Theorems · Theorem · commutative algebra
Submodule.mulExact_unitsMap_spanSingleton_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], Function.MulExact ⇑(Units.map ↑(Submodule.spanSingleton R)) ⇑(Submodule.unitsToPic R A)
Exactness of the sequence 1 → Rˣ → Aˣ → (Submodule R A)ˣ → Pic R → Pic A
at (Submodule R A)ˣ.
- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement · cited by 7,192
- MonoidHomstatement · cited by 3,629
- Unitsstatement · cited by 2,804
- FaithfulSMulstatement and proof · cited by 340
- Units.mapstatement · cited by 95
- MonoidWithZeroHom.toMonoidHomstatement · cited by 39
- CommRing.Picstatement · cited by 37
- Function.MulExactstatement · cited by 28
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