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On the comaximal graph of a non-quasi-local atomic domain | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 11، شماره 1، خرداد 2026، صفحه 33-48 اصل مقاله (429.54 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.28332.1508 | ||
| نویسندگان | ||
| Subramanian Visweswaran* 1؛ Premkumar T. Lalchandani2 | ||
| 1Department of Mathematics, Saurashtra University, Rajkot, India | ||
| 2Department of Mathematics, Dr. Subhash University, Dr. Subhash Road Junagadh, India | ||
| چکیده | ||
| Let $R$ be an atomic domain such that $R$ has at least two maximal ideals. Let $Irr(R)$ denote the set of all irreducible elements of $R$ and let $J(R)$ denote the Jacobson radical of $R$. Let $\mathcal{I}(R) = \{R\pi\mid \pi\in Irr(R)\backslash J(R)\}$. In this paper, with $R$, we associate an undirected graph denoted by $\mathbb{CGI}(R)$ whose vertex set is $\mathcal{I}(R)$ and distinct vertices $R\pi_{1}$ and $R\pi_{2}$ are adjacent if and only if $R\pi_{1} + R\pi_{2} = R$. The aim of this paper is to study the interplay between some graph properties of $\mathbb{CGI}(R)$ and the algebraic properties of $R$. | ||
| کلیدواژهها | ||
| irreducible element؛ atomic domain؛ , maximal ideal,؛ connected graph,؛ clique number | ||
| مراجع | ||
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