Characterizations of U-frames and frames that are finitely a U-frame

Abstract

In this article, we give algebraic characterizations of U-frames in terms of ring-theoretic properties of the ring \(\mathcal {R}L\) of real-valued continuous functions on a completely regular frame L. We show that a frame is a U-frame if and only if it is an F-frame and its Čech–Stone compactification is zero-dimensional. We will also introduce frames that are finitely a U-frame and we will characterize them in terms of ring-theoretic properties in \(\mathcal {R}L\).