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Poset properties with respect to semi-ideal based zero-divisor graph | ||
| Journal of Algebra and Related Topics | ||
| دوره 9، شماره 2، اسفند 2021، صفحه 111-120 اصل مقاله (278.99 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2021.19454.1268 | ||
| نویسندگان | ||
| B Elavarasan* 1؛ K Porselvi2 | ||
| 1Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore - 641 114, India. | ||
| 2Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore - 641 114, Tamilnadu, India. | ||
| چکیده | ||
| 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 $P$. | ||
| کلیدواژه‌ها | ||
| Posets؛ semi-ideals؛ prime semi-ideals؛ cycle؛ and neighborhood | ||
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