Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)Khayyam Journal of Mathematics2423-47886120200101Some Properties of Prime and Z-Semi-Ideals in Posets46569709510.22034/kjm.2019.97095ENKasi PorselviDepartment of Mathematics, Karunya Institute of Technology and Sciences,
Coimbatore - 641 114, India.Balasubramanian ElavarasanDepartment of Mathematics, Karunya Institute of Technology and Sciences,
Coimbatore - 641 114, India.0000-0002-1414-2814Journal Article20181201We 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 $P.$https://www.kjm-math.org/article_97095_c7b4d571f0807aca269c3e30f1b3b35f.pdf