Theorems · Theorem · commutative algebra
Module.Relations.range_map
∀ {A : Type u} [inst : Ring A] (relations : Module.Relations A),
relations.map.range = Submodule.span A (Set.range relations.relation)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 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.
- RingHom.idstatement · cited by 18,349
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- Finsuppstatement · cited by 5,255
- Set.rangestatement · cited by 4,705
- Submodule.spanstatement · cited by 1,504
- LinearMap.rangestatement · cited by 893
- Module.Relations.Gstatement · cited by 103
- Module.Relationsstatement and proof · cited by 97
- Module.Relations.Rstatement · cited by 57
- Module.Relations.relationstatement · cited by 38
- Finsupp.range_linearCombinationproof · cited by 24
Cited by3
Results whose statement or proof uses this declaration.
- Module.Relations.Solution.injective_fromQuotient_iff_ker_π_eq_spanproof · cited by 2
- Module.Relations.Solution.IsPresentation.exactproof · cited by 0
- Algebra.Presentation.differentialsSolution_isPresentationproof · cited by 0