Theorems · Theorem · commutative algebra
CommRing.Pic.mk_eq_one_iff
∀ {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 = 1 ↔ Nonempty (M ≃ₗ[R] R)- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Module.Invertiblestatement and proof · cited by 41
- CommRing.Picstatement and proof · cited by 37
- CommRing.Pic.mkstatement and proof · cited by 17
- CommRing.Pic.mk_eq_mk_iffproof · cited by 3
- CommRing.Pic.mk_selfproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Submodule.range_unitsToPicproof · cited by 4
- CommRing.Pic.mk_eq_one_iff_freeproof · cited by 2
- Submodule.ker_unitsToPicproof · cited by 1
- Ideal.eq_top_of_mk_tensor_eq_oneproof · cited by 0