Bernstein algebras with associative bilinear forms (Q757572)

We prove that associative bilinear forms over Bernstein algebras of type \((1+r,s)\), \(r\geq 1\), are always degenerate. Algebras of type (1,s) may have nondegenerate associative bilinear forms, whose classification reduces to the classical problem of classification of nondegenerate bilinear forms over a vector space of dimension s. Our preliminary results are valid for Bernstein algebras of arbitrary dimension, even for infinite dimensional ones.