%0 Journal Article
%T Some Properties of Prime and Z-Semi-Ideals in Posets
%J Khayyam Journal of Mathematics
%I 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)
%Z 2423-4788
%A Porselvi, Kasi
%A Elavarasan, Balasubramanian
%D 2020
%\ 01/01/2020
%V 6
%N 1
%P 46-56
%! Some Properties of Prime and Z-Semi-Ideals in Posets
%K Posets
%K semi-ideals
%K prime semi-ideals
%K minimal prime semi-ideals
%K m-system
%R 10.22034/kjm.2019.97095
%X 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 $P.$
%U http://www.kjm-math.org/article_97095_c7b4d571f0807aca269c3e30f1b3b35f.pdf