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Prime idealPrincipal ideal ringSimple ringProduct ringPrimary idealReduced ringMinimal idealFactor ringUnique factorization ringPrincipal idealFactor idealQuotient ringDivision ringPrimitive polynomialIntegral domainZero divisorOrdered ringDirect productRight idealIdealRadical idealNoetherian ringLocal ringGroup ringMaximal idealRadicalPseudoradicalCharacteristicValuation ringPrincipal ideal domainDomainPolynomial ringPrime fieldPolynomial algebraPrimeCommutative ringIdeal numberTwo-sided idealKummer ringBoolean ringReduced algebraRingVanishing idealDedekind domainLeft idealSubringRing of fractionsFractional idealPseudoringTotal ring of fractionsRing homomorphismPrime numberCenterPrime number theoremRegular elementIdealizerNullstellensatzIntegral elementNear-ringSimple algebraPrimorialRing theoryField of quotientsResidue fieldAlgebra over a ringZeroCoringRegular primePolynomial basisRing isomorphismModuleCommutatorUnique factorization domainPerfect fieldRingoidAlmost primePrimitive elementCentral simple algebraPrime factorHyperringField of fractionsMinimal primeSemiringSplitting fieldRing theoristOverorderChen primeProductSemiprimeMinimal polynomialPrimitive rootDivision algebraPrincipal rootPrime decompositionFree groupSkew fieldEuclid's lemmaNormal extensionLocalizationPrime triplet