Theorems · Theorem · commutative algebra
Ideal.Filtration.Stable.of_le
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {I : Ideal R}
{F : I.Filtration M} [IsNoetherianRing R] [Module.Finite R M], F.Stable → ∀ {F' : I.Filtration M}, F' ≤ F → F'.Stable- Defined in
- Mathlib.RingTheory.Filtration
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Polynomialproof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Module.Finitestatement and proof · cited by 1,032
- IsNoetherianRingstatement and proof · cited by 268
- IsNoetherianproof · cited by 208
- PolynomialModuleproof · cited by 76
- IsNoetherian.noetherianproof · cited by 32
- Ideal.Filtrationstatement and proof · cited by 32
- Ideal.Filtration.Nproof · cited by 29
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.Filtration.Stable.inter_rightproof · cited by 2
- Ideal.Filtration.Stable.inter_leftproof · cited by 0