Theorems · Theorem · commutative algebra

Submodule.unitsQuotEquivRelPic_symm_apply

∀ (R : Type u) (A : Type u_4) [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Algebra R A]
  [inst_3 : FaithfulSMul R A] (a : ↥(CommRing.relPic R A)),
  (Submodule.unitsQuotEquivRelPic R A).symm a =
    (QuotientGroup.congr (Submodule.unitsToPic R A).ker (Units.map ↑(Submodule.spanSingleton R)).range
        (MulEquiv.refl (Submodule R A)ˣ) ⋯)
      ((QuotientGroup.quotientKerEquivRange (Submodule.unitsToPic R A)).symm ((MulEquiv.subgroupCongr ⋯).symm a))

Defined in

Mathlib.RingTheory.PicardGroup

Cited by

0 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraFaithfulSMul