关于素理想和图为线图的环
On rings whose prime ideal sum graphs are line graphs
AI总结：
该研究针对含单位元的交换环，围绕素理想和图的结构性质展开，刻画了素理想和图为线图及线图补图的所有交换Artinian环，丰富了环与图交叉领域的结构刻画结果。
摘要：
设$R$为含单位元的交换环。环$R$的素理想和图是简单无向图，其顶点集为$R$的所有非零真理想的集合，两个不同顶点$I$、$J$相邻当且仅当$I+J$是$R$的素理想。本文刻画了所有素理想和图为线图的交换Artinian环。最后，我们描述了所有素理想和图为线图补图的交换Artinian环。
英文摘要：
Let $R$ be a commutative ring with unity. The prime ideal sum graph of the ring $R$ is the simple undirected graph whose vertex set is the set of all nonzero proper ideals of $R$ and two distinct vertices $I$, $J$ are adjacent if and only if $I + J$ is a prime ideal of $R$. In this paper, we characterize all commutative Artinian rings whose prime ideal sum graphs are line graphs. Finally, we give a description of all commutative Artinian rings whose prime ideal sum graph is the complement of a line graph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
