Theorems · Theorem · commutative algebra
AdicCompletion.pow_smul_top_le_ker_eval
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
(n : ℕ), I ^ n • ⊤ ≤ (AdicCompletion.eval I M n).ker- Defined in
- Mathlib.RingTheory.AdicCompletion.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- LinearMap.kerstatement · cited by 848
- map_smulproof · cited by 566
- AdicCompletionstatement and proof · cited by 160
- Quotient.outproof · cited by 141
Cited by1
Results whose statement or proof uses this declaration.
- AdicCompletion.pow_smul_top_eq_ker_evalproof · cited by 4