论文标题
压缩交汇处歼灭器图
Compressed Intersection Annihilator Graph
论文作者
论文摘要
令R为具有非零身份的交换环。在本文中，我们定义了一个新图，即用$ ia（r）$表示的压缩交叉歼灭仪图，并研究了其一些理论属性及其与环结构的关系。这是扭转图$γ_{r}（r）$的概括。我们研究了$ r $的零分师集合之间的等效性的戒指，是理想的和$ ia（r）$的完整性。我们还研究$γ_{r}（r）$和$ ia（r）$之间的关系。此外，我们表明，如果压缩的相互交叉点的nihihilator图是有限的，则存在一个$ s $ r $的$ s $ s $，以便$ ia（s）\ cong ia（r）$。另外，我们表明压缩的交点歼灭器图永远不会是完整的两部分图。此外，我们证明了至少连接了三个顶点的图形$ ia（r）$，其直径小于或等于三个。最后，我们在$ r $是整数模型$ n $的情况下确定图形的属性，积分域的直接乘积，Artinine Local Rings的直接乘积以及两个环的直接乘积，因此其中一个不是一个积分域。
Let R be a commutative ring with a non-zero identity. In this paper, we define a new graph, the compressed intersection annihilator graph, denoted by $IA(R)$, and investigate some of its theoretical properties and its relation with the structure of the ring. It is a generalization of the torsion graph $Γ_{R}(R)$. We study classes of rings for which the equivalence between the set of zero-divisors of $R$ being an ideal and the completeness of $IA(R)$ holds. We also study the relation between $Γ_{R}(R)$ and $IA(R)$. In addition, we show that if the compressed intersection annihilator graph of a ring $R$ is finite, then there exists a subring $S$ of $R$ such that $IA(S)\cong IA(R)$. Also, we show that the compressed intersection annihilator graph will never be a complete bipartite graph. Besides, we show that the graph $IA(R)$ with at least three vertices is connected and its diameter is less than or equal to three. Finally, we determine the properties of the graph in the cases when $R$ is the ring of integers modulo $n$, the direct product of integral domains, the direct product of Artinine local rings and the direct product of two rings such that one of them is not an integral domain.
