Abstract
In this paper, we investigate the additive structure of the algebra F(5), i.e., a relatively free, associative, countably-generated algebra with the identity [x1, . . . , x5] = 0 over an infinite field of characteristic ≠2, 3. We study the space of proper multilinear polynomials in this algebra and means of basis construction in one of its basic subspaces. As an additional result, we obtain estimations of codimensions cn = dimPn/Pn ∩ T(5), where Pn is the space of multilinear polynomials of degree n in F(5) and T(5) is the T-ideal generated by the long commutator [x1, . . . , x5].
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