the function ring functors of pointfree topology revisited

This paper establishes two new connections between the familiar function ring functor r on the category crfrm of completely regular frames and the category crσfrm of completely regular σ-frames as well as their counterparts for the analogous functor z on the category odfrm of 0-dimensional frames, given by the integer-valued functions, and for the related functors r ∗ and z ∗ corresponding to the bounded functions. further it is shown that some familiar facts concerning these functors are simple consequences of the present results.