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On the comaximal graph of a non-quasi-local atomic domain | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 اردیبهشت 1403 اصل مقاله (429.7 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.28332.1508 | ||
| نویسندگان | ||
| S. Visweswaran* 1؛ Premkumar T. Lalchandani2 | ||
| 1Saurashtra University | ||
| 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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[12] K. Samei, On the comaximal graph of a commutative ring, Canad. Math. Bull. 57 (2014), no. 2, 413–423. https://doi.org/10.4153/CMB-2013-033-7 [13] P.K. Sharma and S.M. Bhatwadekar, A note on graphical representation of rings, J. Algebra 176 (1995), no. 1, 124–127. https://doi.org/10.1006/jabr.1995.1236 | ||
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