Theorems · Definition · commutative algebra

IsIntegralClosure.equiv

(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] →
                  (A' : Type u_4) →
                    [inst_6 : CommRing A'] →
                      [inst_7 : Algebra A' B] →
                        [IsIntegralClosure A' R B] →
                          [inst_9 : Algebra R A] →
                            [inst_10 : Algebra R A'] → [IsScalarTower R A B] → [IsScalarTower R A' B] → A ≃ₐ[R] A'

Integral closures are all isomorphic to each other.

Defined in

Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic

Cited by

11 results in Mathlib

Foundations

Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraIsIntegralClosureCommRingAlgebraIsIntegralClosureAlgebraAlgebraIsScalarTowerIsScalarTower