Theorems · Theorem · commutative algebra
Module.Free.of_basis
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type w}
(b : Module.Basis ι R M), Module.Free R M- Defined in
- Mathlib.LinearAlgebra.FreeModule.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Set.Elemproof · cited by 7,166
- Set.rangeproof · cited by 4,705
- Module.Basisstatement and proof · cited by 1,477
- Module.Freestatement · cited by 597
- Module.Basis.reindexRangeproof · cited by 16
- Module.free_defproof · cited by 3
Cited by20
Results whose statement or proof uses this declaration.
- Module.Free.of_equivproof · cited by 23
- Module.free_of_flat_of_isLocalRingproof · cited by 7
- Polynomial.Monic.free_adjoinRootproof · cited by 3
- Module.FinitePresentation.exists_free_localizedModule_powersproof · cited by 2
- LinearMap.polyCharpolyAux_basisIndepproof · cited by 2
- Algebra.norm_eq_zero_iff_of_basisproof · cited by 2
- Algebra.traceMatrix_localizationLocalizationproof · cited by 1
- AddSubgroup.index_eq_natAbs_detproof · cited by 1
- Module.free_of_maximalIdeal_rTensor_injectiveproof · cited by 1
- Module.Projective.iff_split'proof · cited by 1
- dualTensorHomEquiv_eq_dualTensorHomEquivOfBasisstatement · cited by 1
- Module.Free.of_det_ne_oneproof · cited by 1