Theorems · Inductive type · commutative algebra

Submodule.IsMinimalPrimaryDecomposition

{R : Type u_1} →
  {M : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → Submodule R M → Finset (Submodule R M) → Prop

A Finset of submodules is a minimal primary decomposition of N if the submodules Nᵢ intersect to N, are primary, the √Ann(M/Nᵢ) are distinct, and each Nᵢ is necessary.

Defined in

Mathlib.RingTheory.Lasker

Cited by

13 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CommSemiringAddCommMonoidModule