Theorems · Theorem · commutative algebra
Module.Finite.exists_fin
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[Module.Finite R M], ∃ n s, Submodule.span R (Set.range s) = ⊤See also Module.Finite.exists_fin'.
- Defined in
- Mathlib.RingTheory.Finiteness.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- Set.rangestatement · cited by 4,705
- Submodule.spanstatement · cited by 1,504
- Module.Finitestatement and proof · cited by 1,032
- Module.Finite.fg_topproof · cited by 28
- Submodule.fg_iff_exists_fin_generating_familyproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- Module.Finite.of_finite_tensorProduct_of_faithfullyFlatproof · cited by 2
- Ideal.FinrankQuotientMap.span_eq_topproof · cited by 1
- Module.exists_isPrincipal_quotient_of_finiteproof · cited by 1
- Module.torsion_by_prime_power_decompositionproof · cited by 1
- Finsupp.Countable.of_moduleFiniteproof · cited by 1