Theorems · Theorem · commutative algebra

IsIntegral.map

∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {B : Type u_6}
  {C : Type u_7} {F : Type u_8} [inst_3 : Ring B] [inst_4 : Ring C] [inst_5 : Algebra R B] [inst_6 : Algebra A B]
  [inst_7 : Algebra R C] [IsScalarTower R A B] [inst_9 : Algebra A C] [IsScalarTower R A C] {b : B}
  [inst_11 : FunLike F B C] [AlgHomClass F A B C] (f : F), IsIntegral R b → IsIntegral R (f b)

Defined in

Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic

Cited by

22 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraRingRingAlgebraAlgebraAlgebraIsScalarTowerAlgebraIsScalarTowerFunLikeAlgHomClass