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chore: delete wrong docstring for irrelevant ideal (leanprover-community#30337)
The expression given `{a | ∀ (i : ι), i ≤ 0 → aᵢ = 0}` does not define an ideal, because it is not closed under (external) multiplication. For example, if x has grade 1 and y has grade -2, then x will be in this "ideal", but xy will not. Zulip discussion: [#mathlib4 > irrelevant ideal cannot be generalised](https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/irrelevant.20ideal.20cannot.20be.20generalised/near/543800961)
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  • Mathlib/RingTheory/GradedAlgebra/Homogeneous

Mathlib/RingTheory/GradedAlgebra/Homogeneous/Ideal.lean

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@@ -562,11 +562,6 @@ open GradedRing SetLike.GradedMonoid DirectSum
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refers to `⨁_{i>0} 𝒜ᵢ`, or equivalently `{a | a₀ = 0}`. This definition is used in `Proj`
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construction where `ι` is always `ℕ` so the irrelevant ideal is simply elements with `0` as
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0-th coordinate.
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# Future work
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Here in the definition, `ι` is assumed to be `CanonicallyOrderedAddCommMonoid`. However, the notion
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of irrelevant ideal makes sense in a more general setting by defining it as the ideal of elements
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with `0` as i-th coordinate for all `i ≤ 0`, i.e. `{a | ∀ (i : ι), i ≤ 0 → aᵢ = 0}`.
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-/
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def HomogeneousIdeal.irrelevant : HomogeneousIdeal 𝒜 :=
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⟨RingHom.ker (GradedRing.projZeroRingHom 𝒜), fun i r (hr : (decompose 𝒜 r 0 : A) = 0) => by

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