Theorems · Theorem · commutative algebra
Module.Relations.toQuotient_map_apply
∀ {A : Type u} [inst : Ring A] (relations : Module.Relations A) (x : relations.R →₀ A),
relations.toQuotient (relations.map x) = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
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.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Finsuppstatement and proof · cited by 5,255
- DFunLike.congr_funproof · cited by 288
- Module.Relations.Gstatement · cited by 103
- Module.Relationsstatement and proof · cited by 97
- Module.Relations.Rstatement and proof · cited by 57
- Module.Relations.Quotientstatement · cited by 22
- Module.Relations.toQuotientstatement · cited by 15
- Module.Relations.mapstatement · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Module.Relations.Solution.injective_fromQuotient_iff_ker_π_eq_spanproof · cited by 2