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Theorems · Theorem · nonassociative algebras

Submodule.mem_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} {h_mul : ∀ (x y : A), x ∈ p → y ∈ p → x * y ∈ p} {x : A},
  x ∈ p.toNonUnitalSubalgebra h_mul ↔ x ∈ p
Defined in
Mathlib.Algebra.Algebra.NonUnitalSubalgebra
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Foundations
Depth 15 from the axioms · uses no axioms
Assumes
CommSemiringNonUnitalNonAssocSemiringModule
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Module · cited by 20661ModuleCommSemiring · cited by 10911CommSemiringSubmodule · cited by 7192SubmoduleNonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringNonUnitalSubalgebra · cited by 215NonUnitalSubalgebraSubmodule.toNonUnitalSubalgebra · cited by 5Submodule.toNonUnitalSuba…Submodule.mem_toNonUnitalSuba…CITED BYCITES

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