Theorems · Theorem · commutative algebra

Submodule.smithNormalFormCoeffs_ne_zero

∀ {ι : Type u_1} {R : Type u_2} [inst : CommRing R] {M : Type u_3} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : IsDomain R] [inst_4 : IsPrincipalIdealRing R] {N : Submodule R M} [inst_5 : Finite ι]
  (b : Module.Basis ι R M) (h : Module.finrank R ↥N = Module.finrank R M) (i : ι),
  Submodule.smithNormalFormCoeffs b h i ≠ 0

Defined in

Mathlib.LinearAlgebra.FreeModule.PID

Cited by

1 results in Mathlib

Foundations

Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleIsDomainIsPrincipalIdealRingFinite