Theorems · Theorem · commutative algebra

Module.Relations.Solution.IsPresentation.free

∀ {A : Type u} [inst : Ring A] {relations : Module.Relations A} (M : Type v) [inst_1 : AddCommGroup M]
  [inst_2 : Module A M] [IsEmpty relations.R] {solution : relations.Solution M},
  solution.IsPresentation → Module.Free A M

Defined in: Mathlib.Algebra.Module.Presentation.Free
Cited by: 1 results in Mathlib
Foundations: Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring AddCommGroup Module IsEmpty

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Ringstatement and proof · cited by 7,463
IsEmptystatement and proof · cited by 759
Module.Freestatement · cited by 597
Module.Relationsstatement and proof · cited by 97
Module.Relations.Solutionstatement and proof · cited by 70
Module.Relations.Rstatement and proof · cited by 57
Module.Relations.Solution.IsPresentationstatement and proof · cited by 39
Module.Free.of_equivproof · cited by 23
Module.Relations.Solution.IsPresentation.uniqproof · cited by 5
Module.Relations.solutionFinsupp_isPresentationproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

Module.free_iff_exists_presentationproof · cited by 0