Theorems · Theorem · commutative algebra

Submodule.mem_mul_span_singleton

∀ {R : Type u} [inst : CommSemiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Algebra R A] {P : Submodule R A}
  {x y : A}, x ∈ P * (R ∙ y) ↔ ∃ z ∈ P, z * y = x

Defined in

Mathlib.Algebra.Algebra.Operations

Cited by

2 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebra