Theorems · Theorem · commutative algebra
IsLocalization.AtPrime.radical_map_of_mem_minimalPrimes
∀ {R : Type u_1} [inst : CommSemiring R] (A : Type u_2) [inst_1 : CommSemiring A] [inst_2 : Algebra R A] (q : Ideal R)
[hqp : q.IsPrime] [IsLocalization.AtPrime A q] (I : Ideal R),
q ∈ I.minimalPrimes → (Ideal.map (algebraMap R A) I).radical = Ideal.map (algebraMap R A) q- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Top.topproof · cited by 9,680
- Set.preimageproof · cited by 4,946
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- le_antisymmproof · cited by 2,068
- InfSet.sInfproof · cited by 935
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.mapstatement and proof · cited by 692
Cited by1
Results whose statement or proof uses this declaration.
- isDedekindDomainDvr.of_formallyUnramifiedproof · cited by 1