Theorems · Theorem · commutative algebra

IsIntegral.tower_top

∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Ring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : Algebra A B] [IsScalarTower R A B] {x : B},
  IsIntegral R x → IsIntegral A x

If R → A → B is an algebra tower, then if the entire tower is an integral extension so is A → B.

Defined in

Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic

Cited by

30 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingRingAlgebraAlgebraAlgebraIsScalarTower