on rings of real-valued rcl-supercontinuous functions

The notion of rcl-supercontinuity, a strong variant of continuity, is considered. the ring rcl(x) consists of all real-valued rclsupercontinuous functions on a topological space x is studied. it is shown that rcl(x) ∼= c(y), where y is an ultra-hausdorff rcl-quotient of x and it turns out that whenever x is rcl-compact, then y is zerodimensional. the maximal ideals of rcl(x) are specified. the spaces x are determined for which every maximal ideal in rcl(x) is fixed. finally, prcl -spaces and almost prcl -spaces are defined and characterized both algebraically and topologically