Theorems · Theorem · commutative algebra
Submodule.pow_smul_top_le
∀ {R : Type u_1} [inst : Ring R] (I : Ideal R) (M : Type u_2) [inst_1 : AddCommGroup M] [inst_2 : Module R M] {m n : ℕ},
m ≤ n → I ^ n • ⊤ ≤ I ^ m • ⊤- Cited by
- 5 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Ideal.pow_le_pow_rightproof · cited by 39
- Submodule.smul_mono_leftproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- AdicCompletion.ofPowSMul_val_apply_eq_zeroproof · cited by 2
- IsHausdorff.StrictMono.funextproof · cited by 1
- IsHausdorff.StrictMono.funext'proof · cited by 1
- AdicCompletion.map_surjective_of_mkQ_comp_surjectiveproof · cited by 1
- AdicCompletion.exists_smodEq_pow_smul_top_and_mkQ_eqstatement and proof · cited by 1