The identities of vector spaces embedded in a linear algebra

摘要

In this paper we study the identities of vector spaces embeddedin linear algebras. We prove that the identities of the class of allvector spaces embedded in associative algebras do not follow from a finiteset of the identities that are true in this class. Similar result is provedfor the spaces embedded in Lie algebras. We constructed the exampleof a four-dimensional algebra over a field of characteristic zero which isa strongly not finitely based. The authors describe strongly nonfinitelybased vector spaces that are finite-dimensional associative algebras withunity over a field of characteristic zero.