Linked from

The 13 pages that link to Unique factorization domain, each with the reason it gives.

• Prime factorizationNarrower topic: It generalizes the uniqueness principle behind prime factorization to other algebraic systems.

• Fundamental theorem of arithmeticNarrower topic: The theorem is the integer case of this broader algebraic property.

• Gaussian integerRelated: Every Gaussian integer has unique factorization into Gaussian primes.

• Ring of integersCompared with: A ring of integers need not have unique factorization of elements, though its ideals factor uniquely.

• Ideal class groupCompared with: Element factorization can fail even when ideal factorization remains unique.

• Euclid's lemmaNarrower topic: In these rings, irreducibles satisfy a prime-divides-product property that yields unique factorization.

• Dedekind domainCompared with: Unique factorization of elements is stronger than the ideal factorization guaranteed here.

• Jordan–Hölder theoremCompared with: The analogy is useful, but group factors are series quotients, not products of elements.

• Algebraic integerCompared with: Rings of integers need not have unique factorization of elements.

• Unique factorizationNarrower topic: The integer theorem is the basic example of this broader algebraic property.

• Fermat's theorem on sums of two squaresNarrower topic: Unique factorization in the Gaussian integers explains why primes congruent to 1 modulo 4 split.

• Cubic reciprocityRelated: The Eisenstein integers allow prime elements to support the law's classical formulation.

• Stark–Heegner theoremRelated: The theorem classifies when rings of integers in imaginary quadratic fields have this property.