Theorems · Theorem · commutative algebra
Submodule.annihilator_top_inter_nonZeroDivisors
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[Module.Finite R M], Module.IsTorsion R M → (↑⊤.annihilator ∩ ↑(nonZeroDivisors R)).Nonempty- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.Elemproof · cited by 7,166
- Idealstatement · cited by 4,748
- Submonoidstatement · cited by 3,086
- Set.Nonemptystatement · cited by 2,627
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.isInternal_prime_power_torsionproof · cited by 2