It is shown that the von Neumann algebra ℜ_Dg which is generated by field operators of an open space-time domain ‡ is never a factor of type I_n (withn < ∞) or II₁ An argument is sketched to show that the factor oR_Dgassociated with a bounded and open space-time domain ‡ is not of type I_∞ either. It is noticed that a variant of this argument may be utilized for showing that the factors associated with special space-time domains are not of type II_∞. The arguments for ruling out the possibility of «types» 1_∞ and 11_∞ are incomplete to the extent of two unproved mathematical propositions which however are likely to be true. Some of the known results pertaining to the structure of the algebra oR_∞ which is generated by all field operators are also rederived from a slightly different point of view than the usual.