Module

FreeModuleRegularSequence.lean

Nyll.SchemeTheory.RingTheory.FreeModuleRegularSequence
1 declaration indexed from sourceView source ↗

Weak regular sequences on free modules

Weak regularity of a sequence on a nontrivial free module is equivalent to weak regularity on the ring. The public statement uses the free-module comparison proved in the auxiliary module.

Declarations

RingTheory.Sequence.isWeaklyRegular_of_free
Source context 4 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace AlgebraicCurves.Foundations.CommutativeAlgebra.Proofs
namespace RingTheory_Sequence_isWeaklyRegular_of_free
open scoped Pointwise TensorProduct
theorem _root_.RingTheory.Sequence.isWeaklyRegular_of_free {R M : Type*}
    [CommRing R] [AddCommGroup M] [Module R M] [Module.Free R M]
    [Nontrivial M] {s : List R} :
    RingTheory.Sequence.IsWeaklyRegular M s ↔ RingTheory.Sequence.IsWeaklyRegular R s