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The annihilator-inclusion Ideal graph of a commutative ring | ||
| Communications in Combinatorics and Optimization | ||
| دوره 6، شماره 2، اسفند 2021، صفحه 231-248 اصل مقاله (462.03 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2020.26752.1139 | ||
| نویسندگان | ||
| J. Amjadi* 1؛ R. khoeilar1؛ A. Alilou2 | ||
| 1Azarbaijan Shahid Madani University | ||
| 2Jabir Ibn Hayyan research center | ||
| چکیده | ||
| Let $R$ be a commutative ring with non-zero identity. The annihilator-inclusion ideal graph of $R$, denoted by $\xi_R$, is a graph whose vertex set is the of all non-zero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either ${\rm Ann}(I)\subseteq J$ or ${\rm Ann}(J)\subseteq I$. The purpose of this paper is to provide some basic properties of the graph $\xi_R$. In particular, shows that $\xi_R$ is a connected graph with diameter at most three, and has girth 3 or $\infty$. Furthermore, is determined all isomorphic classes of non-local Artinian rings whose annihilator-inclusion ideal graphs have genus zero or one. | ||
| کلیدواژهها | ||
| annihilator؛ graph؛ annihilator-inclusion ideal graph | ||
| مراجع | ||
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