Theorems · Theorem · nonassociative algebras

NonUnitalAlgHom.mem_range

∀ {F : Type v'} {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A]
  [inst_2 : Module R A] [inst_3 : NonUnitalNonAssocSemiring B] [inst_4 : Module R B] [inst_5 : FunLike F A B]
  [inst_6 : NonUnitalAlgHomClass F R A B] (φ : F) {y : B}, y ∈ NonUnitalAlgHom.range φ ↔ ∃ x, φ x = y

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

3 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleNonUnitalNonAssocSemiringModuleFunLikeNonUnitalAlgHomClass