Theorems · Theorem · commutative algebra

isIntegral_algHom_iff

∀ {R : Type u_1} [inst : CommRing R] {A : Type u_6} {B : Type u_7} [inst_1 : Ring A] [inst_2 : Ring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] (f : A →ₐ[R] B),
  Function.Injective ⇑f → ∀ {x : A}, IsIntegral R (f x) ↔ IsIntegral R x

Defined in

Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic

Cited by

15 results in Mathlib

Foundations

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

Assumes

CommRingRingRingAlgebraAlgebra