Spaces with Vanishing Characteristic Coefficients

We prove that the maximal dimension of a subspace Formula: see text of the generic tensor product of Formula: see text symbol algebras of prime degree Formula: see text with Formula: see text for all Formula: see text is Formula: see text. The same upper bound is thus obtained for Formula: see text with Formula: see text, Formula: see text, Formula: see text, Formula: see text being 0 for all Formula: see text. We make use of the fact that given any subset Formula: see text of Formula: see text (Formula: see text times) with Formula: see text, for all Formula: see text there exist Formula: see text, Formula: see text in Formula: see text and Formula: see text in Formula: see text such that Formula: see text.