Theorems · Theorem · commutative algebra
LinearIndependent.set_finite_of_isNoetherian
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [IsNoetherian R M]
[Nontrivial R] {s : Set M}, LinearIndependent R Subtype.val → s.Finite- Defined in
- Mathlib.RingTheory.Noetherian.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Nontrivialstatement and proof · cited by 2,416
- Set.Finitestatement · cited by 1,814
- LinearIndependentstatement and proof · cited by 560
- IsNoetherianstatement and proof · cited by 208
- LinearIndependent.finite_of_isNoetherianproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.eq_top_of_finrank_eqproof · cited by 15
- IsNoetherian.iff_rank_lt_aleph0proof · cited by 2