A note on certain subrings of R(L)

Abstract

We introduce a new subring R♯(L) of R(L) for a completely regular frame L and characterize pseudocompact frames via these subrings. Also we obtain several sufficient conditions on L which guarantee that the cozero part of R♯(L) generates L. Further, we prove that the Stone-Cech compactication L of L is determined by these subrings whenever L is pseudocompact or strongly zero-dimensional. Finally, we have conjectured that if L is zero-dimensional and realcompact then the zero- dimensional (universal) compactication L of L is determined via these subrings.

Key words: Pseudocompact frame, zero-dimensional frame, realcompact frame, Stone-Cech compactication, zero-dimensional (universal) compactication.