Theorems · Theorem · commutative algebra

Submodule.mem_smul_span_singleton

∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {I : Ideal R}
  [I.IsTwoSided] {m x : M}, x ∈ I • (R ∙ m) ↔ ∃ y ∈ I, y • m = x

Defined in

Mathlib.RingTheory.Ideal.Operations

Cited by

2 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleIdeal.IsTwoSided