[Merged by Bors] - refactor(linear_algebra/finite_dimensional): generalize finite_dimensional.iff_fg to division rings #7644
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Vierkantor
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Very nice results, thanks! The only thing I'm not totally convinced by is the rename from finite_dimensional to is_noetherian (as discussed on Zulip). But this criticism goes for a lot of the vector space stuff, so let's leave that to a future clean up.
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Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
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May 20, 2021
…ional.iff_fg to division rings (#7644) Replace `finite_dimensional.iff_fg` (working over a field) with `is_noetherian.iff_fg` (working over a division ring). Also, use the `module.finite` predicate. Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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…13386) Some lemmas have typeclass arguments that are in fact inferrable from the earlier ones, at least when everything is Prop valued this is unecessary so we clean up a few cases as they likely stem from typos or library changes. - `src/field_theory/finiteness.lean` it wasn't known at the time (#7644) that a division ring was noetherian, but now it is (#7661) - `src/category_theory/simple.lean` any abelian category has all cokernels so no need to assume it seperately - `src/analysis/convex/extreme.lean` assumed `linear_ordered_field` and `no_smul_zero_divisors` which is unnecessary, we take this as a sign that this and a couple of other convexity results should be generalized to densely ordered linear ordered rings (of which there are examples that are not fields) cc @YaelDillies
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Replace
finite_dimensional.iff_fg(working over a field) withis_noetherian.iff_fg(working over a division ring). Also, use themodule.finitepredicate.This is the beginning of an attempt to remove
finite_dimensionalentirely, in favour of just usingmodule.finite.module.rank#7634