Theorems · Theorem · commutative algebra

IsLocalRing.isWeaklyRegular_of_perm_of_subset_maximalIdeal

∀ {R : Type u_1} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : IsLocalRing R] [IsNoetherian R M] {rs rs' : List R},
  RingTheory.Sequence.IsWeaklyRegular M rs →
    rs.Perm rs' → (∀ r ∈ rs, r ∈ IsLocalRing.maximalIdeal R) → RingTheory.Sequence.IsWeaklyRegular M rs'

Defined in: Mathlib.RingTheory.Regular.RegularSequence
Cited by: 1 results in Mathlib
Foundations: Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module IsLocalRing IsNoetherian

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Cites11

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
Idealstatement · cited by 4,748
IsLocalRingstatement and proof · cited by 339
IsLocalRing.maximalIdealstatement and proof · cited by 297
IsNoetherianstatement and proof · cited by 208
Module.annihilatorproof · cited by 61
RingTheory.Sequence.IsWeaklyRegularstatement and proof · cited by 40
IsLocalRing.maximalIdeal_le_jacobsonproof · cited by 16
RingTheory.Sequence.IsWeaklyRegular.of_perm_of_subset_jacobson_annihilatorproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

IsLocalRing.isRegular_of_permproof · cited by 0