Theorems · Theorem · commutative algebra
CommRing.Pic.mk_eq_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] {N : CommRing.Pic R}, CommRing.Pic.mk R M = N ↔ Nonempty (M ≃ₗ[R] N.AsModule)- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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 and proof · 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 and proof · cited by 3,317
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.transproof · cited by 298
Cited by5
Results whose statement or proof uses this declaration.
- CommRing.Pic.mk_eq_selfproof · cited by 5
- Submodule.range_unitsToPicproof · cited by 4
- CommRing.Pic.mk_eq_mk_iffproof · cited by 3
- CommRing.Pic.mapAlgebra_self_applyproof · cited by 1
- CommRing.Pic.ext_iffproof · cited by 0