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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
Affiliation  

Let Γ(R), ΓE(R), ΓAnn(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 ΓE(R)ΓAnn(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 𝔽qCn and proved several structural properties of Γ(𝔽qCn) and ΓE(𝔽qCn), where 𝔽q is a field with q elements and Cn is a cyclic group with n elements.

中文翻译:

半单群环的零除数图

Γ(R),Γ(R),Γ(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(R)Γ(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𝔽qCn并证明了几个结构性质Γ(𝔽qCn)Γ(𝔽qCn), 在哪里𝔽q是一个领域q元素和Cn是一个循环群n元素。
更新日期:2020-11-25
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