论文标题
用两个Cozero二元组属的环表征
Characterization of rings with genus two cozero-divisor graphs
论文作者
论文摘要
让$ r $成为团结的戒指。环$ r $的COZERO划分图是一个无向的简单图形，其顶点是$ r $的所有非零和非单位元素的集合，两个不同的顶点$ x $和$ y $相邻，并且仅当$ x \ notin ry $和$ ynotin ry $和$ y ynotin y \ notin rx rx。 RING $ r $的简化Cozero-Divisor图是一个无方向的简单图形，其顶点集是所有非繁琐的主要理想的$ r $和两个独特的顶点$（a）$（a）$和$（b）$的集合，并且仅当$（a）\ b）\ sebset（b）$和（b）$和（b）$（b）$（b）$（b）$（b）$（b）$（a）\ spet（a）时（a）。在本文中，我们表征了所有类别的有限非本地换向环，而Cozero-Divisor图和降低的Cozero-Divisor图的所有类别都是二属。
Let $R$ be a ring with unity. The cozero-divisor graph of a ring $R$ is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $x \notin Ry$ and $y \notin Rx$. The reduced cozero-divisor graph of a ring $R$, is an undirected simple graph whose vertex set is the set of all nontrivial principal ideals of $R$ and two distinct vertices $(a)$ and $(b)$ are adjacent if and only if $(a) \not\subset (b)$ and $(b) \not\subset (a)$. In this paper, we characterize all classes of finite non-local commutative rings for which the cozero-divisor graph and reduced cozero-divisor graph is of genus two.
