[Merged by Bors] - feat(ring_theory/finiteness): add finiteness of restrict_scalars #9363
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Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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We add `module.finitte.of_restrict_scalars_finite` and related lemmas: if `A` is an `R`-algebra and `M` is an `A`-module that is finite as `R`-module, then it is finite as `A`-module (similarly for `finite_type`).
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We add `module.finitte.of_restrict_scalars_finite` and related lemmas: if `A` is an `R`-algebra and `M` is an `A`-module that is finite as `R`-module, then it is finite as `A`-module (similarly for `finite_type`).
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We add
module.finitte.of_restrict_scalars_finiteand related lemmas: ifAis anR-algebra andMis anA-module that is finite asR-module, then it is finite asA-module (similarly forfinite_type).