Theorems · Inductive type · commutative algebra

Submodule.IsAssociatedPrime

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

I : Ideal R is an associated prime of a submodule N : Submodule R M if I is prime and I = (colon N {x}).radical for some x : M.

Defined in

Mathlib.RingTheory.Ideal.AssociatedPrime.Basic

Cited by

5 results in Mathlib

Foundations

Depth 15 from the axioms · uses no axioms

Assumes

CommSemiringAddCommMonoidModule