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.