@article {
author = {Porselvi, Kasi and Elavarasan, Balasubramanian},
title = {Some Properties of Prime and Z-Semi-Ideals in Posets},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {1},
pages = {46-56},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2019.97095},
abstract = {We define the notion of z-semi-ideals in a poset $P$ and we show that if a z-semi-ideal $J$ satisfies $(\ast )$-property, then every minimal prime semi-ideal containing $J$ is also a z-semi-ideal of $P.$ We also show that every prime semi-ideal is a z-semi-ideal or the maximal z-semi-ideals contained in it are prime z-semi-ideals. Further, we characterize some properties of union of prime semi-ideals of $P$ provided the prime semi-ideals are contained in the unique maximal semi-ideal of $P.$},
keywords = {Posets,semi-ideals,prime semi-ideals,minimal prime semi-ideals,m-system},
url = {http://www.kjm-math.org/article_97095.html},
eprint = {http://www.kjm-math.org/article_97095_c7b4d571f0807aca269c3e30f1b3b35f.pdf}
}