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Theorems · Theorem · commutative algebra

Ideal.LiesOver.tower_bot

∀ {A : Type u_2} [inst : CommSemiring A] {B : Type u_3} [inst_1 : CommSemiring B] {C : Type u_4} [inst_2 : Semiring C]
  [inst_3 : Algebra A B] [inst_4 : Algebra B C] [inst_5 : Algebra A C] [IsScalarTower A B C] (𝔓 : Ideal C) (P : Ideal B)
  (p : Ideal A) [hp : 𝔓.LiesOver p] [hP : 𝔓.LiesOver P], P.LiesOver p
Defined in
Mathlib.RingTheory.Ideal.Over
Cited by
2 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringCommSemiringSemiringAlgebraAlgebraAlgebraIsScalarTowerIdeal.LiesOverIdeal.LiesOver
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ideal.inertiaDeg_tower · cited by 7Ideal.inertiaDeg_towerIdeal.ramificationIdx_tower' · cited by 2Ideal.ramificationIdx_tow…Semiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringIdeal · cited by 4748IdealIsScalarTower · cited by 3896IsScalarTowerIdeal.LiesOver · cited by 272Ideal.LiesOverIdeal.under · cited by 170Ideal.underIdeal.over_def · cited by 60Ideal.over_defIdeal.under_under · cited by 7Ideal.under_underLiesOver.tower_botCITED BYCITES

Cites9

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Cited by2

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