On representability of finitely generated algebras (Q1203555)

The author studies finitely generated algebras \(R\) over a field \(k\) which are representable, i.e. there exists a finite-dimensional algebra \(W\) over an extension \(K\) of \(k\) such that \(R \subseteq W\) and \(W = KR\). The main result gives sufficient conditions on \(R\) (which are also necessary for \(K\) algebraically closed) which guarantee that \(R\) is representable and the algebra \(W\) has one simple component modulo its radical.