Theorems · Theorem · commutative algebra

RingTheory.Sequence.IsWeaklyRegular.of_perm_of_subset_jacobson_annihilator

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

Defined in: Mathlib.RingTheory.Regular.RegularSequence
Cited by: 2 results in Mathlib
Foundations: Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module IsNoetherian

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Cites23

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
Top.topproof · cited by 9,680
Idealstatement · cited by 4,748
HasQuotient.Quotientproof · cited by 2,301
le_transproof · cited by 985
Submodule.subtypeproof · cited by 480
Submodule.mkQproof · cited by 232
IsNoetherianstatement and proof · cited by 208
Ideal.jacobsonstatement and proof · cited by 88
Module.annihilatorstatement and proof · cited by 61

Cited by2

Results whose statement or proof uses this declaration.

IsLocalRing.isWeaklyRegular_of_perm_of_subset_maximalIdealproof · cited by 1
RingTheory.Sequence.IsRegular.of_perm_of_subset_jacobson_annihilatorproof · cited by 0