@article {
author = {Estaji, A.A. and Karimi Feizabad, A. and Zarghani, M.},
title = {Zero elements and $z$-ideals in modified pointfree topology},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {43},
number = {7},
pages = {2205-2226},
year = {2017},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {In this paper, we define and study the notion of zero elements in topoframes; a topoframe is a pair $(L, \tau)$, abbreviated $L_{ \tau}$, consisting of a frame $L$ and a subframe $ \tau $ all of whose elements are complemented elements in $L$. We show that the $f$-ring $ \mathcal{R}(L_\tau)$, the set of $\tau$-real continuous functions on $L$, is uniformly complete. Also, the set of all zero elements in a topoframe is closed under the formation of countable meets and finite joins. Also, we introduce the notion of $z$-filters and $z$-ideals in modified pointfree topology and make ready some results about them. },
keywords = {Topoframe,zero element,$z$-filter,$z$-ideal,prime ideal},
url = {http://bims.iranjournals.ir/article_1090.html},
eprint = {http://bims.iranjournals.ir/article_1090_17ec79f62279ac897d5fe7ebab2a0ff0.pdf}
}