Theorems · Theorem · commutative algebra
Module.finite_of_finite
∀ (R : Type u_1) {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Finite R]
[Module.Finite R M], Finite M- Cited by
- 8 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idproof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapproof · cited by 10,215
- Finitestatement and proof · cited by 3,029
- Module.Finitestatement and proof · cited by 1,032
- Finite.of_surjectiveproof · cited by 14
- Module.Finite.exists_fin'proof · cited by 10
Cited by8
Results whose statement or proof uses this declaration.
- FiniteField.nonempty_algHom_of_finrank_dvdproof · cited by 3
- Submodule.finite_quotient_smulproof · cited by 2
- exists_linearIndependent_algEquiv_applyproof · cited by 1
- Projectivization.card_of_finrankproof · cited by 1
- Module.finite_iff_finiteproof · cited by 1
- ax_grothendieck_of_locally_finiteproof · cited by 1
- IsLocalRing.ResidueField.finite_of_finiteproof · cited by 0
- Ring.HasFiniteQuotients.of_module_finiteproof · cited by 0