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Principal ideal domainDedekind ringUnique factorization domainPrincipal ideal ringIntegral domainDomainEuclidean domainOrdered integral domainUnique factorization ringDedekind cutNoetherian domainValuation ringFractional idealPrimitive polynomialIdealPerfect fieldPrimary idealFactor idealPrincipal idealIdeal numberMaximal idealField of fractionsRight idealPrime idealLocal ringProduct ringRadical idealFactor ringAdeleNoetherian ringDomain theoryField of quotientsMinimal idealAlgebraic number fieldSimple ringPolynomial ringRadicalQuotient ringDivision ringPrime ringLeft idealIdeleTotal ring of fractionsPolynomial algebraReduced algebraCharacteristicTwo-sided idealAssociateLocalizationCommutative ringNumber fieldNormal extensionWeyl algebraSplitting fieldCentral simple algebraVanishing idealReduced ringArchimedean ordered fieldK-algebraDivision algebraCodomainDirect productPrime fieldRing of fractionsAlgebraic closureContentOverringPolynomial formCommutative algebraRing theoryIntegral elementPower domainDegreeSeparable polynomialDioidResidue fieldEuclid's lemmaAntidomainSubringStark-heegner theoremOrdered ringAlgebraic integerLeibniz algebraBoolean ringModuleReal number systemPseudoradicalZero divisorFrobenius endomorphismFixed fieldFunctionEndofunctionConductorPolynomial basisGröbner basisQuadratic fieldIdentity functionPolynomial functionIntegralField theory