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

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

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

• 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.

• 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.

• 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.