Research Article

A note on certain subrings of ℛ (L)

Published in: Quaestiones Mathematicae
Volume 44 , issue 1 , 2021 , pages: 99–107

DOI: 10.2989/16073606.2019.1672114

Author(s): Goutam Bhunia , India

Keywords: Primary: 06D22 , Secondary: 54D35 , Primary: 06D22 , Secondary: 54D35

Abstract

We introduce a new subring (L) of (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 generates L. Further, we prove that the Stone-Čech compactification βL 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) compactification ζL of L is determined via these subrings.

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