Theorems · Definition · commutative algebra
Module.Free.ChooseBasisIndex
(R : Type u) → (M : Type v) → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → [Module.Free R M] → Type v
If Module.Free R M then ChooseBasisIndex R M is the ι which indexes the basis
ι → M. Note that this is defined such that this type is finite if R is trivial.
- Defined in
- Mathlib.LinearAlgebra.FreeModule.Basic
- Cited by
- 133 results in Mathlib
- Foundations
- Depth 86 from the axioms, rests on 1,797 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Set.Elemproof · cited by 7,166
- Module.Freestatement and proof · cited by 597
Cited by144
Results whose statement or proof uses this declaration.
- Module.Free.chooseBasisstatement · cited by 121
- Module.Basis.ofZLatticeBasisproof · cited by 36
- NumberField.integralBasisstatement · cited by 25
- Module.Free.of_equivproof · cited by 23
- Module.finrank_eq_card_chooseBasisIndexstatement and proof · cited by 21
- Ideal.absNorm_span_singletonproof · cited by 18
- NumberField.RingOfIntegers.basisstatement · cited by 12
- Module.Basis.ofZLatticeBasis_applyproof · cited by 11
- NumberField.mixedEmbedding.fractionalIdealLatticeBasisstatement and proof · cited by 11
- NumberField.mixedEmbedding.latticeBasisstatement · cited by 11
- Module.Free.rank_eq_card_chooseBasisIndexstatement · cited by 10
- LinearMap.charpoly_toMatrixproof · cited by 9