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Join maximal element graph of lattice modules | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، S1، تیر 2026، صفحه 115-123 اصل مقاله (165.7 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2026.28291.1704 | ||
| نویسندگان | ||
| L. Sherpa1؛ V. Kharat1؛ M. Agalave2؛ N. M. Phadatare* 3 | ||
| 1Department of Mathematics, Savitribai Phule Pune University, Pune, India | ||
| 2Department of Mathematics, Fergusson College(Autonomus), Pune, India | ||
| 3Bharati Vidyapeeth Deemed to be University College of Engineering, Pune, India | ||
| چکیده | ||
| Let $\pounds$ be a $C$-lattice and $M$ be a lattice module over $\pounds$. The join maximal element graph $\mathbb{G}(M)$ is a simple, undirected graph with all proper non-zero elements of $M$ as vertices, and two distinct vertices, $N$ and $K$, are adjacent if and only if $N\vee K\in Max(M)$, where $Max(M)$ is the collection of all maximal elements of $M$. In this paper, some properties of the graph $\mathbb{G}(M)$ like diameter, girth and clique number are investigated. Also, the interplay between the algebraic properties of $M$ and the properties of those graphs is studied. | ||
| کلیدواژهها | ||
| Maximal element؛ Jacobson radical $J_{rad}(M)$؛ Join maximal element graph $\mathbb{G}(M)$ | ||
| مراجع | ||
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