Theorems · Theorem · commutative algebra

RingTheory.Sequence.isWeaklyRegular_append_iff

∀ {R : Type u_1} (M : Type u_3) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (rs₁ rs₂ : List R),
  RingTheory.Sequence.IsWeaklyRegular M (rs₁ ++ rs₂) ↔
    RingTheory.Sequence.IsWeaklyRegular M rs₁ ∧ RingTheory.Sequence.IsWeaklyRegular (M ⧸ Ideal.ofList rs₁ • ⊤) rs₂

Defined in: Mathlib.RingTheory.Regular.RegularSequence
Cited by: 1 results in Mathlib
Foundations: Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module

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Cites21

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 and proof · cited by 7,192
Idealstatement and proof · cited by 4,748
Bot.botproof · cited by 4,720
LinearEquivproof · cited by 3,317
HasQuotient.Quotientstatement and proof · cited by 2,301
IsSMulRegularproof · cited by 128
QuotSMulTopproof · cited by 46

Cited by1

Results whose statement or proof uses this declaration.

RingTheory.Sequence.isWeaklyRegular_append_iff'proof · cited by 0