理想基零因子图的可补性和唯一可补性
When Ideal-based Zero-divisor Graphs are Complemented or Uniquely Complemented
摘要：
设$R$是具有非零单位元的交换环，$I$是$R$的真理想. $R$相对于理想$I$的{ \it理想基零因子图}，记为$Γ_I(R)$，是对于某个$y\in R\setminus I \}$的顶点$\{x \in R\setminus I \mid xy\in I$上的图，其中不同的顶点$x$和$y$相邻当且仅当$xy\in I$。本文对交换环的理想基零因子图的可补性和唯一可补性进行了分类。
英文摘要：
Let $R$ be a commutative ring with nonzero identity and $I$ a proper ideal of $R$. The {\it ideal-based zero-divisor graph} of $R$ with respect to the ideal $I$, denoted by $Γ_I(R)$, is the graph on vertices $\{x \in R\setminus I \mid xy\in I$ for some $y\in R\setminus I \}$, where distinct vertices $x$ and $y$ are adjacent if and only if $xy\in I$. In this paper, we classify when an ideal-based zero-divisor graph of a commutative ring is complemented or uniquely complemented.
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。
