Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585311Special Issue Dedicated to Prof. George A. Grätzer20190701The function ring functors of pointfree topology revisited19328711710.29252/cgasa.11.1.19ENBernhardBanaschewskiDepartment of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada.Journal Article20180910This 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.http://cgasa.sbu.ac.ir/article_87117_d2e1481a97bb9235d4ea8ec563e32744.pdf