[Merged by Bors] - feat(RingTheory/LinearDisjoint): properties of linearly disjoint of subalgebras (2)#15346
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[Merged by Bors] - feat(RingTheory/LinearDisjoint): properties of linearly disjoint of subalgebras (2)#15346
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PR summary aaa7fe6e3c
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| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.RingTheory.LinearDisjoint | 1585 | 1586 | +1 (+0.06%) |
Import changes for all files
| Files | Import difference |
|---|---|
Mathlib.RingTheory.LinearDisjoint |
1 |
Declarations diff
+ adjoin_rank_eq_rank_left
+ adjoin_rank_eq_rank_right
+ finrank_sup_of_free
+ of_finrank_coprime_of_free
+ of_finrank_sup_of_free
+ rank_eq_one_of_commute_of_flat_of_self_of_inj
+ rank_eq_one_of_flat_of_self_of_inj
+ rank_inf_eq_one_of_commute_of_flat_left_of_inj
+ rank_inf_eq_one_of_commute_of_flat_of_inj
+ rank_inf_eq_one_of_commute_of_flat_right_of_inj
+ rank_inf_eq_one_of_flat_left_of_inj
+ rank_inf_eq_one_of_flat_of_inj
+ rank_inf_eq_one_of_flat_right_of_inj
+ rank_sup_of_free
You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>
## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>The doc-module for script/declarations_diff.sh contains some details about this script.
erdOne
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Jul 31, 2024
kbuzzard
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Oct 15, 2024
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kbuzzard
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This PR is very long. Are you sure that you want a one field structure for your definition of LinearDisjoint?
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Author
Fine. I'll try to split this as two separate PRs. Note that the first one can only contain very basic results which can almost do nothing. |
Collaborator
Author
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OK I've split half of them to #17820. It's 450 lines but I think it can't be shorten. Please review it first. |
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This PR/issue depends on: |
# Conflicts: # Mathlib/RingTheory/LinearDisjoint.lean
Member
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Thanks! |
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🚀 Pull request has been placed on the maintainer queue by erdOne. |
Member
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Thanks! bors merge |
mathlib-bors bot
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Oct 29, 2024
…ubalgebras (2) (#15346) Some new results: - `Subalgebra.LinearDisjoint.rank_sup_of_free`, `Subalgebra.LinearDisjoint.finrank_sup_of_free`: if subalgebras `A` and `B` are linearly disjoint and they are free modules, then the rank of `A ⊔ B` is equal to the product of the rank of `A` and `B`. - `Subalgebra.LinearDisjoint.of_finrank_sup_of_free`: conversely, if `A` and `B` are subalgebras which are free modules of finite rank, such that rank of `A ⊔ B` is equal to the product of the rank of `A` and `B`, then `A` and `B` are linearly disjoint. - `Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_left`: `Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_right`: if `A` and `B` are linearly disjoint, if `A` is free and `B` is flat (resp. `B` is free and `A` is flat), then `[B[A] : B] = [A : R]` (resp. `[A[B] : A] = [B : R]`). See also `Subalgebra.adjoin_rank_le`. - `Subalgebra.LinearDisjoint.of_finrank_coprime_of_free`: if the rank of `A` and `B` are coprime, and they satisfy some freeness condition, then `A` and `B` are linearly disjoint.
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Pull request successfully merged into master. Build succeeded: |
jcommelin
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Oct 29, 2024
…ubalgebras (2) (#15346) Some new results: - `Subalgebra.LinearDisjoint.rank_sup_of_free`, `Subalgebra.LinearDisjoint.finrank_sup_of_free`: if subalgebras `A` and `B` are linearly disjoint and they are free modules, then the rank of `A ⊔ B` is equal to the product of the rank of `A` and `B`. - `Subalgebra.LinearDisjoint.of_finrank_sup_of_free`: conversely, if `A` and `B` are subalgebras which are free modules of finite rank, such that rank of `A ⊔ B` is equal to the product of the rank of `A` and `B`, then `A` and `B` are linearly disjoint. - `Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_left`: `Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_right`: if `A` and `B` are linearly disjoint, if `A` is free and `B` is flat (resp. `B` is free and `A` is flat), then `[B[A] : B] = [A : R]` (resp. `[A[B] : A] = [B : R]`). See also `Subalgebra.adjoin_rank_le`. - `Subalgebra.LinearDisjoint.of_finrank_coprime_of_free`: if the rank of `A` and `B` are coprime, and they satisfy some freeness condition, then `A` and `B` are linearly disjoint.
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Some new results:
Subalgebra.LinearDisjoint.rank_sup_of_free,Subalgebra.LinearDisjoint.finrank_sup_of_free:if subalgebras
AandBare linearly disjoint and they arefree modules, then the rank of
A ⊔ Bis equal to the product of the rank ofAandB.Subalgebra.LinearDisjoint.of_finrank_sup_of_free:conversely, if
AandBare subalgebras which are free modules of finite rank,such that rank of
A ⊔ Bis equal to the product of the rank ofAandB,then
AandBare linearly disjoint.Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_left:Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_right:if
AandBare linearly disjoint, ifAis free andBis flat (resp.Bis free andAis flat), then[B[A] : B] = [A : R](resp.[A[B] : A] = [B : R]).See also
Subalgebra.adjoin_rank_le.Subalgebra.LinearDisjoint.of_finrank_coprime_of_free:if the rank of
AandBare coprime, and they satisfy some freeness condition,then
AandBare linearly disjoint.discussion: https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/Linearly.20disjoint