تعداد نشریات | 31 |
تعداد شمارهها | 743 |
تعداد مقالات | 7,077 |
تعداد مشاهده مقاله | 10,167,565 |
تعداد دریافت فایل اصل مقاله | 6,862,676 |
The annihilator graph of modules over commutative rings | ||
Journal of Algebra and Related Topics | ||
دوره 9، شماره 1، شهریور 2021، صفحه 93-108 اصل مقاله (312.61 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22124/jart.2021.18226.1241 | ||
نویسنده | ||
F. Esmaeili Khalil Saraei* | ||
Fouman Faculty of Engineering, College of Engineering, University of Tehran, Fouman, Iran. | ||
چکیده | ||
Let $M$ be a module over a commutative ring $R$, $Z_{*}(M)$ be its set of weak zero-divisor elements, and if $m\in M$, then let $I_m=(Rm:_R M)=\{r\in R : rM\subseteq Rm\}$. The annihilator graph of $M$ is the (undirected) graph $AG(M)$ with vertices $\tilde{Z_{*}}(M)=Z_{*}(M)\setminus \{0\}$, and two distinct vertices $m$ and $n$ are adjacent if and only if $(0:_R I_{m}I_{n}M)\neq (0:_R m)\cup (0:_R n)$. We show that $AG(M)$ is connected with diameter at most two and girth at most four. Also, we study some properties of the zero-divisor graph of reduced multiplication-like $R$-modules. | ||
کلیدواژهها | ||
Annihilator graph؛ reduced module؛ multiplication-like module | ||
آمار تعداد مشاهده مقاله: 657 تعداد دریافت فایل اصل مقاله: 736 |