Theorems · Theorem · commutative algebra
RingTheory.Sequence.isRegular_iff
∀ {R : Type u_1} (M : Type u_3) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (rs : List R),
RingTheory.Sequence.IsRegular M rs ↔ RingTheory.Sequence.IsWeaklyRegular M rs ∧ ⊤ ≠ Ideal.ofList rs • ⊤- Cited by
- 6 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Idealstatement · cited by 4,748
- RingTheory.Sequence.IsWeaklyRegularstatement and proof · cited by 40
- Ideal.ofListstatement and proof · cited by 33
- RingTheory.Sequence.IsRegularstatement and proof · cited by 29
- RingTheory.Sequence.IsRegular.casesOnproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- RingTheory.Sequence.isRegular_cons_iffproof · cited by 2
- AddEquiv.isRegular_congrproof · cited by 1
- ModuleCat.exists_isRegular_of_exists_subsingleton_extproof · cited by 1
- RingTheory.Sequence.isRegular_cons_iff'proof · cited by 1
- RingTheory.Sequence.eq_nil_of_isRegular_on_artinianproof · cited by 0