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Zero-divisor graph of semisimple group-rings
Journal of Algebra and Its Applications ( IF 0.8 ) Pub Date : 2020-11-25 , DOI: 10.1142/s0219498822500281 Krishnan Paramasivam 1 , K. Muhammed Sabeel 1
Journal of Algebra and Its Applications ( IF 0.8 ) Pub Date : 2020-11-25 , DOI: 10.1142/s0219498822500281 Krishnan Paramasivam 1 , K. Muhammed Sabeel 1
Affiliation
Let Γ ( R ) , Γ E ( R ) , Γ Ann ( R ) denote the zero-divisor graph, compressed zero-divisor graph and annihilating ideal graph of a commutative ring R , respectively. In this paper, we prove that Γ E ( R ) ≅ Γ Ann ( R ) for a semisimple commutative ring R and represent Γ ( R ) as a generalized join of a finite set of graphs. Further, we study the zero-divisor graph of a semisimple group-ring 𝔽 q C n and proved several structural properties of Γ ( 𝔽 q C n ) and Γ E ( 𝔽 q C n ) , where 𝔽 q is a field with q elements and C n is a cyclic group with n elements.
中文翻译:
半单群环的零除数图
让Γ ( R ) ,Γ 乙 ( R ) ,Γ 安 ( R ) 表示交换环的零除数图、压缩零除数图和湮灭理想图R , 分别。在本文中,我们证明Γ 乙 ( R ) ≅ Γ 安 ( R ) 对于一个半单交换环R 并代表Γ ( R ) 作为有限图集的广义连接。此外,我们研究了半简单群环的零除数图𝔽 q C n 并证明了几个结构性质Γ ( 𝔽 q C n ) 和Γ 乙 ( 𝔽 q C n ) , 在哪里𝔽 q 是一个领域q 元素和C n 是一个循环群n 元素。
更新日期:2020-11-25
中文翻译:
半单群环的零除数图
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