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Some classes of perfect annihilator-ideal graphs associated with commutative rings | ||
Journal of Algebra and Related Topics | ||
دوره 9، شماره 1، شهریور 2021، صفحه 21-29 اصل مقاله (289.43 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22124/jart.2021.17227.1214 | ||
نویسندگان | ||
M. Adlifard1؛ Sh. Payrovi* 2 | ||
1Department of Mathematics, Roudbar Branch Islamic Azad University, Roudbar, Iran | ||
2Department of Mathematics, Imam Khomeini International University, Qazvin, Iran | ||
چکیده | ||
Let $R$ be a commutative ring and let $\Bbb A(R)$ be the set of all ideals of $R$ with nonzero annihilator. The annihilator-ideal graph of $R$ is defined as the graph ${A_I}(R)$ with the vertex set $\Bbb A(R)^*=\Bbb A(R)\setminus\{0\}$ and two distinct vertices $I$ and $J$ are adjacent if and only if ${\rm Ann}_R(IJ)\neq{\rm Ann}_R(I) \cup{\rm Ann}_R(J)$. In this paper, perfectness of ${A_I}(R)$ for some classes of rings is investigated. | ||
کلیدواژهها | ||
Annihilator-ideal graph؛ Perfect graph؛ Chromatic number؛ Clique number | ||
آمار تعداد مشاهده مقاله: 684 تعداد دریافت فایل اصل مقاله: 801 |