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feat(LinearAlgebra/FiniteDimensional): relax condition of results regarding subalgebra = bot
... from requiring F being a field to F satisfying StrongRankCondition and S being a free F-module. This makes the original statement a special case.
The changed results are: Subalgebra.eq_bot_of_(rank_le|finrank)_one, Subalgebra.[fin]rank_eq_one_iff and Subalgebra.bot_eq_top_iff_[fin]rank_eq_one.
Since the generalized results don't requiring division ring anymore, they are moved to an eariler file LinearAlgebra/Dimension/FreeAndStrongRankCondition.
The proof need to use a new result bijective_algebraMap_of_linearEquiv which is put into Algebra/Algebra/Basic.
Seems that a lot of results in this file can be relaxed by the same way. Maybe I'll investigate them later. It's welcomed if someone could compile a list of them.
Since #12963 is merged, is it a good idea to move the results in this PR to that file?
Thanks! maintainer merge
🚀 Pull request has been placed on the maintainer queue by erdOne.
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