Theorems · Theorem · commutative algebra
Submodule.ker_unitsToPic
∀ (R : Type u) (A : Type u_4) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] [inst_3 : FaithfulSMul R A], (Submodule.unitsToPic R A).ker = (Units.map ↑(Submodule.spanSingleton R)).range
- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites49
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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- Algebra.algebraMapproof · cited by 4,706
- Subgroupstatement · cited by 3,593
- LinearEquivproof · cited by 3,317
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.mulExact_unitsMap_spanSingleton_unitsToPicproof · cited by 0