Theorems · Theorem · commutative algebra
AdicCompletion.map_val_apply
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{N : Type u_3} [inst_3 : AddCommGroup N] [inst_4 : Module R N] (f : M →ₗ[R] N) {n : ℕ} (x : AdicCompletion I M),
↑((AdicCompletion.map I f) x) n = (LinearMap.reduceModIdeal (I ^ n) f) (↑x n)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · 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
- AdicCompletion.transitionMapstatement · cited by 49
Cited by2
Results whose statement or proof uses this declaration.
- AdicCompletion.ofPowSMul_val_applyproof · cited by 2
- AdicCompletion.ofPowSMul_val_apply_eq_zeroproof · cited by 2