Concerning strongly divisible, strongly fixed, and strongly z-ideals in \mathcal{R}L

As usual, the ring of continuous real-valued functions on a frame L is denoted by \mathcal{R}L. We determine the relation among strongly z-ideals, strongly divisible ideals and uniformly closed ideals in the ring \mathcal{R}L. We characterize Lindel\"of frames based on strongly fixed ideals in \mathcal{R}L. We observe that a weakly spatial frame L is Lindel\"of if and if every strongly divisible ideal in \mathcal{R}L is strongly fixed; if and only if every closed ideal in \mathcal{R}L is strongly fixed.

Keywords:

Ring of all real-valued continuous functions on a frame , Strongly divisible ideal , Zero set in pointfree topology , Closed ideal , Lindel of frame