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Unique factorization domainNoetherian ringEuclidean domainIntegral domainDedekind ringDedekind domainDomainPrincipal ideal domainOrdered integral domainValuation ringNoetherian modulePrimitive polynomialFractional idealPolynomial algebraFactor ringPrincipal ideal ringOverringNumber fieldHilbert's basis theoremField of quotientsAlgebraic number fieldRing isomorphismField of fractionsRight idealBoolean ringSimple ringPrimary idealFree abelian groupUnique factorization ringIdeal numberPolynomial ringCommutative ringDivision ringQuotient ringCharacteristicRegular elementTotal ring of fractionsAssociateMinimal idealReduced ringZero divisorRing theoristLocal ringIntegral elementFactor idealRingoidRing of fractionsLine integralProduct ringSurface integralLeibniz algebraIdealSplitting fieldPerfect fieldGalois fieldAlgebraic normal formReduced algebraK-algebraLeft idealCyclotomic fieldTopological fieldRing theorySkew fieldNormal extensionOverorderNullstellensatzConductorLocalizationAlgebra over a ringStark-heegner theoremAssociative algebraPrime idealAlgebraic integerArchimedean ordered fieldGroup ringFrobenius endomorphismAdeleSemiringPolynomial functionCentral simple algebraNon-associative algebraQuadratic fieldCoringMaximal idealMatrix algebraModuleFree moduleSubringRingNear-ringOrdered ringInclusionPrime ringZariski-riemann spaceKummer ringRing homomorphismAbelian groupEisenstein integerPrincipal idealPlurigenus