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mmr 2021, 7(3): 591-606 |
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safaeeyan S, Barzegar S. Annihilating Graph of Abelian Groups. mmr 2021; 7 (3) :591-606
URL: http://mmr.khu.ac.ir/article-1-2971-en.html
URL: http://mmr.khu.ac.ir/article-1-2971-en.html
1- University , safaeeyan@yu.ac.ir
2- University
2- University
Abstract: (758 Views)
In [18], the author associated a graph to an R -module M which is precisely a generalization of annihilating ideal graph of a commutative ring, see [15] and [16].
Inasmuch as Abelian groups are precisely Z-modules, in this paper we relate an annihilating graph to an Abelian group , denoted by G(M) , and study this graph. We show that G(M) is an empty graph if and only if either M≅Z or M is a simple Abelian group. Moreover, we show that G(M) is a finite graph if and only if M is a finite Abelian group. Among other things, we characterize Abelian groups for which their annihilating graphs are complete, bipartite or complete bipartite graphs.
Inasmuch as Abelian groups are precisely Z-modules, in this paper we relate an annihilating graph to an Abelian group , denoted by G(M) , and study this graph. We show that G(M) is an empty graph if and only if either M≅Z or M is a simple Abelian group. Moreover, we show that G(M) is a finite graph if and only if M is a finite Abelian group. Among other things, we characterize Abelian groups for which their annihilating graphs are complete, bipartite or complete bipartite graphs.
Type of Study: Research Paper |
Subject:
alg
Received: 2019/07/6 | Revised: 2022/05/7 | Accepted: 2020/02/2 | Published: 2021/12/1 | ePublished: 2021/12/1
Received: 2019/07/6 | Revised: 2022/05/7 | Accepted: 2020/02/2 | Published: 2021/12/1 | ePublished: 2021/12/1
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