Matrix representability of finitely-generated PI-algebras (Q922625)

It is proved that a finitely generated unital PI-algebra containing only one left annihilator is representable (i.e. can be imbedded into a matrix ring over some commutative algebra). On the other hand the author constructs an example of a nonrepresentable finitely generated unital PI- algebra containing exactly two left annihilators and satisfying the quasi-identities \[ \bigwedge_{0\leq p\leq 4}(\sum^{s}_{j=1}a_ jx^ pb_ j=0)\quad \Rightarrow \quad \sum^{s}_{j=1}a_ jx^ 4b_ j=0,\quad s=1,2,...\quad. \]