Theorems · Definition · commutative algebra
CommRing.Pic.mk
(R : Type u) →
(M : Type v) →
[inst : CommSemiring R] →
[inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → [Module.Invertible R M] → CommRing.Pic RThe class of an invertible module in the Picard group.
- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Unitsproof · cited by 2,804
- Module.Dualproof · cited by 583
- equivShrinkproof · cited by 118
- SemimoduleCatproof · cited by 108
- Module.Invertiblestatement and proof · cited by 41
- CommRing.Picstatement · cited by 37
- CategoryTheory.Skeletonproof · cited by 35
- SemimoduleCat.ofproof · cited by 25
Cited by20
Results whose statement or proof uses this declaration.
- CommRing.Pic.mapAlgebraproof · cited by 10
- Submodule.unitsToPicproof · cited by 10
- CommRing.Pic.mk_eq_iffstatement and proof · cited by 5
- CommRing.Pic.mk_eq_selfstatement · cited by 5
- CommRing.Pic.mk_eq_one_iffstatement and proof · cited by 4
- CommRing.Pic.mk.linearEquivstatement · cited by 3
- CommRing.Pic.mk_eq_mk_iffstatement and proof · cited by 3
- CommRing.Pic.mk_eq_one_iff_freestatement · cited by 2
- CommRing.Pic.mk_tensorstatement · cited by 2
- CommRing.Pic.mk_dualstatement · cited by 1
- CommRing.Pic.mk_selfstatement · cited by 1
- CommRing.Pic.subsingleton_iffₛproof · cited by 1