It is shown that any completely preordered topological real algebra admits a continuous utility representation which is an algebra-homomorphism (i.e., it is linear and multiplicative). As an application of this result, we provide an algebraic characterization of the projective (dictatorial) preorders defined on Rⁿ. We then establish some welfare implications derived from our main result. In particular, the connection with the normative property called independence of the relative utility pace is discussed.