Theorems · Inductive type · commutative algebra
Module.FinitePresentation
(R : Type u_1) → (M : Type u_2) → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [Module R M] → Prop
A module is finitely presented if it is finitely generated by some set s
and the kernel of the presentation Rˢ → M is also finitely generated.
- Cited by
- 60 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement · cited by 20,661
- Semiringstatement · cited by 13,802
- AddCommMonoidstatement · cited by 12,281
Cited by64
Results whose statement or proof uses this declaration.
- Module.finitePresentation_of_finitestatement · cited by 6
- Module.finitePresentation_of_surjectivestatement and proof · cited by 6
- Module.FinitePresentation.fg_kerstatement and proof · cited by 6
- Module.FinitePresentation.exists_finstatement and proof · cited by 4
- exists_bijective_map_powersstatement and proof · cited by 3
- Module.finitePresentation_of_free_of_surjectivestatement · cited by 3
- Module.FinitePresentation.casesOnstatement and proof · cited by 3
- Module.projective_of_localization_maximalstatement and proof · cited by 3
- Module.FinitePresentation.exists_lift_of_isLocalizedModulestatement and proof · cited by 3
- Module.FinitePresentation.linearEquivMapExtendScalarsstatement and proof · cited by 3
- Module.injective_of_isLocalizedModuleproof · cited by 2
- Module.injective_of_localization_maximalproof · cited by 2