Theorems · Theorem · commutative algebra
Module.Finite.of_basis
∀ {R : Type u_1} {M : Type u_2} {ι : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[Finite ι] (b : Module.Basis ι R M), Module.Finite R MA free module with a basis indexed by a Fintype is finite.
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topproof · cited by 9,680
- Fintypeproof · cited by 7,736
- Set.imageproof · cited by 5,609
- Finset.univproof · cited by 3,473
- Finitestatement and proof · cited by 3,029
- Submodule.spanproof · cited by 1,504
- Module.Basisstatement and proof · cited by 1,477
- Module.Finitestatement · cited by 1,032
Cited by22
Results whose statement or proof uses this declaration.
- Module.Basis.finiteDimensional_of_finiteproof · cited by 21
- PowerBasis.finiteproof · cited by 9
- Module.rank_lt_aleph0_iffproof · cited by 8
- LinearMap.trace_conj'proof · cited by 8
- LinearMap.det_smulproof · cited by 5
- Subspace.dual_finrank_eqproof · cited by 5
- Polynomial.Monic.finite_adjoinRootproof · cited by 4
- Algebra.norm_eq_one_of_not_module_finiteproof · cited by 3
- Module.finite_of_rank_eq_natproof · cited by 2
- LinearMap.polyCharpolyAux_basisIndepproof · cited by 2
- Algebra.norm_eq_zero_iff_of_basisproof · cited by 2
- Algebra.trace_eq_zero_of_not_isSeparableproof · cited by 2