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].