Theorems · Theorem · commutative algebra

Ideal.Filtration.submodule_eq_span_le_iff_stable_ge

∀ {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) (n₀ : ℕ),
  F.submodule = Submodule.span (↥(reesAlgebra I)) (⋃ i, ⋃ (_ : i ≤ n₀), PolynomialModule.single R i '' ↑(F.N i)) ↔
    ∀ n ≥ n₀, I • F.N n = F.N (n + 1)

Defined in

Mathlib.RingTheory.Filtration

Cited by

1 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule