Theorems · Theorem · linear algebra

Module.Basis.basis_singleton_iff

∀ {R : Type u_7} {M : Type u_8} [inst : Ring R] [IsDomain R] [inst_2 : AddCommGroup M] [inst_3 : Module R M]
  [Module.IsTorsionFree R M] (ι : Type u_9) [Unique ι],
  Nonempty (Module.Basis ι R M) ↔ ∃ x, x ≠ 0 ∧ ∀ (y : M), ∃ r, r • x = y

Defined in

Mathlib.LinearAlgebra.Basis.Basic

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingIsDomainAddCommGroupModuleModule.IsTorsionFreeUnique