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.

中文翻译：

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关于ℛ（L）的某些子环的注释

摘要

我们引入一个新的子环（大号的）（大号）用于完全正帧大号和经由主环表征pseudocompact帧。此外，我们获得几个苏FFI cient条件大号其保证的cozero部分产生大号。此外，我们证明，只要L是伪紧实的或强零维的，L的Stone-Čech压缩βL就由这些子环确定。最后，我们推测，如果L为零维且紧实，则L的零维（通用）压缩ζL 通过这些子环确定。