Theorems · Theorem · commutative algebra
Module.finitePresentation_of_finite
∀ (R : Type u_1) (M : Type u_2) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsNoetherianRing R] [h : Module.Finite R M], Module.FinitePresentation R M
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Finsetproof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Submodule.spanproof · cited by 1,504
- Module.Finitestatement and proof · cited by 1,032
- LinearMap.kerproof · cited by 848
- Finsupp.linearCombinationproof · cited by 269
- IsNoetherianRingstatement and proof · cited by 268
- Submodule.FGproof · cited by 230
Cited by6
Results whose statement or proof uses this declaration.
- Module.injective_of_isLocalizedModuleproof · cited by 2
- ModuleCat.hasProjectiveDimensionLE_iff_forall_maximalSpectrumproof · cited by 2
- Module.injective_of_localization_maximalproof · cited by 2
- Algebra.QuasiFiniteAt.exists_basicOpen_eq_singletonproof · cited by 2
- IsSMulRegular.subsingleton_linearMap_iffproof · cited by 2
- Module.finitePresentation_iff_finiteproof · cited by 0