Representability of Noetherian finitely generated algebras (Q1203533)

Assume \(B\) is a finitely generated PI algebra (over a fixed field \(k\)). The author has found some natural and convenient conditions for \(B\) being representable (i.e. embeddable into some matrix algebra over an extension of the field \(k\)). The first of them states that if \(B\) is right noetherian, then \(B\) is representable. Let \(R(B)\) be the \(k\)-algebra of the multiplications of the algebra \(B\). If the two-sided ideals of \(B\) as well as the left annihilators in \(B\) of the subsets of \(R(B)\) satisfy the ACC, then \(B\) is representable, too. Finally the author shows that in the case when \(B\) is subdirectly indecomposable and if the left (right) annihilators of the two-sided ideals \(I\) of \(B\) coincide with the left (right) annihilators of some finite subsets of \(I\), then the algebra \(B\) is finite dimensional over \(k\).