Theorems · Theorem · commutative algebra
IsLocalization.AtPrime.liesOver_comap_of_liesOver
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal R)
[inst_3 : p.IsPrime] (Rₚ : Type u_3) [inst_4 : CommRing Rₚ] [inst_5 : Algebra R Rₚ] [IsLocalization.AtPrime Rₚ p]
[inst_7 : IsLocalRing Rₚ] {T : Type u_5} [inst_8 : CommRing T] [inst_9 : Algebra R T] [inst_10 : Algebra Rₚ T]
[inst_11 : Algebra S T] [IsScalarTower R S T] [IsScalarTower R Rₚ T] (Q : Ideal T)
[Q.LiesOver (IsLocalRing.maximalIdeal Rₚ)], (Ideal.comap (algebraMap S T) Q).LiesOver p- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.comapstatement · cited by 443
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- Ideal.LiesOverstatement and proof · cited by 272
- IsScalarTower.toAlgHomproof · cited by 232
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