@article { author = {Banaschewski, Bernhard}, title = {The function ring functors of pointfree topology revisited}, journal = {Categories and General Algebraic Structures with Applications}, volume = {11}, number = {Special Issue Dedicated to Prof. George A. Grätzer}, pages = {19-32}, year = {2019}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {10.29252/cgasa.11.1.19}, abstract = {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.}, keywords = {Completely regular frames,zero dimensional frames,completely regular $sigma$-frames,zero dimensional $sigma$-frames,real-valued continuous functions and integer-valued continuous functions on frames}, url = {https://cgasa.sbu.ac.ir/article_87117.html}, eprint = {https://cgasa.sbu.ac.ir/article_87117_d2e1481a97bb9235d4ea8ec563e32744.pdf} }