Theorems · Definition · nonassociative algebras

Submodule.toNonUnitalSubalgebra

{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : NonUnitalNonAssocSemiring A] →
        [inst_2 : Module R A] → (p : Submodule R A) → (∀ (x y : A), x ∈ p → y ∈ p → x * y ∈ p) → NonUnitalSubalgebra R A

A submodule closed under multiplication is a non-unital subalgebra.

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

5 results in Mathlib

Foundations

Depth 13 from the axioms · uses no axioms

Assumes

CommSemiringNonUnitalNonAssocSemiringModule