Theorems · Theorem · commutative algebra
Submodule.range_unitsToPic
∀ (R : Type u) (A : Type u_4) [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Algebra R A] [inst_3 : FaithfulSMul R A], (Submodule.unitsToPic R A).range = CommRing.relPic R A
- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites54
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Top.topproof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Subgroupstatement · cited by 3,593
- LinearEquivproof · cited by 3,317
- Unitsstatement and proof · cited by 2,804
- TensorProductproof · cited by 2,545
- Units.valproof · cited by 1,966
- LinearMap.compproof · cited by 1,642
Cited by5
Results whose statement or proof uses this declaration.
- Submodule.unitsQuotEquivRelPicproof · cited by 2
- Module.Invertible.exists_linearEquiv_idealproof · cited by 0
- Submodule.mulExact_unitsToPic_mapAlgebraproof · cited by 0
- Submodule.unitsQuotEquivRelPic_symm_applystatement · cited by 0
- ClassGroup.equivPic_symm_applystatement · cited by 0