Theorems · Theorem · commutative algebra
Ideal.under_map_of_isLocalizationAtPrime
∀ {R : Type u_1} [inst : CommSemiring R] (q : Ideal R) [inst_1 : q.IsPrime] {S : Type u_4} [inst_2 : CommSemiring S]
[inst_3 : Algebra R S] [IsLocalization.AtPrime S q] {p : Ideal R} [p.IsPrime],
p ≤ q → Ideal.under R (Ideal.map (algebraMap R S) p) = p- Cited by
- 3 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement · cited by 4,706
- Disjointproof · cited by 2,201
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.mapstatement · cited by 692
- Ideal.primeComplproof · cited by 462
- compl_complproof · cited by 229
- Ideal.understatement · cited by 170
Cited by3
Results whose statement or proof uses this declaration.
- PrimeSpectrum.exist_mem_one_of_mem_twoproof · cited by 1
- Algebra.QuasiFiniteAt.eq_of_le_of_under_eqproof · cited by 1
- Algebra.HasGoingDown.of_comap_localRingHom_surjectiveproof · cited by 0