPrime numberGröbner basisRegular primePrime number theoremEisenstein primeAlmost primeNormal extensionHilbert's basis theoremModuleSplitting fieldPrime factor