Theorems · Theorem · commutative algebra
Ideal.prime_generator_of_prime
∀ {A : Type u_2} [inst : CommRing A] [IsDedekindDomain A] {P : Ideal A},
Prime P → ∀ [inst_2 : Submodule.IsPrincipal P], Prime (Submodule.IsPrincipal.generator P)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimeproof · cited by 827
- IsDedekindDomainstatement and proof · cited by 668
- Primestatement and proof · cited by 277
- Submodule.IsPrincipalstatement and proof · cited by 129
- Submodule.IsPrincipal.generatorstatement · cited by 56
- Prime.ne_zeroproof · cited by 47
- Ideal.isPrime_of_primeproof · cited by 17
- Submodule.IsPrincipal.prime_generator_of_isPrimeproof · cited by 4
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