Volume 8, Issue 4 (Vol. 8,No. 4, 2022)
mmr 2022, 8(4): 238-255 |
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Nikandish R. Some Properties of the Nil-Graphs of Ideals of Commutative Rings. mmr 2022; 8 (4) :238-255
URL: http://mmr.khu.ac.ir/article-1-3071-en.html
URL: http://mmr.khu.ac.ir/article-1-3071-en.html
, r.nikandish@ipm.ir
Abstract: (1617 Views)
Let R be a commutative ring with identity and Nil(R) be the set of nilpotent elements of R. The nil-graph of ideals of R is defined as the graph AG_N(R) whose vertex set is {I:(0)and there exists a non-trivial ideal 
such that 
and two distinct vertices 
and are adjacent if and only if 
. Here, we study conditions under which 
is complete or bipartite. Also, the independence number of is determined, where 
is a reduced ring. Finally, we classify Artinian rings whose nil-graphs of ideals have genus at most one.
such that and two distinct vertices and are adjacent if and only if . Here, we study conditions under which is complete or bipartite. Also, the independence number of is determined, where is a reduced ring. Finally, we classify Artinian rings whose nil-graphs of ideals have genus at most one.
Type of Study: Original Manuscript |
Subject:
alg
Received: 2020/03/24 | Revised: 2023/06/17 | Accepted: 2020/12/22 | Published: 2022/12/31 | ePublished: 2022/12/31
Received: 2020/03/24 | Revised: 2023/06/17 | Accepted: 2020/12/22 | Published: 2022/12/31 | ePublished: 2022/12/31
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