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 $$\mathcal {R}L$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mi>L</mml:mi> </mml:mrow> </mml:math> 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 $$\mathcal {R}L$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mi>L</mml:mi> </mml:mrow> </mml:math> .