A GRAPH ASSOCIATED TO ESPECIAL ESSENTIALITY OF SUBMODULES | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 2، فروردین 2025، صفحه 237-256 اصل مقاله (273.57 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2023.12356.1662 | ||
| نویسندگان | ||
| Mehdi Ebrahimi Dorcheh؛ Saeid Bagheri* | ||
| Department of Mathematics, Faculty of Mathematical Sciences, Malayer University, P.O. Box 65719-95863, Malayer, Iran. | ||
| چکیده | ||
| Let $R$ be an associative ring with identity. In this paper we associate to every $R$-module $M$ a simple graph $\Gamma_e(M)$, which we call it the essentiality graph of $M$. The vertices of $\Gamma_e(M)$ are nonzero submodules of $M$ and two distinct vertices $K$ and $L$ are considered to be adjacent if and only if $K\cap L$ is an essential submodule of $K+L$. We investigate the relationship between some module theoretic properties of $M$ such as minimality and closedness of submodules with some graph theoretic properties of $\Gamma_e(M)$. In general, this graph is not connected. We study some special cases in which $\Gamma_e(M)$ is complete or a union of complete connected components and give some examples illustrating each specific case. | ||
| کلیدواژهها | ||
| essential submodules؛ closed submodules؛ UC-module؛ clique number؛ girth | ||
| مراجع | ||
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