@article {
author = {Abedi, M.},
title = {ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS},
journal = {Journal of Algebraic Systems},
volume = {7},
number = {2},
pages = {257-269},
year = {2020},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2019.8150.1399},
abstract = {We study primary ideals of the ring $\mathcal{R}L$ of real-valued continuous functions on a completely regular frame $L$. We observe that prime ideals and primary ideals coincide in a $P$-frame. It is shown that every primary ideal in $\mathcal{R}L$ is contained in a unique maximal ideal, and an ideal $Q$ in $\mathcal{R}L$ is primary if and only if $Q \cap\mathcal{R}^*L$ is a primary ideal in $\mathcal{R}^*L$. We show that every pseudo-prime (primary) ideal in $\mathcal{R}L$ is either an essential ideal or a maximal ideal which is at the same time a minimal prime ideal. Finally, we prove that if $L$ is a connected frame, then the zero ideal in $\mathcal{R}L$ is decomposable if and only if $L={\bf2}$.},
keywords = {Frame,primary ideal,pseudo-prime ideal,ring of continuous real-valued functions,decomposable ideal},
url = {http://jas.shahroodut.ac.ir/article_1594.html},
eprint = {http://jas.shahroodut.ac.ir/article_1594_8108dcd6f42553890dfb9b0ba2055003.pdf}
}