Theorems · Theorem · commutative algebra
Submodule.torsionBySet_le_torsionBySet_pow
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (i j : ℕ),
i ≤ j → ∀ (I : Ideal R), Submodule.torsionBySet R M ↑(I ^ i) ≤ Submodule.torsionBySet R M ↑(I ^ j)- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 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.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement · cited by 8,199
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Ideal.pow_le_pow_rightproof · cited by 39
- Submodule.torsionBySetstatement · cited by 34
- Submodule.torsionBySet_le_torsionBySet_of_subsetproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.iSupIndep_primaryComponentproof · cited by 1