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

Document Type : Research Articles

Author

Esfarayen University of Technology, Esfarayen, North Khorasan, Iran

Abstract

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

Caspian Journal of Mathematical Sciences
Volume 11, Issue 1
2022
Pages 313-323

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