[Merged by Bors] - feat: generalize scalars in Algebra.lsmul #6209
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…ra instance This also moves some lemmas about `IsUnit (_ : Module.End R M)` to an earlier file as they are nothing to do with `Algebra`.
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This generalizes from `Algebra.lsmul R M : A →ₐ[R] Module.End R M` to `Algebra.lsmul R S M : A →ₐ[R] Module.End S M`. This generalization was previously not possible because `Module.End S M` was not an `R`-algebra. Notably this now allows things like `Algebra.lsmul R A A : Aᵐᵒᵖ →ₐ[R] Module.End A A` (right multiplication). This doesn't bother attempting to generalize uses in downstream files, as most of them probably do not need the generality. Instead, we just replace `Algebra.lsmul R` with `Algebra.lsmul R R`.
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This generalizes from `Algebra.lsmul R M : A →ₐ[R] Module.End R M` to `Algebra.lsmul R S M : A →ₐ[R] Module.End S M`. This generalization was previously not possible because `Module.End S M` was not an `R`-algebra. Notably this now allows things like `Algebra.lsmul R A A : Aᵐᵒᵖ →ₐ[R] Module.End A A` (right multiplication). This doesn't bother attempting to generalize uses in downstream files, as most of them probably do not need the generality. Instead, we just replace `Algebra.lsmul R` with `Algebra.lsmul R R`.
semorrison
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Aug 3, 2023
This generalizes from `Algebra.lsmul R M : A →ₐ[R] Module.End R M` to `Algebra.lsmul R S M : A →ₐ[R] Module.End S M`. This generalization was previously not possible because `Module.End S M` was not an `R`-algebra. Notably this now allows things like `Algebra.lsmul R A A : Aᵐᵒᵖ →ₐ[R] Module.End A A` (right multiplication). This doesn't bother attempting to generalize uses in downstream files, as most of them probably do not need the generality. Instead, we just replace `Algebra.lsmul R` with `Algebra.lsmul R R`.
semorrison
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Aug 14, 2023
This generalizes from `Algebra.lsmul R M : A →ₐ[R] Module.End R M` to `Algebra.lsmul R S M : A →ₐ[R] Module.End S M`. This generalization was previously not possible because `Module.End S M` was not an `R`-algebra. Notably this now allows things like `Algebra.lsmul R A A : Aᵐᵒᵖ →ₐ[R] Module.End A A` (right multiplication). This doesn't bother attempting to generalize uses in downstream files, as most of them probably do not need the generality. Instead, we just replace `Algebra.lsmul R` with `Algebra.lsmul R R`.
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This generalizes from
Algebra.lsmul R M : A →ₐ[R] Module.End R MtoAlgebra.lsmul R S M : A →ₐ[R] Module.End S M.This generalization was previously not possible because
Module.End S Mwas not anR-algebra.Notably this now allows things like
Algebra.lsmul R A A : Aᵐᵒᵖ →ₐ[R] Module.End A A(right multiplication).This doesn't bother attempting to generalize uses in downstream files, as most of them probably do not need the generality.
Instead, we just replace
Algebra.lsmul RwithAlgebra.lsmul R R.