Theorems · Theorem · commutative algebra
CommRing.Pic.mk_dual
∀ {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 (Module.Dual R M) = (CommRing.Pic.mk R M)⁻¹- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 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.coeproof · 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
- Equiv.symmproof · cited by 3,681
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- Module.Dualstatement and proof · cited by 583
- Equiv.symm_apply_applyproof · cited by 320
- LinearEquiv.transproof · cited by 298
- Equiv.toFunproof · cited by 279
Cited by1
Results whose statement or proof uses this declaration.
- CommRing.Pic.inv_eq_dualproof · cited by 0