Embedding of nonassociative algebras (Q2706769)

Associative algebras have a well-developed structure theory. The lack of the associativity necessitates troubles in the study of nonassociative algebras. In this paper it is proved that every nonassociative algebra having a right identity element can be embedded into an associative one so that the operations of these two algebras are connected with each other. Further the author investigates the connections between the operations of the two algebras implied by the embedding task, describes the basic properties of a natural representation-like mapping and its connections with the embedding and shows that an embedding is associated with a special kind of representation-like mapping of an associative algebra on a given nonassociative algebra with a right identity element.