Theorems · Theorem · commutative algebra

RingTheory.Sequence.IsRegular.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.IsRegular M rs →
    rs.Perm rs' → (∀ r ∈ rs, r ∈ (Module.annihilator R M).jacobson) → RingTheory.Sequence.IsRegular M rs'

Defined in: Mathlib.RingTheory.Regular.RegularSequence
Cited by: 0 results in Mathlib
Foundations: Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module IsNoetherian

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Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Set.ofPredproof · cited by 6,101
Idealstatement · cited by 4,748
IsNoetherianstatement and proof · cited by 208
Ideal.jacobsonstatement and proof · cited by 88
Ideal.span_leproof · cited by 70
Module.annihilatorstatement and proof · cited by 61
RingTheory.Sequence.IsRegularstatement and proof · cited by 29
Submodule.top_ne_ideal_smul_of_le_jacobson_annihilatorproof · cited by 6
RingTheory.Sequence.IsRegular.toIsWeaklyRegularproof · cited by 3

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