Theorems · Theorem · commutative algebra

Module.Basis.SmithNormalForm.repr_eq_zero_of_notMem_range

∀ {ι : Type u_1} {R : Type u_2} [inst : CommRing R] {M : Type u_3} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {n : ℕ} {N : Submodule R M} (snf : Module.Basis.SmithNormalForm N ι n) (m : ↥N) {i : ι},
  i ∉ Set.range ⇑snf.f → (snf.bM.repr ↑m) i = 0

Defined in: Mathlib.LinearAlgebra.FreeModule.PID
Cited by: 2 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module

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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
Setstatement · cited by 53,352
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Submodulestatement and proof · cited by 7,192
Finsuppstatement and proof · cited by 5,255
Set.rangestatement and proof · cited by 4,705
mul_oneproof · cited by 3,885
LinearEquivstatement · cited by 3,317
Function.Embeddingstatement · cited by 988

Cited by2

Results whose statement or proof uses this declaration.

LinearMap.trace_restrict_eq_of_forall_memproof · cited by 1
Module.Basis.SmithNormalForm.le_ker_coord_of_notMem_rangeproof · cited by 0