On the classification of bilinear maps with radical of a fixed codimension

Let V be an n-dimensional linear space over an algebraically closed base field. We provide a general method for classifying, up to equivalence, all bilinear maps f:V×V→V such that dim(rad(f))=n−m, in case a classification of bilinear maps f:W×W→W when dim(W)=m is known. This is equivalent to giving a procedure to classify (up to isomorphism) all n-dimensional algebras with annihilator of dimension n−m from a given classification of m-dimensional algebras. As an example of application, we consider the case in which m = 2.

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