Theorems · Definition · commutative algebra

AdicCompletion.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) → AdicCompletion I M →ₗ[R] M ⧸ I ^ n • ⊤

Linearly evaluating a sequence in the completion at a given input.

Defined in: Mathlib.RingTheory.AdicCompletion.Basic
Cited by: 24 results in Mathlib
Foundations: Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites10

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
LinearMapstatement · cited by 10,215
Top.topstatement · cited by 9,680
Submodulestatement · cited by 7,192
Idealstatement and proof · cited by 4,748
HasQuotient.Quotientstatement · cited by 2,301
AdicCompletionstatement and proof · cited by 160

Cited by26

Results whose statement or proof uses this declaration.

AdicCompletion.mapproof · cited by 24
AdicCompletion.evalₐproof · cited by 15
AdicCompletion.pow_smul_top_eq_ker_evalstatement and proof · cited by 4
AdicCompletion.eval_ofstatement · cited by 3
IsAdicComplete.mk_liftproof · cited by 2
AdicCompletion.mk_ofAlgEquiv_symmproof · cited by 2
IsAdicComplete.StrictMono.mk_liftproof · cited by 2
AdicCompletion.eval_surjectivestatement · cited by 2
AdicCompletion.of_surjective_iffproof · cited by 2
AdicCompletion.evalₐ_ofproof · cited by 2
AdicCompletion.map_surjective_of_mkQ_comp_surjectiveproof · cited by 1
AdicCompletion.mem_maximalIdeal_iff_eval_one_eq_zeroproof · cited by 1