Theorems · Theorem · commutative algebra
Ideal.disjoint_primeCompl_of_liesOver
∀ {A : Type u_2} [inst : CommSemiring A] {C : Type u_4} [inst_1 : Semiring C] [inst_2 : Algebra A C] (𝔓 : Ideal C)
(p : Ideal A) [inst_3 : p.IsPrime] [hPp : 𝔓.LiesOver p], Disjoint ↑(Algebra.algebraMapSubmonoid C p.primeCompl) ↑𝔓- Defined in
- Mathlib.RingTheory.Ideal.Over
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Set.preimageproof · cited by 4,946
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- Submonoidstatement · cited by 3,086
- Compl.complproof · cited by 2,925
- Disjointstatement and proof · cited by 2,201
Cited by3
Results whose statement or proof uses this declaration.
- IsLocalization.AtPrime.isPrime_map_of_liesOverproof · cited by 5
- IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mkproof · cited by 1
- IsLocalization.AtPrime.exists_algebraMap_quot_eq_of_mem_quotproof · cited by 0