Theorems · Theorem · commutative algebra

RingTheory.Sequence.IsRegular.toIsWeaklyRegular

∀ {R : Type u_1} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {rs : List R},
  RingTheory.Sequence.IsRegular M rs → RingTheory.Sequence.IsWeaklyRegular M rs

Defined in: Mathlib.RingTheory.Regular.RegularSequence
Cited by: 3 results in Mathlib
Foundations: Depth 7 from the axioms · uses no axioms
Assumes: CommRing AddCommGroup Module

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Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
RingTheory.Sequence.IsWeaklyRegularstatement · cited by 40
RingTheory.Sequence.IsRegularstatement and proof · cited by 29

Cited by5

Results whose statement or proof uses this declaration.

RingTheory.Sequence.IsRegular.of_faithfullyFlat_of_isBaseChangeproof · cited by 1
ModuleCat.projectiveDimension_quotient_eq_lengthproof · cited by 0
RingTheory.Sequence.IsRegular.of_perm_of_subset_jacobson_annihilatorproof · cited by 0
RingTheory.Sequence.IsRegular.recIterModByRegularproof · cited by 0
RingTheory.Sequence.IsRegular.recIterModByRegularWithRingproof · cited by 0