Theorems · Theorem · commutative algebra
Ideal.prime_of_mem_primesOver
∀ {A : Type u_2} [inst : CommRing A] [IsDedekindDomain A] {R : Type u_4} [inst_2 : CommRing R] [inst_3 : Algebra R A]
{p : Ideal R} [IsDomain R] [Module.IsTorsionFree R A], p ≠ ⊥ → ∀ {P : Ideal A}, P ∈ p.primesOver A → Prime P- Cited by
- 0 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- IsDedekindDomainstatement and proof · cited by 668
- Module.IsTorsionFreestatement and proof · cited by 600
- Primestatement · cited by 277
- Ideal.primesOverstatement and proof · cited by 84
- Ideal.prime_of_isPrimeproof · cited by 15
- Ideal.ne_bot_of_mem_primesOverproof · cited by 3
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