Theorems · Theorem · commutative algebra

IsIntegralClosure.isIntegral

∀ (R : Type u_1) {A : Type u_2} (B : Type u_3) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : CommRing B]
  [inst_3 : Algebra R B] [inst_4 : Algebra A B] [IsIntegralClosure A R B] [inst_6 : Algebra R A] [IsScalarTower R A B]
  (x : A), IsIntegral R x

Defined in

Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic

Cited by

8 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraIsIntegralClosureAlgebraIsScalarTower