ON EMBEDDINGS OF Q-ALGEBRAS

Firstly, we prove that every Q-algebra can be embedded into a unital Q-algebra. On the basis of this result, we also show that the category of unital Q-algebras is a reflective subcategory of the category of Q-algebras. Secondly, we prove that every Q-algebra is embeddable into the endomorphism Q-algebra of a Q-module. Finally, we introduce the concept of a Girard Q-algebra and show that every Q-algebra can be embedded into a Girard Q-algebra.