Theorems · Theorem · commutative algebra
coe_primesOverFinset
Deprecated since 2026-04-16Use IsDedekindDomain.coe_primesOverFinset instead.
∀ {A : Type u_4} [inst : CommRing A] {p : Ideal A},
p ≠ ⊥ →
∀ [hpm : p.IsMaximal] (B : Type u_5) [inst_1 : CommRing B] [inst_2 : IsDedekindDomain B] [inst_3 : Algebra A B]
[IsDomain A] [Module.IsTorsionFree A B], ↑(IsDedekindDomain.primesOverFinset p B) = p.primesOver BAlias of IsDedekindDomain.coe_primesOverFinset.
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- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement · cited by 17,173
- Finsetstatement · cited by 13,712
- Algebrastatement · cited by 11,388
- SetLike.coestatement · cited by 8,199
- Idealstatement · cited by 4,748
- Bot.botstatement · cited by 4,720
- IsDomainstatement · cited by 2,196
- IsDedekindDomainstatement · cited by 668
- Module.IsTorsionFreestatement · cited by 600
- Ideal.IsMaximalstatement · cited by 452
- Ideal.primesOverstatement · cited by 84
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