Concerning strongly divisible, strongly fixed, and strongly z-ideals in RL

As usual, the ring of continuous real-valued func tions on a frame L is denoted by RL. We determine the rela tion among strongly z-ideals, strongly divisible ideals and uniformly closed ideals in the ring RL. We characterize Lindel¨of frames based on strongly fixed ideals in RL. We observe that a weakly spatial frame L is Lindel¨of if and only if every strongly divisible ideal in RL is strongly fixed; if and only if every closed ideal in RL is strongly fixed.