Mathlib Map

Theorems · Theorem · commutative algebra

Algebra.HasGoingUp.trans

∀ (R : Type u_3) (S : Type u_4) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (T : Type u_5)
  [inst_3 : CommRing T] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [IsScalarTower R S T] [Algebra.HasGoingUp R S]
  [Algebra.HasGoingUp S T], Algebra.HasGoingUp R T

[Stacks Tag 00HX](https://stacks.math.columbia.edu/tag/00HX)

Defined in
Mathlib.RingTheory.Ideal.HasGoingUp
Cited by
0 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTowerAlgebra.HasGoingUpAlgebra.HasGoingUp
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRingHom · cited by 10189RingHomIsScalarTower · cited by 3896IsScalarTowerPrimeSpectrum.comap · cited by 199PrimeSpectrum.comapIsScalarTower.algebraMap_eq · cited by 110IsScalarTower.algebraMap_…SpecializingMap · cited by 21SpecializingMapAlgebra.HasGoingUp · cited by 6Algebra.HasGoingUpAlgebra.HasGoingUp.iff_specializingMap_primeSpectrumComap · cited by 1HasGoingUp.iff_specializi…SpecializingMap.comp · cited by 1SpecializingMap.compHasGoingUp.transCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.