Theorems · Theorem · commutative algebra

IsIntegralClosure.isIntegral_iff

∀ {A : Type u_1} {R : Type u_2} {B : Type u_3} {inst : CommRing R} {inst_1 : CommSemiring A} {inst_2 : CommRing B}
  {inst_3 : Algebra R B} {inst_4 : Algebra A B} [self : IsIntegralClosure A R B] {x : B},
  IsIntegral R x ↔ ∃ y, (algebraMap A B) y = x

Defined in

Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Defs

Cited by

19 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

IsIntegralClosure