Theorems · Theorem · commutative algebra

RingTheory.Sequence.isWeaklyRegular_cons_iff

∀ {R : Type u_1} (M : Type u_3) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (r : R)
  (rs : List R),
  RingTheory.Sequence.IsWeaklyRegular M (r :: rs) ↔
    IsSMulRegular M r ∧ RingTheory.Sequence.IsWeaklyRegular (QuotSMulTop r M) rs

Defined in: Mathlib.RingTheory.Regular.RegularSequence
Cited by: 6 results in Mathlib
Foundations: Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module

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Cites22

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
RingHom.idproof · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Top.topstatement and proof · cited by 9,680
Submodulestatement · cited by 7,192
Idealproof · cited by 4,748
Bot.botproof · cited by 4,720
LinearEquivproof · cited by 3,317
HasQuotient.Quotientproof · cited by 2,301
IsSMulRegularstatement · cited by 128
Submodule.pointwiseDistribMulActionstatement · cited by 105

Cited by6

Results whose statement or proof uses this declaration.

RingTheory.Sequence.IsWeaklyRegular.consproof · cited by 2
RingTheory.Sequence.isRegular_cons_iffproof · cited by 2
RingTheory.Sequence.isWeaklyRegular_cons_iff'proof · cited by 2
RingTheory.Sequence.isWeaklyRegular_append_iffproof · cited by 1
RingTheory.Sequence.isWeaklyRegular_singleton_iffproof · cited by 0
RingTheory.Sequence.eq_nil_of_isRegular_on_artinianproof · cited by 0