The annihilator graph of modules over commutative rings
Publish place: The Journal of Algebra and Related Topics، Vol: 9، Issue: 1
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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JR_JART-9-1_007
تاریخ نمایه سازی: 31 تیر 1403
Abstract:
Let M be a module over a commutative ring R, Z_{*}(M) be its set of weak zero-divisor elements, andif m\in M, then let I_m=(Rm:_R M)=\{r\in R : rM\subseteq Rm\}. The annihilator graph of M is the (undirected) graphAG(M) with vertices \tilde{Z_{*}}(M)=Z_{*}(M)\setminus \{۰\}, and two distinct vertices m and n are adjacent if andonly if (۰:_R I_{m}I_{n}M)\neq (۰:_R m)\cup (۰:_R n). We show that AG(M) is connected with diameter at most two and girth at mostfour. Also, we study some properties of the zero-divisor graph of reduced multiplication-like R-modules.
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Authors
F. Esmaeili Khalil Saraei
Fouman Faculty of Engineering, College of Engineering, University of Tehran, Fouman, Iran.