论文标题
关于Artinian环的压缩零除数图的有限性问题
On the problem of the finiteness of the compressed zero divisor graphs of Artinian rings
论文作者
论文摘要
令r为Artinian环为与R相关的压缩的零分量图。他们证明，如果r的长度最多是四个，则集团的数字是有限的。在六个情况下，他们举了一个示例，其中集团是无限的。在本文中，我们表明，当环的长度为五个时，压缩零径向图的集团数量是有限的。
Let R be an Artinian ring and G be the compressed zero-divisor graph associated to R. The question of when the clique number of compressed zero-divisor graphs is finite was raised by J. Coykendall, S. Sather-Wagstaff, L. Sheppardson, and S. Spiroff, in their survey paper entitled On Zero-divisor Graphs. They proved that if length of R is at most four then the clique number is finite. In the length six case they gave an example of a ring where the clique is infinite. In this paper we show that when length of ring is five then the clique number of compressed zero-divisor graph is finite.
