%0 Journal Article %T The function ring functors of pointfree topology revisited %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Banaschewski, Bernhard %D 2019 %\ 07/01/2019 %V 11 %N Special Issue Dedicated to Prof. George A. Grätzer %P 19-32 %! The function ring functors of pointfree topology revisited %K Completely regular frames %K zero dimensional frames %K completely regular $sigma$-frames %K zero dimensional $sigma$-frames %K real-valued continuous functions and integer-valued continuous functions on frames %R 10.29252/cgasa.11.1.19 %X This paper establishes two new connections between the familiar function ring functor ${\mathfrak R}$ on the category ${\bf CRFrm}$ of completely regular frames and the category {\bf CR}${\mathbf \sigma}${\bf Frm} of completely regular $\sigma$-frames as well as their counterparts for the analogous functor ${\mathfrak Z}$ on the category {\bf ODFrm} of 0-dimensional frames, given by the integer-valued functions, and for the related functors ${\mathfrak R}^*$ and ${\mathfrak Z}^*$ corresponding to the bounded functions.  Further it is shown that some familiar facts concerning these functors are simple consequences of the present results. %U https://cgasa.sbu.ac.ir/article_87117_d2e1481a97bb9235d4ea8ec563e32744.pdf