Theorems · Theorem · commutative algebra
RingTheory.Sequence.IsRegular.top_ne_smul
∀ {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 → ⊤ ≠ Ideal.ofList rs • ⊤- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 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.
Cites8
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 · cited by 9,680
- Submodulestatement · cited by 7,192
- Idealstatement · cited by 4,748
- Ideal.ofListstatement · cited by 33
- RingTheory.Sequence.IsRegularstatement and proof · cited by 29
Cited by6
Results whose statement or proof uses this declaration.
- Module.supportDim_add_length_eq_supportDim_of_isRegularproof · cited by 1
- RingTheory.Sequence.IsRegular.of_faithfullyFlat_of_isBaseChangeproof · cited by 1
- ModuleCat.projectiveDimension_quotient_eq_lengthproof · cited by 0
- RingTheory.Sequence.IsRegular.quot_ofList_smul_nontrivialproof · cited by 0
- RingTheory.Sequence.IsRegular.recIterModByRegularproof · cited by 0
- RingTheory.Sequence.IsRegular.recIterModByRegularWithRingproof · cited by 0