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The 20 pages that link to Prime ideal, each with the reason it gives.

• Algebraic number theoryBroader topic: Prime ideals provide the factors in the unique factorization of ideals.

• Commutative ringRelated: Prime ideals capture divisibility behavior and define the points of a spectrum.

• Maximal idealCompared with: Prime ideals require a domain quotient, while maximal ideals require a field quotient.

• Ring of integersRelated: Prime ideals replace prime elements when elements do not factor uniquely.

• Commutative algebraBroader topic: Prime ideals organize both the spectrum of a ring and its local structure.

• Ideal (ring theory)Compared with: Prime and maximal ideals coincide in some settings but express different conditions.

• Ideal class groupRelated: Prime ideals are the irreducible factors in Dedekind-domain ideal factorization.

• Euclid's lemmaRelated: This ideal-theoretic condition generalizes the lemma's product rule beyond integers.

• Dedekind domainRelated: Nonzero prime ideals are the building blocks of ideals in a Dedekind domain.

• IdealBroader topic: Prime ideals identify irreducible algebraic and arithmetic behavior.

• Dedekind zeta functionBroader topic: Prime ideals supply the local factors in the function's Euler product.

• UltrafilterCompared with: In a Boolean algebra, ultrafilters correspond to complements of maximal ideals, a closely related dual description.

• Boolean ringRelated: In Boolean rings, prime ideals also yield maximal ideals and simple two-element quotient rings.

• Hilbert class fieldRelated: Unramified prime ideals are the inputs to the Artin map.

• Chebotarev density theoremNarrower topic: The theorem counts prime ideals of the base field, excluding the finitely many ramified ones.

• Boolean prime ideal theoremBroader topic: This is the specific kind of ideal guaranteed to exist.

• Krull's principal ideal theoremRelated: The theorem bounds the height of primes minimal over the principal ideal.

• Cubic reciprocityRelated: The general algebraic setting expresses residue arithmetic modulo prime factors.

• Krull's theoremRelated: Every maximal ideal in a commutative ring with identity is prime.

• Schinzel's theoremRelated: Prime moduli generalize to prime ideals when studying polynomial roots in number rings.