Theorems · Definition · commutative algebra

Submodule.unitsToPicEquiv

{R : Type u} →
  {A : Type u_4} →
    [inst : CommSemiring R] →
      [inst_1 : Semiring A] →
        [inst_2 : Algebra R A] →
          [inst_3 : FaithfulSMul R A] → (I : (Submodule R A)ˣ) → ((Submodule.unitsToPic R A) I).AsModule ≃ₗ[R] ↥↑I

The image of an invertible R-submodule I ⊆ A under unitsToPic is isomorphic to I.

Defined in

Mathlib.RingTheory.PicardGroup

Cited by

1 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraFaithfulSMul