Theorems · Theorem · commutative algebra

RingTheory.Sequence.IsRegular.of_isWeaklyRegular_of_mem_maximalIdeal

∀ {R : Type u_7} [inst : CommRing R] [inst_1 : IsLocalRing R] (L : Type u_8) [inst_2 : AddCommGroup L]
  [inst_3 : Module R L] [Module.Finite R L] [Nontrivial L] {rs : List R},
  (∀ r ∈ rs, r ∈ IsLocalRing.maximalIdeal R) →
    RingTheory.Sequence.IsWeaklyRegular L rs → RingTheory.Sequence.IsRegular L rs

Defined in: Mathlib.RingTheory.Regular.RegularSequence
Cited by: 0 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsLocalRing AddCommGroup Module Module.Finite Nontrivial

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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
Idealstatement · cited by 4,748
LE.le.transproof · cited by 3,151
Nontrivialstatement and proof · cited by 2,416
Module.Finitestatement and proof · cited by 1,032
IsLocalRingstatement and proof · cited by 339
IsLocalRing.maximalIdealstatement and proof · cited by 297
Ideal.span_leproof · cited by 70
Module.annihilatorproof · cited by 61
RingTheory.Sequence.IsWeaklyRegularstatement and proof · cited by 40

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