TY - JOUR
ID - 97095
TI - Some Properties of Prime and Z-Semi-Ideals in Posets
JO - Khayyam Journal of Mathematics
JA - KJM
LA - en
SN -
AU - Porselvi, Kasi
AU - Elavarasan, Balasubramanian
AD - Department of Mathematics, Karunya Institute of Technology and Sciences,
Coimbatore - 641 114, India.
Y1 - 2020
PY - 2020
VL - 6
IS - 1
SP - 46
EP - 56
KW - Posets
KW - semi-ideals
KW - prime semi-ideals
KW - minimal prime semi-ideals
KW - m-system
DO - 10.22034/kjm.2019.97095
N2 - 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 $P.$
UR - https://www.kjm-math.org/article_97095.html
L1 - https://www.kjm-math.org/article_97095_c7b4d571f0807aca269c3e30f1b3b35f.pdf
ER -