ON THE SCHUR MULTIPLIER OF AUGMENTED ALGEBRAS

Let k be a field, and A a finitely generated k-algebra, with augmentat ion. Suppose there is a presentation of A 0 --> I --> R --> A --> 0 wh ere R is a finitely generated free k-algebra and I is non-zero. If A i s infinite dimensional over Ic, Lewin proved that R/I-2 is not finitel y presented. A stronger statement would be that the 'Schur multiplier' of R/I-2 is not finite dimensional. In the case that A is an augmente d domain, we prove this stronger statement, and some related statement s.