Characterizations of $J$-prime ideals and $M_{J}$-ideals in posets
نویسندگان
1 Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore-641114, Tamilnadu, India.
2 Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore-641114, Tamilnadu, India.
doi
10.22034/as.2022.2719چکیده
In this paper, we introduce the concepts of $J$-prime ideals and $M_{J}$-ideals in posets, and obtain some of their interesting characterizations in posets. Furthermore, we discuss the properties of $J$-ideals that are analogous to $J$-prime ideals and $M_J$-ideals in posets. Finally, we establish a set of equivalent conditions for an ideal in a poset $\mathcal{P}$ containing an ideal $J$ is an $J$-ideal, and for a semi-prime ideal $J$ to be an $M_{J}$-ideal of $\mathcal{P}$.
