Poset properties with respect to semi-ideal based zero-divisor graph

Document Type : Research Paper

Authors

1 Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore - 641 114, India.

2 Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore - 641 114, Tamilnadu, India.

10.22124/jart.2021.19454.1268

Abstract

In this paper, we discuss some properties of poset $P$ determined by semi-ideal based zero-divisor graph $G_K(P),$ for a semi-ideal $K$ of $P.$ We investigate some interesting properties if $G_K(P)$ contains a cycle. Further, we prove that if $V(G_K(P))$ is a generalized tree, then $(V(G_K(P))\backslash S_x)\cup K$ and $(V(G_K(P))\backslash S_{\geq x})\cup K$ are prime semi-ideals of $P$.

Keywords