To answer my own question, Noam Elkies suggested: K = C(omplex Numbers); one-dimensional V = K Define k * [v] = [Re(k).v], the . being multiplication in K Then all axioms are satisfied except (k1.k2) * v = k1 * (k2 * v) Are there sources on the web of neat examples like this where the independence of the axioms is demonstrated? I know of Gelbaum/Olmstead books I (Analysis) & II. - guy