Theorems · Theorem · commutative algebra

ClassGroup.extendedHom_eq_one_of_forall_isPrincipal

∀ (A : Type u_1) (B : Type u_2) [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B]
  [inst_3 : Module.IsTorsionFree A B] [inst_4 : IsDedekindDomain A] [inst_5 : IsDedekindDomain B],
  (∀ (I : Ideal A), Submodule.IsPrincipal (Ideal.map (algebraMap A B) I)) → ClassGroup.extendedHom A B = 1

Defined in

Mathlib.RingTheory.ClassGroup.ExtendedHom

Cited by

0 results in Mathlib

Foundations

Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraModule.IsTorsionFreeIsDedekindDomainIsDedekindDomain