ANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS | ||
| Journal of Algebraic Systems | ||
| مقاله 5، دوره 3، شماره 1، آذر 2015، صفحه 39-47 اصل مقاله (183.53 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2015.487 | ||
| نویسنده | ||
| M. Baziar* | ||
| Department of Mathematics, University of Yasouj, P.O.Box 75914, Yasouj, Iran. | ||
| چکیده | ||
| In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. We observe that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ is connected and diam$Bbb{AG}_*(_RM)leq 3$. Moreover, if $Bbb{AG}_*(_RM)$ contains a cycle, then $mbox{gr}Bbb{AG}_*(_RM)leq 4$. Also for an $R$-module $M$ with $Bbb{A}_*(M)neq S(M)setminus {0}$, $Bbb{A}_*(M)=emptyset$ if and only if $M$ is a uniform module and ann$(M)$ is a prime ideal of $R$. | ||
| کلیدواژهها | ||
| zero-divisor graph؛ Annihilating submodule graph؛ Weakly annihilating submodule | ||
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آمار تعداد مشاهده مقاله: 2,110 تعداد دریافت فایل اصل مقاله: 2,031 |
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