[Merged by Bors] - feat(ring_theory): definition and properties of relative ideal norm #18299
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This PR provides a definition of the relative ideal norm `ideal.span_norm R I` as the ideal spanned by the norms of elements in `I`. We also give some basic results on this definition. A follow-up PR will bundle this into a homomorphism `ideal.rel_norm`.
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Jan 31, 2023
| def span_norm (I : ideal S) : ideal R := | ||
| ideal.span (algebra.norm R '' (I : set S)) | ||
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| @[simp] lemma span_norm_bot |
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This is false without nontrivial S, right?
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Yes, then this would be ideal.span {algebra.norm 1} = ideal.span {1} = ⊤ (since norm/det breaks the tie between 0 = 1 in favour of 1).
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…18299) This PR provides a definition of the relative ideal norm `ideal.span_norm R I` as the ideal spanned by the norms of elements in `I`. We also give some basic results on this definition. A follow-up PR will bundle this into a homomorphism `ideal.rel_norm`.
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This PR provides a definition of the relative ideal norm
ideal.span_norm R Ias the ideal spanned by the norms of elements inI. We also give some basic results on this definition. A follow-up PR will bundle this into a homomorphismideal.rel_norm.