Theorems · Theorem · commutative algebra

Module.IsLocalRing.linearIndependent_of_flat

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : IsLocalRing R] [Module.Flat R M] {ι : Type u} (v : ι → M),
  LinearIndependent (IsLocalRing.ResidueField R) (⇑((TensorProduct.mk R (IsLocalRing.ResidueField R) M) 1) ∘ v) →
    LinearIndependent R v

Defined in: Mathlib.RingTheory.LocalRing.Module
Cited by: 2 results in Mathlib
Foundations: Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module IsLocalRing Module.Flat

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
Semiringproof · cited by 13,802
Finsetproof · cited by 13,712
AddCommGroupstatement and proof · cited by 12,871
AddCommMonoidproof · cited by 12,281
LinearMapstatement · cited by 10,215
Top.topproof · cited by 9,680
Finset.sumproof · cited by 5,195
mul_oneproof · cited by 3,885

Cited by2

Results whose statement or proof uses this declaration.

Module.free_of_flat_of_isLocalRingproof · cited by 7
Module.IsLocalRing.linearCombination_bijective_of_flatproof · cited by 1