Theorems · Definition · commutative algebra
CommRing.Pic.mk.linearEquiv
(R : Type u) →
(M : Type v) →
[inst : CommSemiring R] →
[inst_1 : AddCommMonoid M] →
[inst_2 : Module R M] → [inst_3 : Module.Invertible R M] → (CommRing.Pic.mk R M).AsModule ≃ₗ[R] Mmk R M is indeed the class of M.
- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Equivstatement · cited by 8,337
- Equiv.symmstatement · cited by 3,681
- LinearEquivstatement · cited by 3,317
- Unitsstatement · cited by 2,804
- Units.valstatement · cited by 1,966
- Module.Dualproof · cited by 583
- Nonempty.someproof · cited by 340
Cited by3
Results whose statement or proof uses this declaration.
- CommRing.Pic.mk_eq_iffproof · cited by 5
- CommRing.Pic.mk_eq_mk_iffproof · cited by 3
- CommRing.Pic.mapAlgebra_mapAlgebraproof · cited by 1