Theorems · Theorem · commutative algebra

RingTheory.Sequence.isRegular_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.IsRegular M (r :: rs) ↔ IsSMulRegular M r ∧ RingTheory.Sequence.IsRegular (QuotSMulTop r M) rs

Defined in: Mathlib.RingTheory.Regular.RegularSequence
Cited by: 2 results in Mathlib
Foundations: Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module

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Cites14

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.topstatement and proof · cited by 9,680
Submodulestatement · cited by 7,192
IsSMulRegularstatement and proof · cited by 128
Submodule.pointwiseDistribMulActionstatement · cited by 105
QuotSMulTopstatement and proof · cited by 46
RingTheory.Sequence.IsWeaklyRegularproof · cited by 40
Ideal.ofListproof · cited by 33
RingTheory.Sequence.IsRegularstatement and proof · cited by 29
RingTheory.Sequence.isRegular_iffproof · cited by 6

Cited by2

Results whose statement or proof uses this declaration.

Module.supportDim_add_length_eq_supportDim_of_isRegularproof · cited by 1
RingTheory.Sequence.IsRegular.consproof · cited by 0