Theorems · Theorem · commutative algebra
AdicCompletion.pow_smul_top_eq_ker_eval
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R} {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{n : ℕ}, I.FG → I ^ n • ⊤ = (AdicCompletion.eval I M n).ker[Stacks Tag 05GG](https://stacks.math.columbia.edu/tag/05GG) ((2))
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 115 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.
Cites58
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- RingHom.idstatement and proof · cited by 18,349
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- LinearMapproof · cited by 10,215
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.imageproof · cited by 5,609
- Finsuppproof · cited by 5,255
Cited by4
Results whose statement or proof uses this declaration.
- AdicCompletion.residueField_map_bijective_of_fgproof · cited by 1
- AdicCompletion.mem_maximalIdeal_iff_eval_one_eq_zeroproof · cited by 1
- AdicCompletion.ker_evalOneₐ_eq_mapproof · cited by 1
- AdicCompletion.spanFinrank_maximalIdeal_eqproof · cited by 0