Theorems · Theorem · linear algebra

Submodule.disjoint_ker_of_finrank_le

∀ {R : Type u_2} {M : Type u} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [HasRankNullity.{u, u_2} R] [StrongRankCondition R] [IsDomain R] [Module.IsTorsionFree R M] {N : Type u_1}
  [inst_7 : AddCommGroup N] [inst_8 : Module R N] {L : Submodule R M} [Module.Finite R ↥L] (f : M →ₗ[R] N),
  Module.finrank R ↥L ≤ Module.finrank R ↥(Submodule.map f L) → Disjoint L f.ker

Defined in

Mathlib.LinearAlgebra.Dimension.RankNullity

Cited by

2 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleHasRankNullityStrongRankConditionIsDomainModule.IsTorsionFreeAddCommGroupModuleModule.Finite