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Diff — Projective module

Revision #1498 → #1785 · back to history

modifiedProjective is free over a PID (Quillen–Suslin)e9a628ec082d
FieldFrom #1498To #1785
mathlib.declSubmodule.exists_basis_of_pidSubmodule.basisOfPid
moderation_flagLabel mentions Quillen–Suslin but that theorem is about polynomial rings, not PIDs in general; the underlying mathematical claim here (projective over PID is free) is correct.
noteMathlib proves submodules of free modules over a PID are free, but not the full 'every projective is free over a PID' as one declaration.Mathlib proves submodules of free modules over a PID are free (Submodule.basisOfPid), but not the full 'every projective is free over a PID' as one declaration.
provenanceaiai-moderated
modifiedProjective abelian groups are free0c9a690b79e5
FieldFrom #1498To #1785
mathlib.declSubmodule.exists_basis_of_pidSubmodule.basisOfPid
notePID infrastructure gives the result for finite-type ℤ-modules, but the general 'projective abelian group is free' iff is not a single declaration.PID infrastructure (Submodule.basisOfPid) gives the result for finite-type ℤ-modules, but the general 'projective abelian group is free' iff is not a single declaration.