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feat(Algebra/Algebra/Operations): add Submodule.mul_eq_bot#37626

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feat(Algebra/Algebra/Operations): add Submodule.mul_eq_bot#37626
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@NoahW314 NoahW314 commented Apr 4, 2026 •
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Generalize Ideal.mul_eq_bot to work for submodules as well.

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@github-actions github-actions bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label Apr 4, 2026
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github-actions bot commented Apr 4, 2026 •
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PR summary 63868fe5ba

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ instance [NoZeroDivisors A] : NoZeroDivisors (Submodule R A)
++- mul_eq_bot
- instance [NoZeroDivisors R] : NoZeroDivisors (Ideal R)

You can run this locally as follows 
## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

No changes to technical debt.

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@github-actions github-actions bot added the t-algebra Algebra (groups, rings, fields, etc) label Apr 4, 2026
artie2000
artie2000 reviewed Apr 4, 2026
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Comment thread Mathlib/RingTheory/Ideal/Operations.lean Outdated
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artie2000 commented Apr 5, 2026

lgtm

eric-wieser
eric-wieser reviewed Apr 5, 2026
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Comment thread Mathlib/Algebra/Algebra/Operations.lean
eric-wieser
eric-wieser reviewed Apr 5, 2026
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Comment thread Mathlib/RingTheory/Ideal/Operations.lean Outdated
themathqueen
themathqueen reviewed Apr 15, 2026
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Comment thread Mathlib/RingTheory/Ideal/Operations.lean

instance [NoZeroDivisors R] : NoZeroDivisors (Ideal R) where
eq_zero_or_eq_zero_of_mul_eq_zero := mul_eq_bot.1
theorem mul_eq_bot [NoZeroDivisors R] : I * J = ⊥ ↔ I = ⊥ ∨ J = ⊥ := Submodule.mul_eq_bot
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@themathqueen themathqueen Apr 15, 2026

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deprecate?

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@eric-wieser eric-wieser Apr 15, 2026

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#37626 (comment)

eric-wieser
eric-wieser reviewed Apr 15, 2026
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Comment thread Mathlib/RingTheory/Spectrum/Prime/Basic.lean
obtain ⟨Wy, h_Wy_le, h_Wx_ne⟩ := hgt (M + span A {y}) (lt_add _ hy) (ne_bot_of_gt (lt_add _ hy))
use Wx + Wy
rw [Multiset.map_add, Multiset.prod_add]
refine ⟨le_trans (mul_le_mul' h_Wx_le h_Wy_le) ?_, mt Ideal.mul_eq_bot.mp ?_⟩
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I guess this change can now be reverted?

bors d+

Thanks!

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mathlib-bors bot commented Apr 15, 2026

✌️ NoahW314 can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@mathlib-triage mathlib-triage bot added the delegated This pull request has been delegated to the PR author (or occasionally another non-maintainer). label Apr 15, 2026
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