Theorems · Theorem · commutative algebra

ClassGroup.mulEquiv_symm_apply

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] {R' : Type u_3} [inst_2 : CommRing R'] [inst_3 : IsDomain R']
  (g : R ≃+* R') (a : ClassGroup R'),
  (ClassGroup.mulEquiv g).symm a =
    (ClassGroup.equiv (FractionRing R)).symm
      ((QuotientGroup.congr (toPrincipalIdeal R' (FractionRing R')).range (toPrincipalIdeal R (FractionRing R)).range
          (Units.mapEquiv (↑(FractionalIdeal.ringEquivOfRingEquiv (FractionRing R) (FractionRing R') g)).symm) ⋯)
        ((ClassGroup.equiv (FractionRing R')) a))

Defined in

Mathlib.RingTheory.ClassGroup.Basic

Cited by

0 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainCommRingIsDomain