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 $P.$
Porselvi, K., & Elavarasan, B. (2020). Some Properties of Prime and Z-Semi-Ideals in Posets. Khayyam Journal of Mathematics, 6(1), 46-56. doi: 10.22034/kjm.2019.97095
MLA
Kasi Porselvi; Balasubramanian Elavarasan. "Some Properties of Prime and Z-Semi-Ideals in Posets". Khayyam Journal of Mathematics, 6, 1, 2020, 46-56. doi: 10.22034/kjm.2019.97095
HARVARD
Porselvi, K., Elavarasan, B. (2020). 'Some Properties of Prime and Z-Semi-Ideals in Posets', Khayyam Journal of Mathematics, 6(1), pp. 46-56. doi: 10.22034/kjm.2019.97095
VANCOUVER
Porselvi, K., Elavarasan, B. Some Properties of Prime and Z-Semi-Ideals in Posets. Khayyam Journal of Mathematics, 2020; 6(1): 46-56. doi: 10.22034/kjm.2019.97095
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