Theorems · Theorem · linear algebra

Submodule.exists_of_finrank_lt

∀ {R : Type u_1} {M : Type u} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [HasRankNullity.{u, u_1} R] [StrongRankCondition R] [Module.Finite R M] (N : Submodule R M),
  Module.finrank R ↥N < Module.finrank R M → ∃ m, ∀ (r : R), r ≠ 0 → r • m ∉ N

Defined in

Mathlib.LinearAlgebra.Dimension.RankNullity

Cited by

0 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleHasRankNullityStrongRankConditionModule.Finite