Algebraic constraints on hidden variables

In the contemporary discussion of hidden variable interpretations of quantum mechanics, much attention has been paid to the no hidden variable proof contained in an important paper of Kochen and Specker. It is a little noticed fact that Bell published a proof of the same result the preceding year, in his well-known 1966 article, where it is modestly described as a corollary to Gleason's theorem. We want to bring out the great simplicity of Bell's formulation of this result and to show how it can be extended in certain respects.Work on this paper was partially supported by National Science Foundation Grants SOC 76-82113 and SOC 76-10659.