Comments (3)
I have the following result on my ideal-span-norm
branch:
noncomputable def basis.localization_localization {R S : Type*} [comm_ring R] [comm_ring S]
[algebra R S] {ι : Type*} [fintype ι] (b : basis ι R S)
(M : submonoid R) (Rₘ Sₘ : Type*)
[comm_ring Rₘ] [algebra R Rₘ] [comm_ring Sₘ] [algebra S Sₘ]
[algebra Rₘ Sₘ] [algebra R Sₘ] [is_scalar_tower R Rₘ Sₘ] [is_scalar_tower R S Sₘ]
[is_localization M Rₘ] [is_localization (M.map (algebra_map R S)) Sₘ]
(hM : submonoid.map (algebra_map R S) M ≤ S ⁰) :
basis ι Rₘ Sₘ :=
That is what we're looking for, right?
from mathlib.
I have the following result on my
ideal-span-norm
branch:noncomputable def basis.localization_localization {R S : Type*} [comm_ring R] [comm_ring S] [algebra R S] {ι : Type*} [fintype ι] (b : basis ι R S) (M : submonoid R) (Rₘ Sₘ : Type*) [comm_ring Rₘ] [algebra R Rₘ] [comm_ring Sₘ] [algebra S Sₘ] [algebra Rₘ Sₘ] [algebra R Sₘ] [is_scalar_tower R Rₘ Sₘ] [is_scalar_tower R S Sₘ] [is_localization M Rₘ] [is_localization (M.map (algebra_map R S)) Sₘ] (hM : submonoid.map (algebra_map R S) M ≤ S ⁰) : basis ι Rₘ Sₘ :=That is what we're looking for, right?
Yes! This should replace basis.localization, whose assumptions essentially never apply (we take a ℤ
-basis of a ℚ
-vector space).
from mathlib.
I PR'd the result above in #18261.
from mathlib.
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from mathlib.