Theorems · Theorem · commutative algebra
CommRing.Pic.mk_eq_mk_iff
∀ {R : Type u} {M : Type v} {N : Type u_1} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid N]
[inst_3 : Module R M] [inst_4 : Module R N] [inst_5 : Module.Invertible R M] [inst_6 : Module.Invertible R N],
CommRing.Pic.mk R M = CommRing.Pic.mk R N ↔ Nonempty (M ≃ₗ[R] N)- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearEquivstatement and proof · cited by 3,317
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.transproof · cited by 298
- Module.Invertiblestatement and proof · cited by 41
- CommRing.Picstatement · cited by 37
- CommRing.Pic.mkstatement and proof · cited by 17
- CommRing.Pic.AsModuleproof · cited by 11
- CommRing.Pic.mk_eq_iffproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- CommRing.Pic.mk_eq_one_iffproof · cited by 4
- CommRing.Pic.mapAlgebra_mapAlgebraproof · cited by 1
- Module.Invertible.exists_linearEquiv_idealproof · cited by 0