论文标题
在通勤环上的模块的歼灭 - 解码图中的统治数
Domination number in the annihilating-submodule graph of modules over commutative rings
论文作者
论文摘要
令$ m $为通勤环$ r $的模块。 $ m $的nihitating-submodule图，由$ ag（m）$表示，是一个简单的图表，在该图中，当存在一个非零的$ n $ a $ m $的$ n $ n $ of $ m $时，只有当时存在非零的subpopor $ k $ k $ k $ k $ k $ m $ m $ $ m $ $（n：m）（k：m）m $和两个不同的顶点$ n $和$ k $相邻，并且仅当$ nk =（0）$时。该图是消灭理想图的子模块版本，在某些条件下，是同构的，具有Zariski拓扑图$ g（τ_t）$的诱导子图（Zariski拓扑图）（Zariski拓扑图模块上的Zariski拓扑图形图上的通勤戒指，通勤，Algebra。在本文中，我们研究了$ ag（m）$的支配数，以及$ ag（m）$的图理论属性与模块$ m $的代数属性之间的一些连接。
Let $M$ be a module over a commutative ring $R$. The annihilating-submodule graph of $M$, denoted by $AG(M)$, is a simple graph in which a non-zero submodule $N$ of $M$ is a vertex if and only if there exists a non-zero proper submodule $K$ of $M$ such that $NK=(0)$, where $NK$, the product of $N$ and $K$, is denoted by $(N:M)(K:M)M$ and two distinct vertices $N$ and $K$ are adjacent if and only if $NK=(0)$. This graph is a submodule version of the annihilating-ideal graph and under some conditions, is isomorphic with an induced subgraph of the Zariski topology-graph $G(τ_T)$ which was introduced in (The Zariski topology-graph of modules over commutative rings, Comm. Algebra., 42 (2014), 3283--3296). In this paper, we study the domination number of $AG(M)$ and some connections between the graph-theoretic properties of $AG(M)$ and algebraic properties of module $M$.
