Theorems · Theorem · commutative algebra
Submodule.mulExact_unitsToPic_mapAlgebra
∀ (R : Type u) (A : Type u_4) [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Algebra R A] [inst_3 : FaithfulSMul R A], Function.MulExact ⇑(Submodule.unitsToPic R A) ⇑(CommRing.Pic.mapAlgebra R A)
Exactness of the sequence 1 → Rˣ → Aˣ → (Submodule R A)ˣ → Pic R → Pic A at Pic R.
- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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- DFunLike.coestatement · cited by 62,936
- 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
- CommRing.Picstatement · cited by 37
- Function.MulExactstatement · cited by 28
- CommRing.Pic.mapAlgebrastatement · cited by 10
- Submodule.unitsToPicstatement · cited by 10
- Submodule.range_unitsToPicproof · cited by 4
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