On the Schur multiplier of augmented algebras (Q1264285)

Let \(R\) be a finitely generated free associative algebra over a field \(k\), \(A=R/I\), \(I\) is not \(0\). If \(A\) is infinite-dimensional over \(k\), J. Lewin (1973) proved that \(R/I^2\) is not finitely presented. A stronger statement would be that the Schur multiplier of \(R/I^2\) is not finite-dimensional. This stronger statement is proved in the case that \(A\) is an augmented domain.