Powers generating 1 #757
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Powers generating 1 #757
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mortberg
approved these changes
Apr 6, 2022
| Σlemma (α , p) = subst-∈ ⟨fⁿ,gⁿ⟩ path ∑Binomial∈⟨fⁿ,gⁿ⟩ | ||
| x = α zero · U zero | ||
| y = linearCombination R' (α ∘ suc) (U ∘ suc) | ||
| -- x + y = linearCombination R' α U |
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the proof relies on those two being the same definitionally, but I removed anyways
mortberg
approved these changes
Apr 6, 2022
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A small PR containing a proof of the fact that if a f.g. ideal generates the whole ring, i.e.
1 ∈ ⟨ x₁ , ... , xₙ ⟩,then taking arbitrary powers of the generators still generates the whole ring, i.e.
1 ∈ ⟨ x₁ᵐ , ... , xₙᵐ ⟩for any m.