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.

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

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)) ∖ S_{x}) \cup K

and

(V (G_{K} (P)) ∖ S_{\geq x}) \cup K

are prime semi-ideals of

P

Keywords